“Beinggoodatscienceandmathematicsisn’tjustsomethingyouare;it’ssomethingyoubecome.Thisusers’guidetothebrainunmasksthemysteryaroundachievingsuccessinmathematicsandscience.Ihaveseenfartoomanystudentsoptoutwhentheyhitaroughpatch.Butnowthatlearnershaveahandyguidefor‘knowingbetter,’theywillalsobeableto‘dobetter.’”

—SHIRLEYMALCOM,HEADOFEDUCATIONANDHUMANRESOURCESPROGRAMS,AMERICANASSOCIATIONFORTHEADVANCEMENTOFSCIENCE

“AMindforNumbersisanexcellentbookabouthowtoapproachmathematics,science,oranyrealmwhereproblemsolvingplaysaprominentrole.”

—J.MICHAELSHAUGHNESSY,PASTPRESIDENTOFTHENATIONALCOUNCILOFTEACHERSOFMATHEMATICS

“Ihavenotbeenthisexcitedaboutabookinalongtime.Givingstudentsdeepknowledgeonhowtolearnwillleadtohigherretentionandstudentsuccessineveryfield.Itisagiftthatwilllastthemalifetime.”

—ROBERTR.GAMACHE,PH.D.,ASSOCIATEVICEPRESIDENT,ACADEMICAFFAIRS,STUDENTAFFAIRS,ANDINTERNATIONALRELATIONS,UNIVERSITYOFMASSACHUSETTS,LOWELL

“AMindforNumbershelpsputstudentsinthedriver’sseat—empoweringthemtolearnmoredeeplyandeasily.Thisoutstandingbookisalsoausefulresourceforinstructionalleaders.GiventheurgentneedforAmericatoimproveitsscienceandmatheducationsoitcanstaycompetitive,AMindforNumbersisawelcomefind.”

—GEOFFREYCANADA,PRESIDENT,HARLEMCHILDREN’SZONE

“Aningeniouslyaccessibleintroductiontothescienceofhumancognition—alongwithpracticaladviceonhowtothinkbetter.”

—JAMESTARANTO,THEWALLSTREETJOURNAL

“It’seasytosay‘worksmarter,notharder,’butBarbaraOakleyactuallyshowsyouhowtodojustthat,inafast-pacedandaccessiblebookthatcollectstipsbasedonexperienceandsoundscience.Infact,I’mgoingtoincorporatesomeofthesetipsintomyownteaching.”

—GLENNHARLANREYNOLDS,BEAUCHAMPBROGANDISTINGUISHEDPROFESSOROFLAW,THEUNIVERSITYOFTENNESSEE

“AMindforNumbersisasplendidresourceforhowtoapproachmathematicslearningand,infact,learninginanyarea.BarbaraOakley’sauthoritativeguideisbasedonthelatestresearchinthecognitivesciences,andprovidesaclear,concise,andentertainingroadmapforhowtogetthemostoutoflearning.Thisisamust-readforanyonewhohasstruggledwithmathematicsandanyoneinterestedinenhancingtheirlearningexperience.”

—DAVIDC.GEARY,CURATORS’PROFESSOROFPSYCHOLOGICALSCIENCESANDINTERDISCIPLINARYNEUROSCIENCE,UNIVERSITYOFMISSOURI

“Forstudentsafraidofmathandscienceandforthosewholovethesubjects,thisengagingbookprovidesguidanceinestablishingstudyhabitsthattakeadvantageofhowthebrainworks.”

—DEBORAHSCHIFTER,PRINCIPALRESEARCHSCIENTIST,SCIENCEANDMATHEMATICSPROGRAMS,EDUCATIONDEVELOPMENTCENTER,INC.

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ISBN978-1-101-62161-51.Mathanxiety.2.Mathematics—Studyandteaching—Psychologicalaspects.3.Educationalpsychology.I.Title.

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AMindforNumbersisdedicatedtoDr.RichardFelder,whosebrillianceandpassionhavelaunchedextraordinaryimprovementsworldwideintheteachingofscience,mathematics,engineering,andtechnology.Myownsuccesses,likethoseoftensofthousandsofothereducators,growoutofhisfertileeducationalapproaches.Ilmigliormaestro.

TheLawofSerendipity:LadyLuckfavorstheonewhotries

contents

PRAISEFORAMINDFORNUMBERS

TITLEPAGE

COPYRIGHT

DEDICATION

EPIGRAPH

FOREWORDbyTerrenceJ.Sejnowski,FrancisCrickProfessor,SalkInstituteforBiologicalStudies

PREFACEbyJeffreyD.Karpicke,JamesV.BradleyAssociateProfessorofPsychologicalSciences,PurdueUniversity

NOTETOTHEREADER

1OpentheDoor

2EasyDoesIt:WhyTryingTooHardCanSometimesBePartoftheProblem

3LearningIsCreating:LessonsfromThomasEdison’sFryingPan

4ChunkingandAvoidingIllusionsofCompetence:TheKeystoBecomingan“EquationWhisperer”

5PreventingProcrastination:EnlistingYourHabits(“Zombies”)asHelpers

6ZombiesEverywhere:DiggingDeepertoUnderstandtheHabitofProcrastination

7ChunkingversusChoking:HowtoIncreaseYourExpertiseandReduceAnxiety

8Tools,Tips,andTricks

9ProcrastinationZombieWrap-Up

10EnhancingYourMemory

11MoreMemoryTips

12LearningtoAppreciateYourTalent

13SculptingYourBrain

14DevelopingtheMind’sEyethroughEquationPoems

15RenaissanceLearning

16AvoidingOverconfidence:ThePowerofTeamwork

17TestTaking

18UnlockYourPotential

AFTERWORDBYDAVIDB.DANIEL,PH.D.,PROFESSOR,PSYCHOLOGYDEPARTMENT,JAMESMADISONUNIVERSITY

ACKNOWLEDGMENTS

ENDNOTES

REFERENCES

CREDITS

INDEX

Y

foreword

ourbrainhasamazingabilities,butitdidnotcomewithaninstructionmanual.You’llfindthatmanualinAMindforNumbers.Whetheryou’reanoviceoranexpert,youwillfindgreatnew

waystoimproveyourskillsandtechniquesforlearning,especiallyrelatedtomathandscience.HenriPoincaréwasanineteenth-centurymathematicianwhooncedescribedhowhecrackeda

difficultmathematicalproblemthathehadbeenintensivelyworkingonforweekswithoutsuccess.Hetookavacation.AshewasgettingonabusinthesouthofFrance,theanswertotheproblemsuddenlycametohim,unbidden,fromapartofhisbrainthathadcontinuedtoworkontheproblemwhilehewasenjoyinghisvacation.HeknewhehadtherightsolutioneventhoughhedidnotwritedownthedetailsuntilhelaterreturnedtoParis.

WhatworkedforPoincarécanworkforyoutoo,asBarbaraOakleyexplainsinthisinsightfulbook.Surprisingly,yourbraincanalsoworkonaproblemevenwhileyouaresleepingandarenotawareofanything.Butitdoesthisonlyifyouconcentrateontryingtosolvetheproblembeforefallingasleep.Inthemorning,asoftenasnot,afreshinsightwillpoptomindthatcanhelpyousolvetheproblem.Theintenseeffortbeforeavacationorfallingasleepisimportantforprimingyourbrain;otherwiseitwillworkonsomeotherproblem.Thereisnothingspecialaboutmathorscienceinthisregard—yourbrainwillworkjustashardatsolvingsocialproblemsasonmathandscienceproblems,ifthatiswhathasbeenonyourmindrecently.

Youwillfindmanymoreinsightsandtechniquesabouthowtolearneffectivelyinthisfascinatingandtimelybook,whichlooksatlearningasanadventureratherthanhardlabor.Youwillseehowyoucanfoolyourselfaboutwhetheryouactuallyknowthematerial;youwillfindwaystoholdyourfocusandspaceoutyourpractice;andyouwilllearntocondensekeyideassoyoucanholdthemmoreeasilyinyourmind.Masterthesimple,practicalapproachesoutlinedhereandyouwillbeabletolearnmoreeffectivelyandwithlessfrustration.Thiswonderfulguidewillenrichbothyourlearningandyourlife.

—TerrenceJ.Sejnowski,FrancisCrickProfessor,SalkInstituteforBiologicalStudies

T

preface

hisbookcanmakeaprofounddifferenceinhowyoulookatandunderstandlearning.Youwilllearnthesimplest,mosteffective,andmostefficienttechniquesresearchersknowabouthowto

learn.Andyou’llhavefunwhileyou’redoingit.What’ssurprisingisthatalotoflearnersuseineffectiveandinefficientstrategies.Inmy

laboratory,forexample,wehavesurveyedcollegestudentsabouttheirlearning.Theymostcommonlyusethestrategyofrepeatedreading—simplyreadingthroughbooksornotesoverandover.Weandotherresearchershavefoundthatthispassiveandshallowstrategyoftenproducesminimalornolearning.Wecallthis“laborinvain”—studentsareputtinginlaborbutnotgettinganywhere.

Wedon’tengageinpassiverereadingbecausewearedumborlazy.Wedoitbecausewefallpreytoacognitiveillusion.Whenwereadmaterialoverandover,thematerialbecomesfamiliarandfluent,meaningitiseasyforourmindstoprocess.Wethenthinkthatthiseasyprocessingisasignthatwehavelearnedsomethingwell,eventhoughwehavenot.

Thisbookwillintroduceyoutothisandotherillusionsoflearningandgiveyoutoolstoovercomethem.Anditwillintroducegreatnewtools,suchasretrievalpractice,thatcanhaveapowerfuleffectinboostingthe“bangforyourbuck”fromyourtimespentinlearning.It’sadeeplypracticalyetinspiringbookthathelpsyouseeclearlywhysomeapproachesaresomuchmoreeffectivethanothers.

We’reontheedgeofanexplosioninknowledgeabouthowtolearnmosteffectively.Inthisnewworldofinsight,you’llfindAMindforNumberstobeanindispensableguide.

—JeffreyD.Karpicke,JamesV.BradleyAssociateProfessorofPsychologicalSciences,PurdueUniversity

P

notetothereader

eoplewhoworkprofessionallywithmathandscienceoftenspendyearsdiscoveringeffectivelearningtechniques.Oncethey’vefiguredthesemethodsout,great!Theyhaveunwittingly

passedtheinitiationritesneededtojointhemysterioussocietyofmathandsciencepractitioners.I’vewrittenthisbooktolayoutthesesimpletechniquessothatyoucanimmediatelybeginusing

them.Whattakesyearsforpractitionerstodiscoverisnowatyourfingertips.Usingtheseapproaches,nomatterwhatyourskilllevelsinmathandscience,youcanchange

yourthinkingandchangeyourlife.Ifyou’realreadyanexpert,thispeekunderthementalhoodwillgiveyouideasforturbochargingsuccessfullearning,includingcounterintuitivetest-takingtipsandinsightsthatwillhelpyoumakethebestuseofyourtimeonhomeworkandproblemsets.Ifyou’restruggling,you’llseeastructuredtreasuretroveofpracticaltechniquesthatwalkyouthroughwhatyouneedtodotogetontrack.Ifyou’veeverwantedtobecomebetteratanything,thisbookwillhelpserveasyourguide.

ThisbookisforhighschoolstudentswholoveartandEnglishclassesbutloathemath.Itismeantaswellasforcollegestudentswhoalreadyexcelinmath,science,engineering,andbusiness,butwhosuspecttherearementaltoolstobeaddedtotheirlearningtoolkits.It’sforparentswhosechildrenareeitherfallingoffthemathtrackortryingtorockettowardmathandsciencestardom.It’sforthefrazzlednine-to-fiveworkerwhohasn’tbeenabletopassanimportantcertificationtest,andforthenight-shiftconveniencestoreclerkwhohasdreamedofbecominganurse—orevenadoctor.It’sforthegrowingarmyofhomeschoolers.It’sforteachersandprofessors—notonlyinmath,science,engineering,andtechnology,butalsoinfieldssuchaseducation,psychology,andbusiness.It’sfortheretireewhofinallyhasthetimetoembracenewknowledgeincomputing,forexample,ortheintricaciesofgreatcooking.Andit’sforreadersofallageswholovetolearnalittleabouteverything.

Inshort,thisbookisforyou.Enjoy!

—BarbaraOakley,Ph.D.,P.E.,Fellow,AmericanInstituteforMedical&BiologicalEngineeringandVicePresident,InstituteforElectricalandElectronicsEngineers—EngineeringinMedicineand

BiologySociety

W

{1}

openthedoor

hataretheoddsyou’dopenyourrefrigeratordoorandfindazombieinthere,knittingsocks?Theoddsareaboutthesamethatatouchy-feely,language-orientedpersonlikeme

wouldendupasaprofessorofengineering.Growingup,Ihatedmathandscience.Iflunkedmywaythroughhighschoolmathandscience

courses,andonlystartedstudyingtrigonometry—remedialtrigonometry—whenIwastwenty-sixyearsold.

Asayoungster,eventhesimpleconceptofreadingaclockfacedidn’tseemtomakesensetome.Whyshouldthelittlehandpointtowardthehour?Shouldn’titbethebighand,sincethehourwasmoreimportantthantheminute?Didtheclockreadtenten?Oronefifty?Iwasperpetuallyconfused.Worsethanmyproblemswithclockswasthetelevision.Inthosedaysbeforetheremotecontrol,Ididn’tevenknowwhichbuttonturnedthetelevisionon.Iwatchedashowonlyinthecompanyofmybrotherorsister.TheynotonlycouldturntheTVon,butcouldalsotunethechanneltotheprogramwewantedtowatch.Nice.

AllIcouldconclude,lookingatmytechnicalineptitudeandflunkinggradesinmathandscience,wasthatIwasn’tverysmart.Atleast,notthatway.Ididn’trealizeitthen,butmyself-portraitasbeingtechnically,scientifically,andmathematicallyincapablewasshapingmylife.Attherootofitallwasmyproblemwithmathematics.Ihadcometothinkofnumbersandequationsasakintooneoflife’sdeadlydiseases—tobeavoidedatallcosts.Ididn’trealizethenthatthereweresimplementaltricksthatcouldhavebroughtmathintofocusforme,tricksthatarehelpfulnotonlyforpeoplewhoarebadatmath,butalsoforthosewhoarealreadygoodatit.Ididn’tunderstandthatmytypeofthinkingistypicalofpeoplewhobelievetheycan’tdomathandscience.Now,Irealizethatmyproblemwasrootedintwodistinctlydifferentmodesforviewingtheworld.Backthen,Ionlyknewhowtotaponemodeforlearning—andtheresultwasthatIwasdeaftothemusicofmath.

Mathematics,asit’sgenerallytaughtinAmericanschoolsystems,canbeasaintlymotherofasubject.Itclimbslogicallyandmajesticallyfromadditionthroughsubtraction,multiplication,anddivision.Thenitsweepsuptowardtheheavensofmathematicalbeauty.Butmathcanalsobeawickedstepmother.Sheisutterlyunforgivingifyouhappentomissanystepofthelogicalsequence—andmissingastepiseasytodo.Allyouneedisadisruptivefamilylife,aburned-outteacher,oranunluckyextendedboutwithillness—evenaweekortwoatacriticaltimecanthrowyouoffyourgame.

Or,aswasthecasewithme,simplynointerestorseemingtalentwhatsoever.Inseventhgrade,disasterstruckmyfamily.Myfatherlosthisjobafteraseriousbackinjury.We

endedupinahardscrabbleschooldistrictwhereacrotchetymathteachermadeussitforhoursinthe

swelteringheatdoingroteadditionandmultiplication.Itdidn’thelpthatMr.Crotchetyrefusedtoprovideanyexplanations.Heseemedtoenjoyseeingusflounder.

MeatagetenwithEarlthelamb.Ilovedcritters,reading,anddreaming.Mathandscienceweren’tonmyplaylist.

Bythistime,Inotonlydidn’tseeanyuseformath—Iactivelyloathedit.Andasfarasthescienceswent—well,theydidn’t.Inmyfirstchemistryexperiment,myteacherchosetogivemylabpartnerandmeadifferentsubstancethantherestoftheclass.Heridiculeduswhenwefudgedthedatainanattempttomatcheveryoneelse’sresults.Whenmywell-meaningparentssawmyfailinggradesandurgedmetogethelpduringtheteacher ’sofficehours,IfeltIknewbetter.Mathandsciencewereworthless,anyway.TheGodsofRequiredCourseworkweredeterminedtoshovemathandsciencedownmythroat.Mywayofwinningwastorefusetounderstandanythingthatwastaught,andtobelligerentlyflunkeverytest.Therewasnowaytooutmaneuvermystrategy.

Ididhaveotherinterests,though.Ilikedhistory,socialstudies,culture,andespeciallylanguage.Luckily,thosesubjectskeptmygradesafloat.

Rightoutofhighschool,Ienlistedinthearmybecausetheywouldactuallypaymetolearnanotherlanguage.IdidsowellinstudyingRussian(alanguageI’dselectedonawhim)thatanROTCscholarshipcamemyway.IheadedofftotheUniversityofWashingtontogetabachelor ’sdegreeinSlaviclanguagesandliterature,whereIgraduatedwithhonors.Russianflowedlikewarmsyrup—myaccentwassogoodthatIfoundmyselfonoccasionmistakenlytakenforanativespeaker.Ispentlots

oftimegainingthisexpertise—thebetterIgot,themoreIenjoyedwhatIwasdoing.AndthemoreIenjoyedwhatIwasdoing,themoretimeIspentonit.Mysuccessreinforcedmydesiretopractice,andthatbuiltmoresuccess.

ButinthemostunlikelysituationIcouldhaveeverimagined,IeventuallyfoundmyselfcommissionedasasecondlieutenantintheU.S.ArmySignalCorps.Iwassuddenlyexpectedtobecomeanexpertinradio,cable,andtelephoneswitchingsystems.Whataturningpoint!Iwentfrombeingontopoftheworld,anexpertlinguist,incontrolofmydestiny,tobeingthrownintoanewtechnologicalworldwhereIwasasstuntedasastump.

Yikes!Iwasmadetoenrollinmathematicallyorientedelectronicstraining(Ifinishedatthebottomof

theclass),andthenoffIwenttoWestGermany,whereIbecameapitiablecommunicationsplatoonleader.Isawthattheofficersandenlistedmemberswhoweretechnicallycompetentwereindemand.Theywereproblemsolversofthefirstorder,andtheirworkhelpedeveryoneaccomplishthemission.

IreflectedontheprogressofmycareerandrealizedthatI’dfollowedmyinnerpassionswithoutalsobeingopentodevelopingnewones.Asaconsequence,I’dinadvertentlypigeonholedmyself.IfIstayedinthearmy,mypoortechnicalknow-howwouldalwaysleavemeasecond-classcitizen.

Ontheotherhand,ifIlefttheservice,whatcouldIdowithadegreeinSlaviclanguagesandliterature?Therearen’talotofjobsforRussianlinguists.Basically,I’dbecompetingforentry-levelsecretarial-typejobswithmillionsofotherswhoalsohadbachelor ’sofartsdegrees.ApuristmightarguethatI’ddistinguishedmyselfinbothmystudiesandmyserviceandcouldfindmuchbetterwork,butthatpuristwouldbeunawareofhowtoughthejobmarketcansometimesbe.

Fortunatelytherewasanotherunusualoption.OneofthegreatbenefitsofmyservicewasthatIhadGIBillmoneytooffsetthecostsoffutureschooling.WhatifIusedthatsupporttodotheunthinkableandtrytoretrainmyself?CouldIretoolmybrainfrommathphobetomathlover?Fromtechnophobetotechnogeek?

I’dneverheardofanyonedoinganythinglikethatbefore,andcertainlynotcomingfromthephobicdepthsI’dsunkto.Therecouldn’tpossiblybeanythingmoreforeigntomypersonalitythanmasteringmathandscience.Butmycolleaguesintheservicehadshownmetheconcretebenefitsofdoingso.

Itbecameachallenge—anirresistiblechallenge.Idecidedtoretrainmybrain.Itwasn’teasy.Thefirstsemesterswerefilledwithfrighteningfrustration.IfeltlikeIwaswearing

ablindfold.Theyoungerstudentsaroundmemostlyseemedtohaveanaturalknackforseeingthesolutions,whileIwasstumblingintowalls.

ButIbegantocatchon.Partofmyoriginalproblem,Ifound,wasthatIhadbeenputtingmyeffortforthinthewrongway—liketryingtoliftapieceoflumberwhenyou’restandingonit.Ibegantopickuplittletricksaboutnotonlyhowtostudybutwhentoquit.Ilearnedthatinternalizingcertainconceptsandtechniquescouldbeapowerfultool.Ialsolearnednottotakeontoomuchatonce,allowingmyselfplentyoftimetopracticeevenifitmeantmyclassmateswouldsometimesgraduateaheadofmebecauseIwasn’ttakingasmanycourseseachsemesterastheywere.

AsIgraduallylearnedhowtolearnmathandscience,thingsbecameeasier.Surprisingly,justaswithstudyinglanguage,thebetterIgot,themoreIenjoyedwhatIwasdoing.ThisformerQueenoftheConfusedinmathwentontoearnabachelor ’sdegreeinelectricalengineeringandthenamaster ’sinelectricalandcomputerengineering.Finally,Iearnedadoctorateinsystemsengineering,

withabroadbackgroundthatincludedthermodynamics,electromagnetics,acoustics,andphysicalchemistry.ThehigherIwent,thebetterIdid.BythetimeIreachedmydoctoralstudies,Iwasbreezingbywithperfectgrades.(Well,perhapsnotquitebreezing.Goodgradesstilltookwork.ButtheworkIneededtodowasclear.)

Nowasaprofessorofengineering,Ihavebecomeinterestedintheinnerworkingsofthebrain.Myinterestgrewnaturallyfromthefactthatengineeringliesattheheartofthemedicalimagesthatallowustoteaseouthowthebrainfunctions.IcannowmoreclearlyseehowandwhyIwasabletochangemybrain.IalsoseehowIcanhelpyoulearnmoreeffectivelywithoutthefrustrationandstruggleIexperienced.1Andasaresearcherwhoseworkstraddlesengineering,thesocialsciences,andthehumanities,I’malsoawareoftheessentialcreativityunderlyingnotjustartandliterature,butalsomathandscience.

Ifyoudon’t(yet)consideryourselfnaturallygoodatmathandscience,youmaybesurprisedtolearnthatthebrainisdesignedtodoextraordinarymentalcalculations.Wedothemeverytimewecatchaball,orrockourbodytothebeatofasong,ormaneuverourcararoundapotholeintheroad.Weoftendocomplexcalculations,solvingcomplexequationsunconsciously,unawarethatwesometimesalreadyknowthesolutionasweslowlyworktowardit.2Infact,weallhaveanaturalfeelandflairformathandscience.Basically,wejustneedtomasterthelingoandculture.

Inwritingthisbook,Iconnectedwithhundredsoftheworld’sleadingprofessor-teachersofmathematics,physics,chemistry,biology,andengineering,aswellaseducation,psychology,neuroscience,andprofessionaldisciplinessuchasbusinessandthehealthsciences.Itwasstartlingtohearhowoftentheseworld-classexpertshadusedpreciselytheapproachesoutlinedinthebookwhentheythemselveswerelearningtheirdisciplines.Thesetechniqueswerealsowhattheexpertsaskedtheirstudentstouse—butsincethemethodssometimesseemcounterintuitive,andevenirrational,instructorshaveoftenfoundithardtoconveytheirsimpleessence.Infact,becausesomeoftheselearningandteachingmethodsarederidedbyordinaryinstructors,superstarteacherssometimesdivulgedtheirteachingandlearningsecretstomewithembarrassment,unawarethatmanyothertopinstructorssharedsimilarapproaches.Bycollectingmanyoftheserewardinginsightsinoneplace,youtoocaneasilylearnandapplypracticaltechniquesgleanedinpartfromthese“bestofthebest”teachersandprofessors.Thesetechniquesareespeciallyvaluableforhelpingyoulearnmoredeeplyandeffectivelyinlimitedtimeframes.You’llalsogaininsightfromstudentsandotherfellowlearners—peoplewhoshareyourconstraintsandconsiderations.

Remember,thisisabookformathexpertsandmathphobesalike.Thisbookwaswrittentomakeiteasierforyoutolearnmathandscience,regardlessofyourpastgradesinthosesubjectsorhowgoodorbadyouthinkyouareatthem.Itisdesignedtoexposeyourthoughtprocessessoyoucanunderstandhowyourmindlearns—andalsohowyourmindsometimesfoolsyouintobelievingyou’relearning,whenyou’reactuallynot.Thebookalsoincludesplentyofskill-buildingexercisesthatyoucanapplydirectlytoyourcurrentstudies.Ifyou’realreadygoodatnumbersorscience,theinsightsinthisbookcanhelpmakeyoubetter.Theywillbroadenyourenjoyment,creativity,andequation-solvingelegance.

Ifyou’resimplyconvincedyoudon’thaveaknackfornumbersorscience,thisbookmaychangeyourmind.Youmayfindithardtobelieve,butthere’shope.Whenyoufollowtheseconcretetipsbasedonhowweactuallylearn,you’llbeamazedtoseethechangeswithinyourself,changesthatcanallownewpassionstobloom.

Whatyoudiscoverwillhelpyoubemoreeffectiveandcreative,notonlyinmathandscience,butinalmosteverythingyoudo.

Let’sbegin!

I

{2}

easydoesit:

WhyTryingTooHardCanSometimesBePartoftheProblem

fyouwanttounderstandsomeofthemostimportantsecretstolearningmathandscience,lookatthefollowingpicture.ThemanontherightislegendarychessgrandmasterGarryKasparov.Theboyontheleftis

thirteen-year-oldMagnusCarlsen.Carlsenhasjustwanderedawayfromtheboardduringtheheightofaspeedchessgame,wherelittletimeisgiventothinkaboutmovesorstrategy.That’salittlelikecasuallydecidingtodoabackflipwhilewalkingatightropeacrossNiagaraFalls.

Yes,Carlsenwaspsychingouthisopponent.Ratherthanobliteratingtheupstartyoungster,theflusteredKasparovplayedtoadraw.ButthebrilliantCarlsen,whowentontobecometheyoungesttop-ratedchessplayerinhistory,wasdoingsomethingfarbeyondplayingmindgameswithhisolderopponent.GaininginsightintoCarlsen’sapproachcanhelpusunderstandhowthemindlearnsmathandscience.BeforewegointohowCarlsenpsychedoutKasparov,weneedtocoveracoupleofimportantideasabouthowpeoplethink.(ButIpromise,we’llcomebacktoCarlsen.)

Thirteen-year-oldMagnusCarlsen(left),andlegendarygeniusGarryKasparovplayingspeedchessatthe“ReykjavíkRapid”in2004.Kasparov’sshockisjustbeginningtobecomeapparent.

We’regoingtobetouchingonsomeofthemainthemesofthebookinthischapter,sodon’tbesurprisedifyouhavetotogglearoundabitinyourthinking.Beingabletotoggleyourthinking—gettingaglimpseofwhatyouarelearningbeforereturninglatertomorefullyunderstandwhat’sgoingon,isitselfoneofthemainideasinthebook!

NOWYOUTRY!

PrimeYourMentalPump

Asyoufirstbeginlookingatachapterorsectionofabookthatteachesconceptsofmathorscience,ithelpstotakea“picturewalk”throughthechapter,glancingnotonlyatthegraphics,diagrams,andphotos,butalsoatthesectionheadings,summary,andevenquestionsattheendofthechapter,ifthebookhasthem.Thisseemscounterintuitive—youhaven’tactuallyreadthechapteryet,butithelpsprimeyourmentalpump.Sogoaheadnowandglancethroughthischapterandthequestionsattheendofthechapter.You’llbesurprisedathowspendingaminuteortwoglancingaheadbeforeyoureadindepthwillhelpyouorganize

yourthoughts.You’recreatinglittleneuralhookstohangyourthinkingon,makingiteasiertograsptheconcepts.

FocusedversusDiffuseThinking

Sincetheverybeginningofthetwenty-firstcentury,neuroscientistshavebeenmakingprofoundadvancesinunderstandingthetwodifferenttypesofnetworksthatthebrainswitchesbetween—highlyattentivestatesandmorerelaxedrestingstatenetworks.1We’llcallthethinkingprocessesrelatedtothesetwodifferenttypesofnetworksthefocusedmodeanddiffusemode,respectively—thesemodesarehighlyimportantforlearning.2Itseemsyoufrequentlyswitchbackandforthbetweenthesetwomodesinyourday-to-dayactivities.You’reineitheronemodeortheother—notconsciouslyinbothatthesametime.Thediffusemodedoesseemtobeabletoworkquietlyinthebackgroundonsomethingyouarenotactivelyfocusingon.3Sometimesyoumayalsoflickerforarapidmomenttodiffuse-modethinking.

Focused-modethinkingisessentialforstudyingmathandscience.Itinvolvesadirectapproachtosolvingproblemsusingrational,sequential,analyticalapproaches.Thefocusedmodeisassociatedwiththeconcentratingabilitiesofthebrain’sprefrontalcortex,locatedrightbehindyourforehead.4Turnyourattentiontosomethingandbam—thefocusedmodeison,likethetight,penetratingbeamofaflashlight.

Theprefrontalcortexisthearearightbehindtheforehead.

Diffuse-modethinkingisalsoessentialforlearningmathandscience.Itallowsustosuddenlygainanewinsightonaproblemwe’vebeenstrugglingwithandisassociatedwith“big-picture”perspectives.Diffuse-modethinkingiswhathappenswhenyourelaxyourattentionandjustletyourmindwander.Thisrelaxationcanallowdifferentareasofthebraintohookupandreturnvaluableinsights.Unlikethefocusedmode,thediffusemodeseemslessaffiliatedwithanyoneareaofthebrain—youcanthinkofitasbeing“diffused”throughoutthebrain.5Diffuse-modeinsightsoftenflowfrompreliminarythinkingthat’sbeendoneinthefocusedmode.(Thediffusemodemusthaveclaytomakebricks!)

Learninginvolvesacomplexflickeringofneuralprocessingamongdifferentareasofthebrain,aswellasbackandforthbetweenhemispheres.6Sothismeansthatthinkingandlearningismorecomplicatedthansimplyswitchingbetweenthefocusedanddiffusemodes.Butfortunately,wedon’tneedtogodeeperintothephysicalmechanisms.We’regoingtotakeadifferentapproach.

TheFocusedMode—ATightPinballMachine

Tounderstandfocusedanddiffusementalprocesses,we’regoingtoplaysomepinball.(Metaphorsarepowerfultoolsforlearninginmathandscience.)Intheoldgameofpinball,youpullbackonaspring-loadedplungeranditwhacksaball,whichendsupbouncingrandomlyaroundthecircularrubberbumpers.

Thishappyzombieisplayingneuralpinball.

Lookatthefollowingillustration.Whenyoufocusyourattentiononaproblem,yourmindpullsbackthementalplungerandreleasesathought.Boom—thatthoughttakesoff,bumpingaroundlikethepinballintheheadontheleft.Thisisthefocusedmodeofthinking.

Noticehowtheroundbumpersareveryclosetogetherinthefocusedmode.Incontrast,thediffusemodeontherighthasitscircularrubberbumpersfartherapart.(Ifyouwanttopursuethemetaphorstillfurther,youcanthinkofeachbumperasaclusterofneurons.)

Theclosebumpersofthefocusedmodemeanthatyoucanmoreeasilythinkaprecisethought.Basically,thefocusedmodeisusedtoconcentrateonsomethingthat’salreadytightlyconnectedinyourmind,oftenbecauseyouarefamiliarandcomfortablewiththeunderlyingconcepts.Ifyoulookcloselyattheupperpartofthefocused-modethoughtpattern,you’llseeawider,“well-trodden”partoftheline.Thatbroaderpathshowshowthefocused-modethoughtisfollowingalongarouteyou’ve

alreadypracticedorexperienced.Forexample,youcanusethefocusedmodetomultiplynumbers—ifyoualreadyknowhowto

multiply,thatis.Ifyou’restudyingalanguage,youmightusethefocusedmodetobecomemorefluentwiththeSpanishverbconjugationyoulearnedlastweek.Ifyou’reaswimmer,youmightusethefocusedmodetoanalyzeyourbreaststrokeasyoupracticestayinglowtoallowmoreenergytogointoyourforwardmotion.

Whenyoufocusonsomething,theconsciouslyattentiveprefrontalcortexautomaticallysendsoutsignalsalongneuralpathways.Thesesignalslinkdifferentareasofyourbrainrelatedtowhatyou’rethinkingabout.Thisprocessisalittlelikeanoctopusthatsendsitstentaclestodifferentareasofitssurroundingstofiddlewithwhateverit’sworkingon.Theoctopushasonlysomanytentaclestomakeconnections,justasyourworkingmemoryhasonlysomanythingsitcanholdatonce.(We’lltalkmoreabouttheworkingmemorylater.)

Inthegame“pinball,”aball,whichrepresentsathought,shootsupfromthespring-loadedplungertobouncerandomlyagainstrowsofrubberbumpers.Thesetwopinballmachinesrepresentfocused(left)anddiffuse(right)waysofthinking.Thefocusedapproachrelatestointenseconcentrationonaspecificproblemorconcept.Butwhileinfocusedmode,sometimesyouinadvertentlyfindyourselffocusingintentlyandtryingtosolveaproblemusingerroneousthoughtsthatareinadifferentplaceinthebrainfromthe“solution”thoughtsyouneedtoactuallyneedtosolvetheproblem.

Asanexampleofthis,notetheupper“thought”thatyourpinballfirstbouncesaroundinontheleft-handimage.Itisveryfarawayandcompletelyunconnectedfromthelowerpatternofthoughtinthesamebrain.Youcanseehowpartoftheupperthoughtseemstohaveanunderlyingbroadpath.Thisisbecauseyou’vethoughtsomethingsimilartothatthoughtbefore.Thelowerthoughtisanewthought—itdoesn’thavethatunderlyingbroadpattern.

Thediffuseapproachontherightofteninvolvesabig-pictureperspective.Thisthinkingmodeisusefulwhenyouarelearningsomethingnew.Asyoucansee,thediffusemodedoesn’tallowyoutofocustightlyandintentlytosolveaspecificproblem—butitcanallowyoutogetclosertowherethatsolutionliesbecauseyou’reabletotravelmuchfartherbeforerunningintoanotherbumper.

Youoftenfirstfunnelaproblemintoyourbrainbyfocusingyourattentiononwords—readingthebookorlookingatyournotesfromalecture.Yourattentionaloctopusactivatesyourfocused

mode.Asyoudoyourinitialfocusednoodlingaroundwiththeproblem,youarethinkingtightly,usingthepinballbumpersthatareclosetogethertofollowalongfamiliarneuralpathwaysrelatedtosomethingyoualreadyknoworarefamiliarwith.Yourthoughtsrattleeasilythroughthepreviouslyingrainedpatternsandquicklysettleonasolution.Inmathandscience,however,itoftendoesn’ttakemuchofachangeforaproblemtobecomequitedifferent.Problemsolvingthengrowsmoredifficult.

WhyMathandScienceCanBeMoreChallenging

Focusedproblemsolvinginmathandscienceisoftenmoreeffortfulthanfocused-modethinkinginvolvinglanguageandpeople.7Thismaybebecausehumanshaven’tevolvedoverthemillenniatomanipulatemathematicalideas,whicharefrequentlymoreabstractlyencryptedthanthoseofconventionallanguage.8Obviously,wecanstillthinkaboutmathandscience—it’sjustthattheabstractnessandencryptednessaddsalevel—sometimesanumberoflevels—ofcomplexity.

WhatdoImeanbyabstractness?Youcanpointtoareallivecowchewingitscudinapastureandequateitwiththelettersc-o-wonthepage.Butyoucan’tpointtoarealliveplussignthatthesymbol“+”ismodeledafter—theideaunderlyingtheplussignismoreabstract.Byencryptedness,Imeanthatonesymbolcanstandforanumberofdifferentoperationsorideas,justasthemultiplicationsignsymbolizesrepeatedaddition.Inourpinballanalogy,it’sasiftheabstractnessandencryptednessofmathcanmakethepinballbumpersabitspongier—ittakesextrapracticeforthebumperstohardenandthepinballtobounceproperly.Thisiswhydealingwithprocrastination,whileimportantinstudyinganydiscipline,isparticularlyimportantinmathandscience.We’llbetalkingmoreaboutthislater.

Relatedtothesedifficultiesinmathandscienceisanotherchallenge.It’scalledtheEinstellungeffect(pronouncedEYE-nshtellung).Inthisphenomenon,anideayoualreadyhaveinmind,oryoursimpleinitialthought,preventsabetterideaorsolutionfrombeingfound.9Wesawthisinthefocusedpinballpicture,whereyourinitialpinballthoughtwenttotheupperpartofthebrain,butthesolutionthoughtpatternwasinthelowerpartoftheimage.(TheGermanwordEinstellungmeans“installation”—basicallyyoucanrememberEinstellungasinstallingaroadblockbecauseofthewayyouareinitiallylookingatsomething.)

Thiskindofwrongapproachisespeciallyeasytodoinsciencebecausesometimesyourinitialintuitionaboutwhat’shappeningismisleading.Youhavetounlearnyourerroneousolderideasevenwhileyou’relearningnewones.10

TheEinstellungeffectisafrequentstumblingblockforstudents.It’snotjustthatsometimesyournaturalintuitionsneedtoberetrained—it’sthatsometimesitistoughevenfiguringoutwheretobegin,aswhentacklingahomeworkproblem.Youbumbleabout—yourthoughtsfarfromtheactualsolution—becausethecrowdedbumpersofthefocusedmodepreventyoufromspringingtoanewplacewherethesolutionmightbefound.

Thisispreciselywhyonesignificantmistakestudentssometimesmakeinlearningmathandscienceisjumpingintothewaterbeforetheylearntoswim.11Inotherwords,theyblindlystartworkingonhomeworkwithoutreadingthetextbook,attendinglectures,viewingonlinelessons,orspeakingwithsomeoneknowledgeable.Thisisarecipeforsinking.It’slikerandomlyallowingathoughttopopoffinthefocused-modepinballmachinewithoutpayinganyrealattentiontowherethe

solutiontrulylies.Understandinghowtoobtainrealsolutionsisimportant,notonlyinmathandscienceproblem

solving,butforlifeingeneral.Forexample,alittleresearch,self-awareness,andevenself-experimentationcanpreventyoufrombeingpartedwithyourmoney—orevenyourgoodhealth—onproductsthatcomewithbogus“scientific”claims.12Andjusthavingalittleknowledgeoftherelevantmathcanhelppreventyoufromdefaultingonyourmortgage—asituationthatcanhaveamajornegativeimpactonyourlife.13

TheDiffuseMode—ASpread-OutPinballMachine

Thinkbackseveralpagestotheillustrationofthediffuse-modepinballmachinebrain,wherethebumperswerespreadfarapart.Thismodeofthinkingallowsthebraintolookattheworldfromamuchbroaderperspective.Canyouseehowathoughtcantravelmuchfurtherbeforeitrunsintoabumper?Theconnectionsarefurtherapart—youcanquicklyzoomfromoneclumpofthoughttoanotherthat’squitefaraway.(Ofcourse,it’shardtothinkprecise,complexthoughtswhileinthismode.)

Ifyouaregrapplingwithanewconceptortryingtosolveanewproblem,youdon’thavepreexistingneuralpatternstohelpguideyourthoughts—there’snofuzzyunderlyingpathwaytohelpguideyou.Youmayneedtorangewidelytoencounterapotentialsolution.Forthis,diffusemodeisjusttheticket!

Anotherwaytothinkofthedifferencebetweenfocusedanddiffusemodesistothinkofaflashlight.Youcansetaflashlightsoithasatightlyfocusedbeamthatcanpenetratedeeplyintoasmallarea.Oryoucansettheflashlightontoamorediffusesettingwhereitcastsitslightbroadly,butnotverystronglyinanyonearea.

Ifyouaretryingtounderstandorfigureoutsomethingnew,yourbestbetistoturnoffyourprecision-focusedthinkingandturnonyour“bigpicture”diffusemode,longenoughtobeabletolatchontoanew,morefruitfulapproach.Aswe’llsee,thediffusemodehasamindofitsown—youcan’tsimplycommandittoturnon.Butwe’llsoongettosometricksthatcanhelpyoutransitionbetweenmodes.

COUNTERINTUITIVECREATIVITY

“WhenIwaslearningaboutthediffusemode,Ibegantonoticeitinmydailylife.Forinstance,IrealizedmybestguitarriffsalwayscametomewhenIwas‘justmessingaround’asopposedtowhenIsatdownintentoncreatingamusicalmasterpiece(inwhichcasemysongswereoftenclichédanduninspiring).SimilarthingshappenedwhenIwaswritingaschoolpaper,tryingtocomeupwithanideaforaschoolproject,ortryingtosolveadifficultmathproblem.Inowfollowtheruleofthumbthatisbasically:Theharderyoupushyourbraintocomeupwithsomethingcreative,thelesscreativeyourideaswillbe.Sofar,Ihavenotfoundasinglesituationwherethisdoesnotapply.Ultimately,thismeansthatrelaxationisanimportantpartofhardwork—andgoodwork,forthatmatter.”

—ShaunWassell,freshman,computerengineering

WhyAreThereTwoModesofThinking?

Whydowehavethesetwodifferentthinkingmodes?Theanswermayberelatedtotwomajorproblemsthatvertebrateshavehadinstayingaliveandpassingtheirgenesontotheiroffspring.Abird,forexample,needstofocuscarefullysoitcanpickuptinypiecesofgrainasitpecksthegroundforfood,andatthesametime,itmustscanthehorizonforpredatorssuchashawks.What’sthebestwaytocarryoutthosetwoverydifferenttasks?Splitthingsup,ofcourse.Youcanhaveonehemisphereofthebrainmoreorientedtowardthefocusedattentionneededtopeckatfoodandtheotherorientedtowardscanningthehorizonfordanger.Wheneachhemispheretendstowardaparticulartypeofperception,itmayincreasethechanceofsurvival.14Ifyouwatchbirds,they’llfirstpeck,andthenpausetoscanthehorizon—almostasiftheyarealternatingbetweenfocusedanddiffusemodes.

Inhumans,weseeasimilarsplittingofbrainfunctions.Theleftsideofthebrainissomewhatmoreassociatedwithcareful,focusedattention.Italsoseemsmorespecializedforhandlingsequentialinformationandlogicalthinking—thefirststepleadstothesecondstep,andsoon.Therightseemsmoretiedtodiffusescanningoftheenvironmentandinteractingwithotherpeople,andseemsmoreassociatedwithprocessingemotions.15Italsoislinkedwithhandlingsimultaneous,big-pictureprocessing.16

Theslightdifferencesinthehemispheresgiveusasenseofwhytwodifferentprocessingmodesmayhavearisen.Butbewaryoftheideathatsomepeopleare“left-brain”or“right-brain”dominant—researchindicatesthatissimplynottrue.17Insteaditisclearthatbothhemispheresareinvolvedinfocusedaswellasdiffusemodesofthinking.Tolearnaboutandbecreativeinmathandscience,weneedtostrengthenanduseboththefocusedanddiffusemodes.19

Here’saquickexamplethatgivesasenseofthedifferencebetweenfocusedanddiffusethinking.Ifyouaregiventwotrianglestoputtogetherintoasquareshape,it’seasytodo,asshownontheleft.Ifyouaregiventwomoretrianglesandtoldtoformasquare,yourfirsttendencyistoerroneouslyputthemtogethertoformarectangle,asshowninthemiddle.Thisisbecauseyou’vealreadylaiddownafocused-modepatternthatyouhaveatendencytofollow.Ittakesanintuitive,diffuseleaptorealizethatyouneedtocompletelyrearrangethepiecesifyouwanttoformanothersquare,asshownontheright.18

Evidencesuggeststhattograpplewithadifficultproblem,wemustfirstputhard,focused-modeeffortintoit.(Welearnedthatingradeschool!)Here’stheinterestingpart:Thediffusemodeisalsooftenanimportantpartofproblemsolving,especiallywhentheproblemisdifficult.Butaslongasweareconsciouslyfocusingonaproblem,weareblockingthediffusemode.

There’sawinneratPing-Pongonlyiftheballisabletogobackandforth.

EMBRACEBEFUDDLEMENT!

“Befuddlementisahealthypartofthelearningprocess.Whenstudentsapproachaproblemanddon’tknowhowtodoit,they’lloftendecidethey’renogoodatthesubject.Brighterstudents,inparticular,canhavedifficultyinthisway—theirbreezingthroughhighschoolleavesthemnoreasontothinkthatbeingconfusedisnormalandnecessary.Butthelearningprocessisallaboutworkingyourwayoutofconfusion.Articulatingyourquestionis80percentofthebattle.Bythetimeyou’vefiguredoutwhat’sconfusing,you’relikelytohaveansweredthequestionyourself!”

—KennethR.Leopold,DistinguishedTeachingProfessor,DepartmentofChemistry,UniversityofMinnesota

Thebottomlineisthatproblemsolvinginanydisciplineofteninvolvesanexchangebetweenthetwofundamentallydifferentmodes.Onemodewillprocesstheinformationitreceivesandthensendtheresultbacktotheothermode.Thisvolleyingofinformationbackandforthasthebrainworksitswaytowardaconscioussolutionappearsessentialforunderstandingandsolvingallbuttrivialproblemsandconcepts.20Theideaspresentedhereareextremelyhelpfulforunderstandinglearninginmathandscience.Butasyouareprobablybeginningtosee,theycanbejustashelpfulformanyothersubjectareas,suchaslanguage,music,andcreativewriting.

NOWYOUTRY!

Shift ingModes

Here’sacognitiveexercisethatcanhelpyoufeeltheshiftfromfocusedtodiffusemode.Seewhetheryoucanformanewtrianglethatpointsdownbymovingonlythreecoins.Whenyourelaxyourmind,releasingyourattentionandfocusingonnothinginparticular,thesolutioncanmosteasily

cometoyou.

Youshouldknowthatsomechildrengetthisexerciseinstantly,whilesomehighlyintelligentprofessorsfinallyjustgiveup.Toanswerthisquestion,ithelpstosummonyourinnerchild.Thesolutionsforthischallengeandforallthe“NowYouTry!”challengesinthebookcanbefoundintheendnotes.21

ProcrastinationPrelude

Manypeoplestrugglewithprocrastination.We’llhavealottosaylaterinthisbookabouthowtodealeffectivelywithprocrastination.Fornow,keepinmindthatwhenyouprocrastinate,youareleavingyourselfonlyenoughtimetodosuperficialfocused-modelearning.Youarealsoincreasingyourstresslevelbecauseyouknowyouhavetocompletewhatfeelslikeanunpleasanttask.Theresultingneuralpatternswillbefaintandfragmentedandwillquicklydisappear—you’llbeleftwithashakyfoundation.Inmathandscienceinparticular,thiscancreatesevereproblems.Ifyoucramforatestatthelastminuteorquicklybreezethroughyourhomework,youwon’thavetimeforeitherlearningmodetohelpyoutacklethetougherconceptsandproblemsortohelpyousynthesizetheconnectionsinwhatyouarelearning.

NOWYOUTRY!

FocusingIntent lybut Briefly

Ifyouoftenfindyourselfprocrastinating,asmanyofusdo,here’satip.Turnoffyourphoneandanysoundsorsights(orwebsites)thatmightsignalaninterruption.Thensetatimerfortwenty-fiveminutesandputyourselftowarddoingatwenty-five-minuteinterludeofworkfocusedonatask—anytask.Don’tworryaboutfinishingthetask—justworryaboutworkingonit.Oncethetwenty-fiveminutesisup,rewardyourselfwithwebsurfing,checkingyourphone,orwhateveryouliketodo.Thisrewardisasimportantastheworkitself.You’llbeamazedathowproductiveafocusedtwenty-five-minutestintcanbe—especiallywhenyou’rejustfocusingontheworkitself,notonfinishing.(Thismethod,knownasthePomodorotechnique,willbediscussedinmoredetailinchapter6.)Ifyouwanttoapplyamoreadvancedversionofthisapproach,imaginethatattheendoftheday,youarereflecting

ontheonemostimportanttaskthatyouaccomplishedthatday.Whatwouldthattaskbe?Writeitdown.Thenworkonit.Trytocompleteatleastthreeofthesetwenty-five-minutesessionsthatday,onwhatevertaskortasksyouthinkaremostimportant.Attheendofyourworkday,lookatwhatyoucrossedoffyourlistandsavorthefeelingofaccomplishment.Then

writeafewkeythingsthatyouwouldliketoworkonthenextday.Thisearlypreparationwillhelpyourdiffusemodebegintothinkabouthowyouwillgetthosetasksdonethenextday.

SUMMINGITUP

Ourbrainusestwoverydifferentprocessesforthinking—thefocusedanddiffusemodes.Itseemsyoutogglebackandforthbetweenthesemodes,usingoneortheother.Itistypicaltobestumpedbynewconceptsandproblemswhenwefirstfocusonthem.Tofigureoutnewideasandsolveproblems,it’simportantnotonlytofocusinitially,butalsotosubsequentlyturnourfocusawayfromwhatwewanttolearn.TheEinstellungeffectreferstogettingstuckinsolvingaproblemorunderstandingaconceptasaresultofbecomingfixatedonaflawedapproach.Switchingmodesfromfocusedtodiffusecanhelpfreeyoufromthiseffect.Keepinmind,then,thatsometimesyouwillneedtobeflexibleinyourthinking.Youmayneedtoswitchmodestosolveaproblemorunderstandaconcept.Yourinitialideasaboutproblemsolvingcansometimesbeverymisleading.

PAUSEANDRECALL

Closethebookandlookaway.What werethemainideasofthischapter?Don’t worryifyoucan’t recallverymuchwhenyoufirst begint ryingthis.Asyoucont inuepract icingthistechnique,you’llbeginnot icingchangesinhowyoureadandhowmuchyourecall.

ENHANCEYOURLEARNING

1.Howwouldyourecognizewhenyouareinthediffusemode?Howdoesitfeeltobeinthediffusemode?

2.Whenyouareconsciouslythinkingofaproblem,whichmodeisactiveandwhichis

blocked?Whatcanyoudotoescapethisblocking?

3.RecallanepisodewhereyouexperiencedtheEinstellungeffect.Howwereyouabletochangeyourthinkingtogetpastthepreconceived,buterroneous,notion?

4.Explainhowthefocusedanddiffusemodesmightbeequatedtoanadjustablebeamonaflashlight.Whencanyouseefarther?Whencanyouseemorebroadly,butlessfar?

5.Whyisprocrastinationsometimesaspecialchallengeforthosewhoarestudyingmathandscience?

SHIFTINGOUTOFBEINGSTUCK:INSIGHTFROMNADIANOUI-MEHIDI,ASENIORSTUDYINGECONOMICS

“ItookCalculusIineleventhgradeanditwasanightmare.ItwassoprofoundlydifferentfromanythingIhadlearnedbeforethatIdidn’tevenknowhowtolearnit.IstudiedlongerandharderthanIeverhadbefore,yetnomatterhowmanyproblemsIdidorhowlongIstayedinthelibraryIwaslearningnothing.IultimatelyjuststucktowhatIcouldgetbywiththroughmemorizing.Needlesstosay,IdidnotdowellontheAP[advancedplacement]exam.“Iavoidedmathforthenexttwoyears,andthenasasophomoreincollege,Itook

CalculusIandgota4.0.Idon’tthinkIwasanysmartertwoyearslater,buttherewasacompleteshiftinthewayIwasapproachingthesubject.“IthinkinhighschoolIwasstuckinthefocusedmodeofthinking(Einstellung!)and

feltthatifIkepttryingtoapproachproblemsinthesamewayitwouldeventuallyclick.“Inowtutorstudentsinmathandeconomicsandtheissuesarealmostalwaysthat

theyarefixatedonlookingatthedetailsoftheproblemforcluesonhowtosolveit,andnotonunderstandingtheproblemitself.Idon’tthinkyoucantutorsomeoneonhowtothink—it’skindofapersonaljourney.Butherearesomethingsthathavehelpedmeunderstandaconceptthatatfirstseemscomplicatedorconfusing.

1.IunderstandbetterwhenIreadthebookratherthanlistentosomeonespeak,soIalwaysreadthebook.IskimfirstsoIknowbasicallywhatthechapteristryingtogetatandthenIreaditindetail.Ireadthechaptermorethanonce(butnotinarow).

2.Ifafterreadingthebook,Istilldon’tfullyunderstandwhat’sgoingon,IGoogleorlookatYouTubevideosonthesubject.Thisisn’tbecausethebookorprofessorisn’tthorough,butratherbecausesometimeshearingaslightlydifferentwayofphrasingsomethingcanmakeyourmindlookattheproblemfromadifferentangleandsparkunderstanding.

3.IthinkmostclearlywhenI’mdriving.SometimesI’lljusttakeabreakanddrivearound—thishelpsalot.IhavetobesomewhatoccupiedbecauseifIjustsitdownandthinkIendupgettingboredordistractedandcan’tconcentrate.

T

{3}

learningiscreating:

LessonsfromThomasEdison’sFryingPan

homasEdisonwasoneofthemostprolificinventorsinhistory,withmorethanonethousandpatentstohisname.Nothinggotinthewayofhiscreativity.Evenashislabwasburningtothe

groundinahorrificaccidentalfire,Edisonwasexcitedlysketchingupplansforanewlab,evenbiggerandbetterthanbefore.HowcouldEdisonbesophenomenallycreative?Theanswer,asyou’llsee,relatestohisunusualtricksforshiftinghismodeofthinking.

ShiftingbetweentheFocusedandDiffuseModes

Formostpeople,shiftingfromfocusedtodiffusemodehappensnaturallyifyoudistractyourselfandthenallowalittletimetopass.Youcangoforawalk,takeanap,orgotothegym.Oryoucanworkonsomethingthatoccupiesotherpartsofyourbrain:listeningtomusic,conjugatingSpanishverbs,orcleaningyourgerbilcage.1Thekeyistodosomethingelseuntilyourbrainisconsciouslyfreeofanythoughtoftheproblem.Unlessothertricksarebroughtintoplay,thisgenerallytakesseveralhours.Youmaysay,“Idon’thavethatkindoftime.”Youdo,however,ifyousimplyswitchyourfocustootherthingsyouneedtodo,andmixinalittlerelaxingbreaktime.

CreativityexpertHowardGruberhassuggestedthatoneofthethreeB’susuallyseemstodothetrick:thebed,thebath,orthebus.2Oneremarkablyinventivechemistofthemid-1800s,AlexanderWilliamson,observedthatasolitarywalkwasworthaweekinthelaboratoryinhelpinghimprogressinhiswork.3(Luckyforhimtherewerenosmartphonesthen.)Walkingspurscreativityinmanyfields;anumberoffamouswriters,suchasJaneAusten,CarlSandburg,andCharlesDickens,foundinspirationduringtheirfrequentlongwalks.

Onceyouaredistractedfromtheproblemathand,thediffusemodehasaccessandcanbeginpingingaboutinitsbig-picturewaytosettleonasolution.4Afteryourbreak,whenyoureturntotheproblemathand,youwilloftenbesurprisedathoweasilythesolutionpopsintoplace.Evenifthesolutiondoesn’tappear,youwilloftenbefurtheralonginyourunderstanding.Itcantakealotofhardfocused-modeworkbeforehand,butthesudden,unexpectedsolutionthatemergesfromthediffusemodecanmakeitfeelalmostlikethe“aha!”mode.

Thatwhispered,intuitivesolutiontowhateverpuzzleyouareattemptingtodealwithisoneofthe

mostelusivelycoolfeelingsofmathandscience—andart,literature,andanythingelsecreative,forthatmatter!Andyes,asyou’llsee,mathandsciencearedeeplycreativeformsofthinkingevenwhenyouarejustlearningtheminschool.

BrilliantinventorThomasEdison(above)isthoughttohaveusedaclevertricktoswitchfromfocusedtodiffusemode.ThiswasthesametrickusedbyfamedsurrealistpainterSalvadorDalí(below)forhisartisticcreations.

Thattwilight,disconnectedfeelingoneexperienceswhiledriftingofftosleepwas,itseems,partofthemagicbehindEdison’sextraordinarycreativity.Whenfacedwithadifficultproblem,insteadoffocusingintentlyonit,Edison,accordingtolegend,tookanap.Buthedidsowhilesittinginaloungechair,holdingaballbearinginhishandaboveaplateonthefloor.Asherelaxed,histhoughtsmovedtowardfreeandopendiffuse-modethinking.(Thisisareminderthatfallingasleepisagoodwaytogetthebrainthinkinglooselyaboutaproblemyouwanttosolve,oranythingyouareworkingoncreatively.)WhenEdisonfellasleep,theballbearingfellfromhishands.Theclatterwokehimsohecouldgraspthefragmentsofhisdiffuse-modethinkingtocreatenewapproaches.5

CreativityIsaboutHarnessingandExtendingYourAbilities

Thereisadeepconnectionbetweentechnical,scientific,andartisticcreativity.WildsurrealistpainterSalvadorDalí,likeThomasEdison,alsousedanapandtheclatterofanobjectfallingfromhishandtotapintohisdiffuse-modecreativeperspectives.(Dalícalledthis“sleepingwithoutsleeping.”6)Enlistingthediffusemodehelpsyoulearnatadeepandcreativelevel.Thereismuchcreativityunderlyingmathandscienceproblemsolving.Manypeoplethinkthatthere’sonlyonewaytodoaproblem,butthereareoftenanumberofdifferentsolutions,ifyouhavethecreativitytoseethem.Forexample,therearemorethanthreehundreddifferentknownproofsofthePythagoreantheorem.Aswewillsoonlearn,technicalproblemsandtheirsolutionsmaybeconsideredaformofpoetry.

Creativity,however,ismorethansimplyhavingadevelopedsetofscientificorartisticcapabilities.Itisaboutharnessingandextendingyourabilities.Manypeoplethinktheyarenotcreative,whenthatissimplyuntrue.Weallhavetheabilitytomakenewneuralconnectionsandpullfrommemorysomethingthatwasneverputthereinthefirstplace—whatcreativityresearchersLianeGaboraandAparaRanjanrefertoas“themagicofcreativity.”7Understandinghowyourmindworkshelpsyoubetterunderstandthecreativenatureofsomeofyourthoughts.

NOWYOUTRY!

FromFocusedtoDiffuse

Readthefollowingsentenceandidentifyhowmanyerrorsitcontains:

Thisssentencecontainsthreeeerrors.

Thefirsttwoerrorsareeasilydiscoveredusingafocused-modeapproach.Thethird,paradoxicalerrorbecomesobviousonlywhenyouchangeperspectivesandadoptamorediffuseapproach.8(Remember,thesolutionisintheendnote.)

WorkingBackandForthbetweenModestoMasterMaterial

Edison’sstoryremindsusofsomethingelse.Welearnagreatdealfromourfailuresinmathandscience.9Knowthatyouaremakingprogresswitheachmistakeyoucatchwhentryingtosolveaproblem—findingerrorsshouldgiveyouasenseofsatisfaction.Edisonhimselfissaidtohavenoted“Ihavenotfailed.I’vejustfound10,000waysthatwon’twork.”10

Mistakesareinevitable.Toworkpastthem,startearlyonyourassignmentsand,unlessyouarereallyenjoyingwhatyouaredoing,keepyourworkingsessionsshort.Remember,whenyoutakebreaks,yourdiffusemodeisstillworkingawayinthebackground.It’sthebestdealaround—youcontinuetolearnwhileyouaretakingiteasy.Somepeoplethinktheyneverenterdiffusemode,butthat’ssimplynottrue.Everytimeyourelaxandthinkofnothinginparticular,yourbrainentersintoanaturaldefaultmodethat’saformofdiffusethinking.Everybodydoesthis.11

Sleepisprobablythemosteffectiveandimportantfactorinallowingyourdiffusemodetotackleadifficultproblem.Butdon’tbefooledbythediffusemode’sseeminglyeasygoing,sometimessleepynature.Onewaytothinkofthediffusemodeisasabasestationwhenyouaremountainclimbing.Basestationsareessentialrestingspotsinthelongjourneytodifficultmountaintops.Youusethemtopause,reflect,checkyourgear,andmakesureyou’vegottherightroutepickedout.Butyouwouldneverconfuserestingatabasestationwiththehardworkofgettingtothetopofamountain.Inotherwords,justusingyourdiffusemodedoesn’tmeanyoucanlollygagaroundandexpecttogetanywhere.Asthedaysandweekspass,it’sthedistributedpractice—thebackandforthbetweenfocused-modeattentionanddiffuse-moderelaxation—thatdoesthetrick.12

Enlistingthefocusedmode,whichisoftenwhatyouneedtodotofirstgetaproblemintoyourbrain,requiresyourfullattention.Studieshaveshownthatwehaveonlysomuchmentalenergy—willpower—forthistypeofthinking.13Whenyourenergyflags,sometimesyoucantakeabreakbyjumpingtootherfocused-typetasks,suchasswitchingfromstudyingmathtostudyingFrench

vocabulary.Butthelongeryouspendinfocusedmode,themorementalresourcesyouuse.It’slikeaconcentrated,extendedsetofmentalweightlifting.That’swhybriefinterludesthatinvolvemovementortalkingwithfriends,whereyoudon’thavetoconcentrateintently,canbesorefreshing.

Youmaywantyourlearningtoprogressmorequickly—tosomehowcommandyourdiffusemodetoassimilatenewideasfaster.Butcompareittoexercise.Constantlyliftingweightswon’tmakeyourmusclesanybigger—yourmusclesneedtimetorestandgrowbeforeyouusethemagain.Takingtimeoffbetweenweightsessionshelpsbuildstrongmusclesinthelongrun.Consistencyovertimeiskey!

USETHESEDIFFUSE-MODETOOLSASREWARDSAFTERFIRMFOCUSED-MODEWORK14

GeneralDiffuse-ModeAct ivatorsGotothegymPlayasportlikesoccerorbasketballJog,walk,orswimDanceGoforadrive(ortagalongfortheride)DraworpaintTakeabathorshowerListentomusic,especiallywithoutwordsPlaysongsyouknowwellonamusicalinstrumentMeditateorpraySleep(theultimatediffusemode!)

Thefollowingdiffuse-modeactivatorsarebestusedbriefly,asrewards.(Theseactivitiesmaypullyouintoamorefocusedmodethantheprecedingactivities.)

PlayvideogamesSurfthewebTalktofriendsVolunteertohelpsomeonewithasimpletaskReadarelaxingbookTextfriendsGotoamovieorplayTelevision(droppingaremoteifyoufallasleepdoesn’tcount)

Don’tWorryaboutKeepingUpwiththeIntellectualJoneses

Studentswhoarebeginningtostruggleinmathandscienceoftenlookatotherswhoareintellectualracehorsesandtellthemselvestheyhavetokeepup.Thentheydon’tgivethemselvestheextratimetheyneedtotrulymasterthematerial,andtheyfallstillfurtherbehind.Asaresultofthisuncomfortableanddiscouragingsituation,studentsendupunnecessarilydroppingoutofmathandscience.

Takeastepbackandlookdispassionatelyatyourstrengthsandweaknesses.Ifyouneedmoretimetolearnmathandscience,that’ssimplythereality.Ifyou’reinhighschool,trytoarrangeyourscheduletogiveyourselfthetimeyouneedtofocusonthemoredifficultmaterials,andlimitthesematerialstomanageableproportions.Ifyou’reincollege,trytoavoidafullloadofheavycourses,

especiallyifyouareworkingontheside.Alighterloadofmathandsciencecoursescan,formany,betheequivalentofaheavyloadofothertypesofcourses.Especiallyintheearlystagesofcollege,avoidthetemptationtokeepupwithyourpeers.

Youmaybesurprisedtodiscoverthatlearningslowlycanmeanyoulearnmoredeeplythanyourfast-thinkingclassmates.Oneofthemostimportanttricksthathelpedmeretoolmybrainwaslearningtoavoidthetemptationtotaketoomanymathandscienceclassesatonce.

AvoidEinstellung(GettingStuck)

Remember,acceptingthefirstideathatcomestomindwhenyouareworkingonanassignmentortestproblemcanpreventyoufromfindingabettersolution.ChessplayerswhoexperienceEinstellungtrulybelievetheyarescanningtheboardforadifferentsolution.Butcarefulstudyofwheretheireyesaremovingshowsthattheyarekeepingtheirfocusontheoriginalsolution.Notonlytheireyes,buttheirminditselfcan’tmoveawayenoughtoseeanewapproachtotheproblem.15

Accordingtorecentresearch,blinkingisavitalactivitythatprovidesanothermeansofreevaluatingasituation.Closingoureyesseemstoprovideamicropausethatmomentarilydeactivatesourattentionandallowsus,forthebriefestofmoments,torefreshandrenewourconsciousnessandperspective.16Soblinkingmaymomentarilydisconnectusfromourfocused-modeperspective.Butontheotherhand,deliberatelyclosingoureyesmayhelpusfocusmoredeeply—peopleoftenlookawayorcloseorcovertheireyestoavoiddistractionsastheyconcentrateonthinkingofananswer.17

NowwecanbegintounderstandMagnusCarlsenandhisgeniusforappreciatingtheimportanceofseeminglytrivialdistractions.WhenCarlsenstoodandturnedhisglance—andhisattention—towardotherchessboards,hemayhavebeenhelpinghismindleapmomentarilyoutoffocusedmode.TurninghiseyesandattentionelsewherelikelywascriticalinallowinghisdiffuseintuitiontogotoworkonhisgamewithKasparov.HowwasCarlsenabletoswitchmodessoquicklytogainhissuddeninsights?Hisexpertiseinchessprobablyplayedarole,alongwithhisownintuitivepracticeskills.Thisisahintthatyou,too,maybeabletodevelopwaystoquicklytogglebetweenthefocusedanddiffusemodesasyoudevelopyourexpertiseinasubject.

Incidentally,CarlsenprobablyalsoknewhisbouncingfromhischairwoulddistractKasparov.Evenslightdistractionsatthatlevelofplaycanbedisconcerting—areminderforyouthatdeepfocusedattentionisanimportantresourcethatyoudon’twanttogetpulledoutof.(Unless,thatis,it’stimetopurposefullytakeastepbackandletthediffusemodetakeover.)

Figuringoutadifficultproblemorlearninganewconceptalmostalwaysrequiresoneormoreperiodswhenyouaren’tconsciouslyworkingontheproblem.Eachinterludeinwhichyouarenotdirectlyfocusedontheproblemallowsyourdiffusemodetolookatitinafreshway.Whenyouturnyourfocusedattentionbacktotheproblem,youconsolidatenewideasandpatternsthatthediffusemodehasdelivered.

Learningwellmeansallowingtimetopassbetweenfocusedlearningsessions,sotheneuralpatternshavetimetosolidifyproperly.It’slikeallowingtimeforthemortartodrywhenyouarebuildingabrickwall,asshownontheleft.Tryingtolearneverythinginafewcramsessionsdoesn’tallowtimeforneuralstructurestobecomeconsolidatedinyourlong-termmemory—theresultisajumbledpileofbrickslikethoseontheright.

ALTERNATINGFOCUSEDANDDIFFUSETHINKING

“Asapianoplayerforadecadeandahalf,Isometimesfoundmyselffacingaparticularlydifficultrun.Ijustcouldn’tgetit,soIwouldforcemyfingerstodoitoverandoveragain(albeitveryslowlyorincorrectly),andthenI’dtakeabreak.ThenextdaywhenItrieditagain,Iwouldbeabletoplayitperfectly,asifbymagic.“Itriedtakingabreaktodaywithacalculusproblemthatwastrickyandwasstartingtoinfuriateme.Inthecaronthe

waytotheRenaissancefestival,itcametomeandIhadtowriteitonanapkinbeforeIforgot!(Alwayshavenapkinsinyourcar.Youneverknow.)”

—TrevorDrozd,junior,computerscienceTherestingtimesbetweenyourfocused-modeeffortsshouldbelongenoughtogetyourconsciousmindcompletelyofftheproblemyou’reworkingon.Usuallyafewhoursislongenoughforthediffusemodetomakesignificantprogressbutnotsolongthatitsinsightsfadeawaybeforebeingpassedontothefocusedmode.Agoodruleofthumb,whenyouarefirstlearningnewconcepts,isnottoletthingsgountouchedforlongerthanaday.

Thediffusemodenotonlyallowsyoutolookatthematerialinnewwaysbutalsoappearstoallowyoutosynthesizeandincorporatethenewideasinrelationtowhatyoualreadyknow.Thisideaoflookingfromfreshperspectivesalsogivesusinsightonwhy“sleepingonit”beforemakingmajordecisionsisgenerallyagoodidea,18andwhytakingvacationsisimportant.

Thetensionbetweenthefocusedanddiffusemodesoflearningtakestimeforyourbraintoresolveasyouworkyourwaythroughlearningnewconceptsandsolvingnewproblems.Workinginthefocusedmodeislikeprovidingthebricks,whileworkinginthediffusemodeislikegraduallyjoiningthebrickstogetherwithmortar.Thepatientabilitytokeepworkingaway,alittlebitatatime,isimportant.Thisiswhy,ifprocrastinationisanissueforyou,itwillbecriticaltolearnsomeoftheupcomingneuraltrickstoeffectivelyaddressit.

NOWYOUTRY!

ObserveYourself

Nexttimeyoufindyourselfbecomingfrustratedatsomethingorsomeone,trytakingamentalstepbackandobservingyourreaction.Angerandfrustrationcanoccasionallyhavetheirplaceinmotivatingustosucceed,buttheycanalsoshutdownkeyareasofthebrainthatweneedinordertolearn.Risingfrustrationisusuallyagoodtime-outsignalforyou,signalingthatyouneedtoshifttodiffusemode.

WhattoDoWhenYou’reReallyStumped

Peoplewithstrongself-controlcanhavethemostdifficultyingettingthemselvestoturnofftheirfocusedmodesothatthediffusemodecanbeginitswork.Afterall,they’vebeensuccessfulbecausesometimestheycouldkeepgoingwhenothersflagged.Ifyouoftenfindyourselfinthissituation,youcanuseanothertrick.Makeitaruletolistentostudypartners,friends,orlovedoneswhocansensewhenyouarebecomingdangerouslyfrustrated.Sometimesit’seasiertolistentosomeoneelsethantoyourself.(Whenmyhusbandorchildren,forexample,tellmetostopworkingwithabuggypieceofsoftware,Ifollowthisrulemyself,albeitalwaysbegrudginglyatthetime.)

Speakingoftalkingtootherpeople,whenyou’regenuinelystuck,nothingismorehelpfulthangettinginsightfromclassmates,peers,ortheinstructor.Asksomeoneelseforadifferentperspectiveonhowtosolvetheproblemoradifferentanalogytounderstandtheconcept;however,it’sbestthatyoufirstwrestlewiththeproblemyourselfbeforeyoutalktoanyoneelse,becauseitcanembedthebasicconceptsdeeplyenoughthatyoubecomereceptivetotheexplanation.Learningoftenmeansmakingsenseofwhatwe’veingested,andforthat,weneedtohaveingestedsomething.(Irememberbelligerentlystaringatmyscienceteachersinhighschool,blamingthemformylackofunderstanding,withoutrealizingthatIwastheonewhoneededtotaketheinitialsteps.)Anddon’twaituntiltheweekbeforemidtermsorfinalexamsforthisassistance.Goearlyandoften.Theteachercanoftenrephraseorexplaininadifferentwaythatallowsyoutograspthetopic.

FAILURECANBEAGREATTEACHER

“WhenIwasintenthgradeIdecidedtotakeanAPcomputerscienceclass.IendedupfailingtheAPexam.ButIwouldnotacceptthefailure,soItooktheclassandthetestagainthefollowingyear.Somehow,stayingawayfromprogrammingfornearlyayearandthencomingbacktoitmademerealizehowmuchItrulyenjoyedit.Ipassedthetesteasilyonthesecondtry.IfIhadbeentooafraidoffailuretotakethecomputerscienceclassthefirsttime,andthenasecondtime,IwouldcertainlynotbewhatIamtoday,apassionateandhappycomputerscientist.”

—CassandraGordon,sophomore,computerscience

NOWYOUTRY!

UnderstandtheParadoxesofLearning

Learningisoftenparadoxical.Theverythingweneedinordertolearnimpedesourabilitytolearn.Weneedtofocusintentlytobeabletosolveproblems—yetthatfocuscanalsoblockusfromaccessingthefreshapproachwemayneed.Successisimportant,butcritically,soisfailure.Persistenceiskey—butmisplacedpersistencecausesneedlessfrustration.Throughoutthisbook,youwillencountermanyparadoxesoflearning.Canyouanticipatewhatsomeofthemmight

be?

IntroductiontoWorkingandLong-TermMemory

Atthispoint,it’shelpfultotouchonsomeofthebasicsofmemory.Forourpurposes,we’regoingtotalkaboutonlytwomajormemorysystems:workingmemoryandlong-termmemory.19

Workingmemoryisthepartofmemorythathastodowithwhatyouareimmediatelyandconsciouslyprocessinginyourmind.Itusedtobethoughtthatourworkingmemorycouldholdaroundsevenitems,or“chunks,”butit’snowwidelybelievedthattheworkingmemoryholdsonlyaboutfourchunksofinformation.(Wetendtoautomaticallygroupmemoryitemsintochunks,soitseemsourworkingmemoryisbiggerthanitactuallyis.20)

Youcanthinkofworkingmemoryasthementalequivalentofajuggler.Thefouritemsonlystayintheair—orinworkingmemory—becauseyoukeepaddingalittleenergy.Thisenergyisneededsoyourmetabolicvampires—naturaldissipatingprocesses—don’tsuckthememoriesaway.Inotherwords,youneedtomaintainthesememoriesactively;otherwise,yourbodywilldivertyourenergyelsewhere,andyou’llforgettheinformationyou’vetakenin.

Generally,youcanholdaboutfouritemsinyourworkingmemory,asshowninthefour-itemmemoryontheleft.Whenyoumasteratechniqueorconceptinmathorscience,itoccupieslessspaceinyourworkingmemory.Thisfreesyourmentalthinkingspacesothatitcanmoreeasilygrapplewithotherideas,asshownontheright.

Yourworkingmemoryisimportantinlearningmathandsciencebecauseit’slikeyourownprivatementalblackboardwhereyoucanjotdownafewideasthatyouareconsideringortryingtounderstand.

Howdoyoukeepthingsinworkingmemory?Oftenit’sthroughrehearsal;forexample,youcanrepeataphonenumbertoyourselfuntilyouhaveachancetowriteitdown.Youmayfindyourselfshuttingyoureyestokeepanyotheritemsfromintrudingintothelimitedslotsofyourworkingmemoryasyouconcentrate.

Incontrast,long-termmemorymightbethoughtofasastoragewarehouse.Onceitemsareinthere,theygenerallystayput.Thewarehouseislarge,withroomforbillionsofitems,anditcanbeeasyforstoredparcelstogetburiedsodeeplythatit’sdifficulttoretrievethem.Researchhasshownthatwhenyourbrainfirstputsanitemofinformationinlong-termmemory,youneedtorevisititafewtimestoincreasethechancesyou’lllaterbeabletofinditwhenyouneedit.21(Techietypessometimesequateshort-termmemorytorandom-accessmemory[RAM],andlong-termmemorytoharddrivespace.)

Long-termmemoryisimportantforlearningmathandsciencebecauseitiswhereyoustorethefundamentalconceptsandtechniquesthatyouneedtouseinproblemsolving.Ittakestimetomoveinformationfromworkingmemorytolong-termmemory.Tohelpwiththisprocess,useatechniquecalledspacedrepetition.Asyoumayhaveguessed,thistechniqueinvolvesrepeatingwhatyouaretryingtoretain,likeanewvocabularywordoranewproblem-solvingtechnique,butspacingthisrepetitionoutoveranumberofdays.

Puttingadaybetweenboutsofrepetition—extendingyourpracticeoveranumberofdays—doesmakeadifference.Researchhasshownthatifyoutrytogluethingsintoyourmemorybyrepeatingsomethingtwentytimesinoneevening,forexample,itwon’tsticknearlyaswellasitwillifyoupracticeitthesamenumberoftimesoverseveraldaysorweeks.22Thisissimilartobuildingthebrickwallwesawearlier.Ifyoudon’tleavetimeforthemortartodry(timeforthesynapticconnectionstoformandstrengthen),youwon’thaveaverygoodstructure.

NOWYOUTRY!

Let YourMindWorkintheBackground

Thenexttimeyouaretacklingatoughproblem,workonitforafewminutes.Whenyougetstuck,moveontoanotherproblem.Yourdiffusemodecancontinueworkingonthetougherprobleminthebackground.Whenyoulaterreturntothetougherproblem,youwilloftenbepleasantlysurprisedbytheprogressyou’vemade.

ADVICEONSLEEPING

“Manypeoplewilltellyouthattheycan’tnap.TheonethingIlearnedfromasingleyogaclassItookmanyyearsagowastoslowdownmybreathing.Ijustkeepbreathingslowlyinandoutanddon’tthinkImustfallasleep.Instead,Ithinkthingslike,Sleepytime!andjustfocusonmybreathing.Ialsomakesureit’sdarkintheroom,orIcovermyeyeswithoneofthoseairplanesleepmasks.Also,Isetmyphonealarmfortwenty-oneminutesbecauseturningashortpowernapintoalongersleepcanleaveyougroggy.Thisamountoftimegivesmewhat’sbasicallyacognitivereboot.”

—AmyAlkon,syndicatedcolumnistandcatnapqueen

TheImportanceofSleepinLearning

Youmaybesurprisedtolearnthatsimplybeingawakecreatestoxicproductsinyourbrain.Duringsleep,yourcellsshrink,causingastrikingincreaseinthespacebetweenyourcells.Thisisequivalenttoturningonafaucet—itallowsfluidtowashpastandpushthetoxinsout.23Thisnightlyhousecleaningispartofwhatkeepsyourbrainhealthy.Whenyougettoolittlesleep,thebuildupofthesetoxicproductsisbelievedtoexplainwhyyoucan’tthinkveryclearly.(ToolittlesleepisaffiliatedwithconditionsrangingfromAlzheimer ’stodepression—prolongedsleeplessnessislethal.)

Studieshaveshownthatsleepisavitalpartofmemoryandlearning.24Partofwhatthisspecialsleep-timetidyingdoesiserasetrivialaspectsofmemoriesandsimultaneouslystrengthenareasofimportance.Duringsleep,yourbrainalsorehearsessomeofthetougherpartsofwhateveryouaretryingtolearn—goingoverandoverneuralpatternstodeepenandstrengthenthem.25

Finally,sleephasbeenshowntomakearemarkabledifferenceinpeople’sabilitytofigureoutdifficultproblemsandtofindmeaningandunderstandinginwhattheyarelearning.It’sasifthecompletedeactivationoftheconscious“you”intheprefrontalcortexhelpsotherareasofthebrainstarttalkingmoreeasilytooneanother,allowingthemtoputtogethertheneuralsolutiontoyourproblemasyousleep.26(Ofcourse,youmustplanttheseedforyourdiffusemodebyfirstdoingfocused-modework.)Itseemsthatifyougooverthematerialrightbeforetakinganaporgoingtosleepfortheevening,youhaveanincreasedchanceofdreamingaboutit.Ifyougoevenfurtherandsetitinmindthatyouwanttodreamaboutthematerial,itseemstoimproveyourchancesofdreamingaboutitstillfurther.27Dreamingaboutwhatyouarestudyingcansubstantiallyenhanceyourabilitytounderstand—itsomehowconsolidatesyourmemoriesintoeasier-to-graspchunks.28

Ifyou’retired,it’softenbesttojustgotosleepandgetupalittleearlierthenextday,soyourreadingisdonewithabetter-restedbrain.Experiencedlearnerswillattesttothefactthatreadingforonehourwithawell-restedbrainisbetterthanreadingforthreehourswithatiredbrain.Asleep-deprivedbrainsimplycan’tmaketheusualconnectionsyoumakeduringnormalthinkingprocesses.Goingwithoutsleepthenightbeforeanexaminationcanmeanthatevenifyouareperfectlyprepared,yourmindissimplyunabletofunctionproperly,soyoudopoorlyonthetest.

AMETHODFORMANYDISCIPLINES

Focusedanddiffuseapproachesarevaluableforallsortsoffieldsanddisciplines,notjustmathandscience.AsPaulSchwalbe,aseniormajoringinEnglish,notes:“IfIhavetroubleworkingonaproblem,Iliedowninmybedwithanopennotebookandpenandjustwriteout

thoughtsabouttheproblemasIfallasleep,aswellassometimesrightafterwakingup.SomeofwhatIwritemakesnosense,butsometimesIgainatotallynewwayoflookingatmyproblem.”

SUMMINGITUP

Usethefocusedmodetofirststartgrapplingwithconceptsandproblemsinmathandscience.Afteryou’vedoneyourfirsthardfocusedwork,allowthediffusemodetotakeover.Relaxanddosomethingdifferent!

Whenfrustrationarises,it’stimetoswitchyourattentiontoallowthediffusemodetobeginworkinginthebackground.It’sbesttoworkatmathandscienceinsmalldoses—alittleeveryday.Thisgivesboththefocusedanddiffusemodesthetimetheyneedtodotheirthingsoyoucanunderstandwhatyouarelearning.That’showsolidneuralstructuresarebuilt.Ifprocrastinationisanissue,trysettingatimerfortwenty-fiveminutesandfocusingintentlyonyourtaskwithoutallowingyourselftobedrawnasidebytextmessages,websurfing,orotherattractivedistractions.Therearetwomajormemorysystems:

Workingmemory—likeajugglerwhocankeeponlyfouritemsintheair.Long-termmemory—likeastoragewarehousethatcanholdlargeamountsofmaterial,butneedstoberevisitedoccasionallytokeepthememoriesaccessible.

Spacedrepetitionhelpsmoveitemsfromworkingmemorytolong-termmemory.Sleepisacriticalpartofthelearningprocess.Ithelpsyou:

Maketheneuralconnectionsneededfornormalthinkingprocesses—whichiswhysleepthenightbeforeatestissoimportant.Figureouttoughproblemsandfindmeaninginwhatyouarelearning.Strengthenandrehearsetheimportantpartsofwhatyouarelearningandpruneawaytrivialities.

PAUSEANDRECALL

Get upandtakealit t lebreak—get aglassofwaterorsnack,orpretendyou’reanelect ronandorbit anearbytable.Asyoumove,checkyourrecallofthemainideasofthischapter.

ENHANCEYOURLEARNING

1.Namesomeactivitiesyouwouldfindhelpfulforswitchingfromfocusedtodiffusemode.

2.Sometimesyoucanfeelcertainyouhaveexplorednewapproachestoanalyzingaproblem,whenyouactuallyhaven’t.Whatcanyoudotobecomemoreactivelyawareofyourthinkingprocessestohelpkeepyourselfopentootherpossibilities?Shouldyoualwayskeepyourselfopentonewpossibilities?

3.Whyisitimportanttouseself-controltomakeyourselfstopdoingsomething?Canyouthinkoftimesoutsidestudyingandacademicswhenthisskillmightalsobeimportant?

4.Whenyouarelearningnewconcepts,youwanttoreviewthematerialwithinadaysothattheinitialchangesyoumadeinyourbraindon’tfadeaway.Butyourmindoftenbecomespreoccupiedwithothermatters—it’seasytoletseveraldaysormorepassbeforeyougetaroundtolookingatthematerial.Whatkindofactionplancouldyoudeveloptoensurethatyoureviewimportantnewmaterialinatimelyfashion?

NEUROPSYCHOLOGISTROBERTBILDER’SADVICEONCREATIVITY

RobertBilderjustdoingitinMakapu’u,Hawaii

PsychiatryprofessorRobertBilderisthedirectorofUCLA’sTennenbaumCenterfortheBiologyofCreativityandleadsthe“MindWell”initiativetoenhancethecreativeachievementandpsychologicalwell-beingofstudents,staff,andfacultyatUCLA.Researchonthebiologyofcreativitysuggestsseveralingredientsthatweallcanbakeintoourpersonalrecipesforsuccess.

NumberoneistheNikefactor:Justdoit!

Creativityisanumbersgame:Thebestpredictorofhowmanycreativeworksweproduceinourlifetimeis...thenumberofworksweproduce.Isometimesfinditexcruciatingtopullthetriggerandexposemyworktootherpeople,buteverytimeIdo,itturnsoutforthebest.Dealingwithfear:AmotivationalposterIreceivedaftergivingatalkatFacebookheadquartersreads:“Whatwouldyoudoifyouweren’tafraid?”Itrytolookatthisdaily,andIaimtodosomethingfearlesseveryday.Whatareyouafraidof?Don’tletitstopyou!Redoscomewiththeterritory:Ifyoudon’tlikethewayitturnedout—doitagain!Criticismmakesusbetter:Byexposingourworktoothers,andbyexternalizingitsowecaninspectitourselves,wegainuniqueperspectiveandinsightanddevelopnewandimprovedplansforthenextversion.Bewillingtobedisagreeable.Thereisanegativecorrelationbetweenthelevelofcreativityand“agreeableness,”sothosewhoarethemostdisagreeabletendtobemostcreative.LookingbackatthefewtimeswhenIfoundsomethingnovel,itwasbecauseIchallengedtheexistinganswers.SoIbelievethecreativewayisadvancedwheneverwestripaproblembacktoitsrootsandquestionourownassumptions(alongwithassumptions

suggestedbyothers);thenrepeat!

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chunkingandavoidingillusionsofcompetence:

TheKeystoBecomingan“EquationWhisperer”

olomonShereshevskyfirstcametohisboss’sattentionbecausehewaslazy.Orsohisbossthought.

Solomonwasajournalist.Atthattime,inthemid-1920sintheSovietUnion,beingajournalistmeantreportingwhatyouweretold,nomore,noless.Dailyassignmentsweregivenout—detailingwhomtosee,atwhataddress,andtoobtainwhatinformation.Theeditorinchargebegantonoticethateveryonetooknotes.Everyone,thatis,exceptSolomonShereshevsky.Curious,theeditoraskedSolomonwhatwasgoingon.

Solomonwassurprised—whyshouldhetakenotes,heasked,whenhecouldrememberwhateverheheard?Withthat,Solomonrepeatedpartofthemorning’slecture,wordforword.WhatSolomonfoundsurprisingwasthathethoughteveryonehadamemorylikehis.Perfect.Indelible.1

Wouldn’tyoulovetohavethegiftofsuchamemory?Actually,youprobablywouldn’t.Becausehand-in-handwithhisextraordinarymemory,Solomon

hadaproblem.Inthischapter,we’llbetalkingaboutpreciselywhatthatproblemis—involvinghowfocuslinkstobothunderstandingandmemory.

WhatHappensWhenYouFocusYourAttention?

Welearnedinthelastchapteraboutthatirritatingsituationwhenyoubecomestuckinonewayoflookingataproblemandcan’tstepbacktoseeeasier,betterways—Einstellung.Focusedattention,inotherwords,canoftenhelpsolveproblems,butitcanalsocreateproblemsbyblockingourabilitytoseenewsolutions.

Whenyouturnyourattentiontosomething,yourattentionaloctopusstretchesitsneuraltentaclestoconnectdifferentpartsofthebrain.Areyoufocusingonashape?Ifso,onetentacleofconsciousnessreachesfromthethalamusbacktowardtheoccipitallobe,evenasanothertentaclereachestowardthewrinkledsurfaceofthecortex.Theresult?Awhisperedsenseofroundness.

Areyoufocusinginsteadoncolor?Theattentionaltentacleintheoccipitallobeshiftsslightlyand

asenseofgreenarises.Moretentacleconnections.Youconcludethatyouarelookingataparticulartypeofapple—a

GrannySmith.Yum!Focusingyourattentiontoconnectpartsofthebrainisanimportantpartofthefocusedmodeof

learning.Interestingly,whenyouarestressed,yourattentionaloctopusbeginstolosetheabilitytomakesomeofthoseconnections.Thisiswhyyourbraindoesn’tseemtoworkrightwhenyou’reangry,stressed,orafraid.2

Let’ssayyouwanttolearnhowtospeakSpanish.Ifyou’reachildhangingaroundaSpanish-speakinghousehold,learningSpanishisasnaturalasbreathing.Yourmothersays“mama,”andyouparrot“mama”backtoher.Yourneuronsfireandwiretogetherinashimmeringmentalloop,cementingtherelationshipinyourmindbetweenthesoundmamaandyourmother ’ssmilingface.Thatscintillatingneuralloopisonememorytrace—connected,ofcourse,tomanyotherrelatedmemorytraces.

Theoctopusofyourfocusedattention(left)reachesoutthroughthefourslotsofyourworkingmemorytodeliberatelyconnecttheneuralbumpersofyourtightlyfocusedbrain.Thediffusemode(right)hasitsbumpersspreadfartherapart.Thismodeconsistsofawildandcrazyhodgepodgeofpotentialconnections.

Thebestlanguageprograms—suchasthoseattheDefenseLanguageInstitute,whereIlearnedRussian—incorporatestructuredpracticethatincludesplentyofrepetitionandrote,focused-modelearningofthelanguage,alongwithmorediffuse-likefreespeechwithnativespeakers.ThegoalistoembedthebasicwordsandpatternssoyoucanspeakasfreelyandcreativelyinyournewlanguageasyoudoinEnglish.3

Focusedpracticeandrepetition—thecreationofmemorytraces—arealsoattheheartofanimpeccablyplayedgolfstroke,amasterchef’spracticedflipofanomelet,orabasketballfreethrow.Indance,it’salongwayfromatoddler ’sclumsypirouettetothechoreographedgraceofa

professionaldancer.Butthatpathtoexpertiseisbuiltbitbybit.Smallmemorizedfreespins,heelturns,andkicksbecomeincorporatedintolarger,morecreativeinterpretations.

Theleftimagesymbolizesthecompactconnectionswhenonechunkofknowledgeisformed—neuronsthatfiretogetherwiretogether.Theimageontherightshowsthesamepatterninyourmind’ssymbolicpinballmachine.Suchamemorytraceiseasytorecallwhenyouneedit.

WhatIsaChunk?Solomon’sChunkingProblem

SolomonShereshevsky’sextraordinarymemorycamewithasurprisingdrawback.Hisindividualmemorytraceswereeachsocolorfulandemotional—sorichwithconnections—thattheyinterferedwithhisabilitytoputthosetracestogetherandcreateconceptualchunks.Hecouldn’tseetheforest,inotherwords,becausehisimageryofeachoftheindividualtreeswassovivid.

Chunksarepiecesofinformationthatareboundtogetherthroughmeaning.Youcantakethelettersp,o,andpandbindthemintooneconceptual,easy-to-rememberchunk,thewordpop.It’slikeconvertingacumbersomecomputerfileintoa.zipfile.Underneaththatsimplepopchunkisasymphonyofneuronsthathavelearnedtotrillintunewithoneanother.Thecomplexneuralactivitythattiestogetheroursimplifying,abstractchunksofthought—whetherthosethoughtspertaintoacronyms,ideas,orconcepts—arethebasisofmuchofscience,literature,andart.

Let’stakeanexample.Intheearly1900s,GermanresearcherAlfredWegenerputtogetherhistheoryofcontinentaldrift.AsWegeneranalyzedmapsandthoughtabouttheinformationhe’dgleanedfromhisstudiesandexploration,herealizedthatthedifferentlandmassesfittogetherlikepuzzlepieces.Thesimilarityofrocksandfossilsbetweenthelandmassesreinforcedthefit.OnceWegenerputthecluestogether,itwasclearthatallthecontinentshadonce,verylongago,beenjoinedtogetherinasinglelandmass.Overtime,themasshadbrokenupandthepieceshaddriftedaparttoformthecontinentsseparatedbyoceansweseetoday.

Continentaldrift!Wow—whatagreatdiscovery!ButifSolomonShereshevskyhadreadthissamestoryaboutthediscoveryofcontinentaldrift,he

wouldn’thavegottenthepoint.Eventhoughhewouldhavebeenabletorepeateveryindividualwordinthestory,theconceptofcontinentaldriftwouldhavebeenverydifficultforhimtograsp,sincehewasunabletolinkhisindividualmemorytracestogethertocreateconceptualchunks.

Asitturnsout,oneofthefirststepstowardgainingexpertiseinmathandscienceistocreateconceptualchunks—mentalleapsthatuniteseparatebitsofinformationthroughmeaning.4Chunkingtheinformationyoudealwithhelpsyourbrainrunmoreefficiently.Onceyouchunkanideaorconcept,youdon’tneedtorememberallthelittleunderlyingdetails;you’vegotthemainidea—thechunk—andthat’senough.It’slikegettingdressedinthemorning.Usuallyyoujustthinkonesimplethought—I’llgetdressed.Butit’samazingwhenyourealizethecomplexswirlofunderlyingactivitiesthattakeplacewiththatonesimplechunkofathought.

Whenyouarestudyingmathandscience,then,howdoyouformachunk?

BasicStepstoFormingaChunk

Chunksrelatedtodifferentconceptsandprocedurescanbemoldedinmanydifferentways.It’softenquiteeasy.Youformedasimplechunk,forexample,whenyougraspedtheideaofcontinentaldrift.Butsincethisisabookabouthowtolearnmathandscienceingeneralratherthangeologyinparticular,we’regoingtotakeasourinitial,illustrativechunktheabilitytounderstandandworkacertaintypeofmathorscienceproblem.

Whenyouarelearningnewmathandsciencematerial,youarealmostalwaysgivensampleproblemswithworked-outsolutions.Thisisbecause,whenyouarefirsttryingtounderstandhowtoworkaproblem,youhaveaheavycognitiveload—soithelpstostartoutwithafullyworked-throughexample.It’slikeusingaGPSunitwhenyouaredrivingonunfamiliarroadsinthemiddleofthenight.Mostofthedetailsintheworked-outsolutionarerightthere,andyourtaskissimplytofigureoutwhythestepsaretakenthewaytheyare.Thatcanhelpyouseethekeyfeaturesandunderlyingprinciplesofaproblem.

Someinstructorsdonotliketogivestudentsextraworked-outproblemsoroldtests,astheythinkitmakesmatterstooeasy.Butthereisbountifulevidencethathavingthesekindsofresourcesavailablehelpsstudentslearnmuchmoredeeply.5Theoneconcernaboutusingworked-outexamplestoformchunksisthatitcanbealltooeasytofocustoomuchonwhyanindividualstepworksandnotontheconnectionbetweensteps—thatis,onwhythisparticularstepisthenextthingyoushoulddo.SokeepinmindthatI’mnottalkingaboutacookie-cutter“justdoasyou’retold”mindlessapproachwhenfollowingaworked-outsolution.It’smorelikeusingaguidetohelpyouwhentravelingtoanewplace.Payattentiontowhat’sgoingonaroundyouwhenyou’rewiththeguide,andsoonyou’llfindyourselfabletogetthereonyourown.Youwillevenbegintofigureoutnewwaysofgettingtherethattheguidedidn’tshowyou.

Whenyoufirstlookatabrand-newconceptinscienceormath,itsometimesdoesn’tmakemuchsense,asshownbythepuzzlepiecesaboveontheleft.Justmemorizingafact(center)withoutunderstandingorcontextdoesn’thelpyouunderstandwhat’sreallygoingon,orhowtheconceptfitstogetherwiththeotherconceptsyouarelearning—noticetherearenointerlockingpuzzleedgesonthepiecetohelpyoufitintootherpieces.Chunking(right)isthementalleapthathelpsyouunitebitsofinformationtogetherthroughmeaning.Thenewlogicalwholemakesthechunkeasiertoremember,andalsomakesiteasiertofitthechunkintothelargerpictureofwhatyouarelearning.

1.Thefirststepinchunking,then,istosimplyfocusyourattentionontheinformationyouwanttochunk.6Ifyouhavethetelevisiongoinginthebackground,oryou’relookingupeveryfewminutestocheckoransweryourphoneorcomputermessages,itmeansthatyou’regoingtohavedifficultymakingachunk,becauseyourbrainisnotreallyfocusingonthechunking.Whenyoufirstbegintolearnsomething,youaremakingnewneuralpatternsandconnectingthemwithpreexistingpatternsthatarespreadthroughmanyareasofthebrain.7Youroctopustentaclescan’tmakeconnectionsverywellifsomeofthemareoffonotherthoughts.

2.Thesecondstepinchunkingistounderstandthebasicideayouaretryingtochunk,whetheritisunderstandingaconceptsuchascontinentaldrift,theideathatforceisproportionaltomass,theeconomicprincipleofsupplyanddemand,oraparticulartypeofmathproblem.Althoughthisstepofbasicunderstanding—synthesizingthegistofwhat’simportant—wasdifficultforSolomonShereshevsky,moststudentsfigureoutthesemainideasnaturally.Oratleast,theycangraspthoseideasiftheyallowthefocusedanddiffusemodesofthinkingtotaketurnsinhelpingthemfigureoutwhat’sgoingon.

Understandingislikeasupergluethathelpsholdtheunderlyingmemorytracestogether.Itcreatesbroad,encompassingtracesthatlinktomanymemorytraces.8Canyoucreateachunkifyoudon’tunderstand?Yes,butit’sauselesschunkthatwon’tfitinwithothermaterialyouarelearning.

Thatsaid,it’simportanttorealizethatjustunderstandinghowaproblemwassolveddoesnotnecessarilycreateachunkthatyoucaneasilycalltomindlater.Donotconfusethe“aha!”ofabreakthroughinunderstandingwithsolidexpertise!(That’spartofwhyyoucangraspanideawhenateacherpresentsitinclass,butifyoudon’treviewitfairlysoonafteryou’vefirstlearnedit,itcanseemincomprehensiblewhenitcomestimetoprepareforatest.)Closingthebookandtestingyourselfonhowtosolvetheproblemswillalsospeedup

yourlearningatthisstage.

3.Thethirdsteptochunkingisgainingcontextsoyouseenotjusthow,butalsowhentousethischunk.Contextmeansgoingbeyondtheinitialproblemandseeingmorebroadly,repeatingandpracticingwithbothrelatedandunrelatedproblemssoyouseenotonlywhentousethechunk,butwhennottouseit.Thishelpsyouseehowyournewlyformedchunkfitsintothebiggerpicture.Inotherwords,youmayhaveatoolinyourstrategyorproblem-solvingtoolbox,butifyoudon’tknowwhentousethattool,it’snotgoingtodoyoualotofgood.Ultimately,practicehelpsyoubroadenthenetworksofneuronsconnectedtoyourchunk,ensuringthatitisnotonlyfirm,butalsoaccessiblefrommanydifferentpaths.

Therearechunksrelatedtobothconceptsandproceduresthatreinforceoneanother.Solvingalotofmathproblemsprovidesanopportunitytolearnwhytheprocedureworksthewayitdoesorwhyitworksatall.Understandingtheunderlyingconceptmakesiteasiertodetecterrorswhenyoumakethem.(Trustme,youwillmakeerrors,andthat’sagoodthing.)Italsomakesitmucheasiertoapplyyourknowledgetonovelproblems,aphenomenoncalledtransfer.We’lltalkmoreabouttransferlater.

Asyoucanseefromthefollowing“top-down,bottom-up”illustration,learningtakesplaceintwoways.Thereisabottom-upchunkingprocesswherepracticeandrepetitioncanhelpyoubothbuildandstrengtheneachchunk,soyoucaneasilygainaccesstoitwhenneeded.Andthereisatop-down“bigpicture”processthatallowsyoutoseewherewhatyouarelearningfitsin.9Bothprocessesarevitalingainingmasteryoverthematerial.Contextiswherebottom-upandtop-downlearningmeet.Toclarifyhere—chunkingmayinvolveyourlearninghowtouseacertainproblem-solvingtechnique.Contextmeanslearningwhentousethattechniqueinsteadofsomeothertechnique.

Thosearetheessentialstepstomakingachunkandfittingthatchunkintoagreaterconceptualoverviewofwhatyouarelearning.

Butthere’smore.

Bothtop-down,big-picturelearning,andbottom-upchunkingareimportantinbecominganexpertinmathandscience.

NOWILAYMEDOWNTOSLEEP

“Itellmystudentsthatinternalizingtheaccountingfundamentalsislikeinternalizinghowtotypeonakeyboard.Infact,asIwritethismyself,I’mnotthinkingoftheactoftyping,butofformulatingmythoughts—thetypingcomesnaturally.MymantraattheendofeachclassistotellstudentstolookattheDebitandCreditRulesaswellastheAccountingEquationjustbeforetheytuckthemselvesinatnight.Letthosebethelastthingstheyrepeattothemselvesbeforefallingasleep.Well,exceptmeditationorprayers,ofcourse!”

—DebraGassnerDragone,AccountingInstructor,UniversityofDelaware

Skimmingthroughachapterorlisteningtoaverywell-organizedlecturecanallowyoutogainasenseofthebigpicture.Thiscanhelpyouknowwheretoputthechunksyouareconstructing.Learnthemajorconceptsorpointsfirst—theseareoftenthekeypartsofagoodinstructororbookchapter’soutline,flowcharts,tables,orconceptmaps.Onceyouhavethisdone,fillinthedetails.Evenifafewofthepuzzlepiecesaremissingattheendofyourstudies,youcanstillseethebigpicture.

IllusionsofCompetenceandtheImportanceofRecall

Attemptingtorecallthematerialyouaretryingtolearn—retrievalpractice—isfarmoreeffectivethansimplyrereadingthematerial.10PsychologistJeffreyKarpickeandhiscolleagueshaveshownthatmanystudentsexperienceillusionsofcompetencewhentheyarestudying.Moststudents,Karpickefound,“repeatedlyreadtheirnotesortextbook(despitethelimitedbenefitsofthisstrategy),butrelativelyfewengageinself-testingorretrievalpracticewhilestudying.”11Whenyouhavethebook(orGoogle!)openrightinfrontofyou,itprovidestheillusionthatthematerialisalso

inyourbrain.Butit’snot.Becauseitcanbeeasiertolookatthebookinsteadofrecalling,studentspersistintheirillusion—studyinginafarlessproductiveway.

This,indeed,iswhyjustwantingtolearnthematerial,andspendingalotoftimewithit,doesn’tguaranteeyou’llactuallylearnit.AsAlanBaddeley,arenownedpsychologistandexpertonmemory,notes:“Intentiontolearnishelpfulonlyifitleadstotheuseofgoodlearningstrategies.”12

Youmaybesurprisedtolearnthathighlightingandunderliningmustbedonecarefully—otherwisetheycanbenotonlyineffectivebutalsomisleading.It’sasifthemotionofyourhandcanfoolyouintothinkingyou’veplacedtheconceptinyourbrain.Whenmarkingupthetext,trainyourselftolookformainideasbeforemakinganymarks,andkeepyourtextmarkingstoaminimum—onesentenceorlessperparagraph.13Wordsornotesinamarginthatsynthesizekeyconceptsareagoodidea.14

Usingrecall—mentalretrievalofthekeyideas—ratherthanpassiverereadingwillmakeyourstudytimemorefocusedandeffective.Theonlytimerereadingtextseemstobeeffectiveisifyoulettimepassbetweenrereadingssothatitbecomesmoreofanexerciseinspacedrepetition.15

Alongthesesamelines,alwaysworkthroughhomeworkproblemsinmathandscienceonyourown.Sometextbooksincludesolutionsatthebackofthebook,butyoushouldlookattheseonlytocheckyouranswer.Thiswillhelpensurethatthematerialismoredeeplyrootedinyourmindandmakeitmuchmoreaccessiblewhenyoureallyneedit.Thisiswhyinstructorsplacesomuchemphasisonshowingyourworkandgivingyourreasoningontestsandhomeworkproblems.Doingsoforcesyoutothinkyourwaythroughaproblemandprovidesaself-testofyourunderstanding.Thisadditionalinformationaboutyourthinkingalsogivesgradersabetteropportunitytoprovideusefulfeedback.

Youdon’twanttowaittoolongfortherecallpractice,sothatyouhavetostartthereinforcementoftheconceptfromscratcheverytime.Trytotouchagainonsomethingyou’relearningwithinaday,especiallyifit’snewandratherchallenging.Thisiswhymanyprofessorsrecommendthat,ifatallpossible,yourewriteyournotesduringtheeveningafteralecture.Thishelpstosolidifynewlyformingchunksandrevealstheholesinyourunderstandingthatprofessorsjustlovetotargetontests.Knowingwheretheholesare,ofcourse,isthefirststeptowardgettingthemfilledin.

Onceyou’vegotsomethingdown,youcanexpandthetimebetween“upkeep”repetitionstoweeksormonths—andeventuallyitcanbecomeclosetopermanent.(ReturningtoRussiaonavisit,forexample,Ifoundmyselfannoyedbyanunscrupuloustaxidriver.Tomyamazement,wordsIhadn’tthoughtorusedfortwenty-fiveyearspoppedfrommymouth—Ihadn’tevenbeenconsciouslyawareIknewthosewords!)

MAKEYOURKNOWLEDGESECONDNATURE

“Gettingaconceptinclassversusbeingabletoapplyittoagenuinephysicalproblemisthedifferencebetweenasimplestudentandafull-blownscientistorengineer.TheonlywayIknowoftomakethatjumpistoworkwiththeconceptuntilitbecomessecondnature,soyoucanbegintouseitlikeatool.”

—ThomasDay,ProfessorofAudioEngineering,McNallySmithCollegeofMusic

Later,we’lldiscussusefulappsandprogramsthatcanhelpwithlearning.Butfornow,it’sworthknowingthatwell-designedelectronicflashcardsystems,suchasAnki,havebuiltintothemthe

appropriatespacedrepetitiontimetooptimizetherateoflearningnewmaterial.Onewaytothinkaboutthistypeoflearningandrecallisshowninthefollowingworking-

memoryillustration.Aswementionedearlier,therearefourorsospotsinworkingmemory.

Whenyouarefirstchunkingaconcept,itspre-chunkedpartstakeupallyourworkingmemory,asshownontheleft.Asyoubegintochunktheconcept,youwillfeelitconnectingmoreeasilyandsmoothlyinyourmind,asshowninthecenter.Oncetheconceptischunked,asshownattheright,ittakesuponlyoneslotinworkingmemory.Itsimultaneouslybecomesonesmoothstrandthatiseasytofollowandusetomakenewconnections.Therestofyourworkingmemoryisleftclear.Thatdanglingstrandofchunkedmaterialhas,insomesense,increasedtheamountofinformationavailabletoyourworkingmemory,asiftheslotinworkingmemoryisahyperlinkthathasbeenconnectedtoabigwebpage.16

Whenyouarefirstlearninghowtosolveaproblem,yourentireworkingmemoryisinvolvedintheprocess,asshownbythemadtangleofconnectionsbetweenthefourslotsofworkingmemoryontheleft.Butonceyoubecomesmoothlyfamiliarwiththeconceptormethodyouarelearningandhaveitencapsulatedasasinglechunk,it’slikehavingonesmoothribbonofthought,asshownontheright.Thechunking,whichenlistslong-termmemory,freestherestofyourworkingmemorytoprocessotherinformation.Wheneveryouwant,youcanslipthatribbon(chunk)fromlong-termmemoryintoyourworkingmemoryandfollowalongthestrand,smoothlymakingnewconnections.

Nowyouunderstandwhyitiskeythatyouaretheonedoingtheproblemsolving,notwhoeverwrotethesolutionmanual.Ifyouworkaproblembyjustlookingatthesolution,andthentellyourself,“Ohyeah,Iseewhytheydidthat,”thenthesolutionisnotreallyyours—you’vedonealmostnothingtoknittheconceptsintoyourunderlyingneurocircuitry.Merelyglancingatthesolutiontoaproblemandthinkingyoutrulyknowityourselfisoneofthemostcommonillusionsofcompetenceinlearning.

NOWYOUTRY!

UnderstandingIllusionsofCompetence

Anagramsarerearrangementsofletterssothatonewordorphrasecanspellsomethingdifferent.Let’ssayyouhavethephrase“Me,radiumace.”Canyourearrangeittospellthelastnameofahonorificfamousphysicist?17Itmaytakeyouabitofthoughttodoit.Butifyousawthesolutionhereonthepage,yoursubsequent“aha!”feelingwouldmakeyouthinkthatyouranagram-solvingskillsarebetterthantheyactuallyare.Similarly,studentsoftenerroneouslybelievethattheyarelearningbysimplyrereadingmaterialthatisonthepagein

frontofthem.Theyhaveanillusionofcompetencebecausethesolutionisalreadythere.18Pickamathematicalorscientificconceptfromyournotesorfromapageinthebook.Readitover,thenlookaway

andseewhatyoucanrecall—workingtowardunderstandingwhatyouarerecallingatthesametime.Thenglanceback,rereadtheconcept,andtryitagain.Attheendofthisexercise,youwillprobablybesurprisedtoseehowmuchthissimplerecallexercisehelpedimprove

yourunderstandingoftheconcept.

Youmusthaveinformationpersistinginyourmemoryifyouaretomasterthematerialwellenoughtodowellontestsandthinkcreativelywithit.19Theabilitytocombinechunksinnovelwaysunderliesmuchofhistoricalinnovation.StevenJohnson,inhisbrilliantbookWhereGoodIdeasComeFrom,describesthe“slowhunch”—thegentle,years-longsimmeringoffocusedanddiffuseprocessesthathasresultedincreativebreakthroughsrangingfromDarwin’sevolutionarytheorytothecreationoftheWorldWideWeb.20Keytotheslowhunchissimplyhavingmentalaccesstoaspectsofanidea.Thatway,someaspectscantentativelyandrandomlycombinewithothersuntileventually,beautifulnoveltycanemerge.21BillGatesandotherindustryleaders,Johnsonnotes,setasideextended,weeklongreadingperiodssothattheycanholdmanyandvariedideasinmindduringonetime.Thisfosterstheirowninnovativethinkingbyallowingfresh-in-mind,not-yet-forgottenideastonetworkamongthemselves.(Animportantsidenotehereisthatakeydifferencebetweencreativescientistsandtechnicallycompetentbutnonimaginativeonesistheirbreadthofinterest.22)

Thebiggeryourchunkedmentallibrary,themoreeasilyyouwillbeabletosolveproblems.Also,asyougainmoreexperienceinchunking,youwillseethatthechunksyouareabletocreatearebigger—theribbonsarelonger.

Youmaythinktherearesomanyproblemsandconceptsjustinasinglechapterofthescienceormathsubjectyouarestudyingthatthere’snowaytodothemall!ThisiswheretheLawofSerendipitycomestoplay:LadyLuckfavorstheonewhotries.23

Justfocusonwhateversectionyouarestudying.You’llfindthatonceyouputthefirstproblemorconceptinyourlibrary,whateveritis,thenthesecondconceptwillgoinabitmoreeasily.Andthethirdmoreeasilystill.Notthatallofthisisasnap,butitdoesgeteasier.

Ifyouhavealibraryofconceptsandsolutionsinternalizedaschunkedpatterns,youcanmoreeasilyskiptotherightsolutiontoaproblembylisteningtothewhispersfromyourdiffusemode.Yourdiffusemodecanalsohelpyouconnecttwoormorechunkstogetherinnewwaystosolveunusualproblems.

Therearetwowaystosolveproblems—first,throughsequential,step-by-stepreasoning,andsecond,throughmoreholisticintuition.Sequentialthinking,whereeachsmallstepleadsdeliberatelytowardthesolution,involvesthefocusedmode.Intuition,ontheotherhand,oftenseemstorequireacreative,diffusemodelinkingofseveralseeminglydifferentfocusedmodethoughts.

Most difficult problemsaresolvedthroughintuit ion,becausetheymakealeapawayfromwhat youarefamiliarwith.24Keepinmindthatthediffusemode’ssemi-randomwayofmakingconnectionsmeansthatthesolutionsitprovideswithshouldbecarefullyverifiedusingthefocusedmode.Intuitiveinsightsaren’talwayscorrect!25

Inbuildingachunkedlibrary,youaretrainingyourbraintorecognizenotonlyaspecificproblem,butdifferenttypes˙andclassesofproblemssothatyoucanautomaticallyknowhowtoquicklysolvewhateveryouencounter.You’llstarttoseepatternsthatsimplifyproblemsolvingforyouandwillsoonfindthatdifferentsolutiontechniquesarelurkingattheedgeofyourmemory.Beforemidtermsorfinals,itiseasytobrushupandhavethesesolutionsatthementalready.

NOWYOUTRY!

What toDoIfYouCan’t GraspIt

Ifyoudon’tunderstandamethodpresentedinacourseyouaretaking,stopandworkbackward.GototheInternetanddiscoverwhofirstfiguredoutthemethodorsomeoftheearliestpeopletouseit.Trytounderstandhowthecreativeinventorarrivedattheideaandwhytheideaisused—youcanoftenfindasimpleexplanationthatgivesabasicsenseofwhyamethodisbeingtaughtandwhyyouwouldwanttouseit.

PracticeMakesPermanent

I’vealreadymentionedthatjustunderstandingwhat’sgoingonisnotusuallyenoughtocreateachunk.YoucangetasenseofwhatImeanbylookingatthe“brain”pictureshownonp.69.Thechunks(loops)shownarereallyjustextendedmemorytracesthathavearisenbecauseyouhaveknittogetheranunderstanding.Achunk,inotherwords,issimplyamorecomplexmemorytrace.Atthetopisafaintchunk.Thatchunkiswhatbeginstoformafteryou’veunderstoodaconceptorproblemandpracticedjustatimeortwo.Inthemiddle,thepatternisdarker.Thisisthestrongerneuralpatternthatresultsafteryou’vepracticedalittlemoreandseenthechunkinmorecontexts.Atthebottom,thechunkisverydark.You’venowgotasolidchunkthat’sfirmlyembeddedinlong-termmemory.

Solvingproblemsinmathandscienceislikeplayingapieceonthepiano.Themoreyoupractice,thefirmer,darker,andstrongeryourmentalpatternsbecome.

Incidentally,strengtheninganinitiallearningpatternwithinadayafteryoufirstbeginformingitisimportant.Withoutthestrengthening,thepatterncanquicklyfadeaway.Later,we’lltalkmoreabouttheimportanceofspacedrepetitioninlearning.Also,youcanreinforcea“wrong”processbydoingthesameproblemsoverandoverthewrongway.Thisiswhycheckingthingsissoimportant.Evengettingtherightanswercanoccasionallymisleadyouifyougetitbyusinganincorrectprocedure.

THEIMPORTANCEOFCHUNKING

“Mathematicsisamazinglycompressible:youmaystrugglealongtime,stepbystep,toworkthroughthesameprocessorideafromseveralapproaches.Butonceyoureallyunderstanditandhavethementalperspectivetoseeitasawhole,thereisoftenatremendousmentalcompression.Youcanfileitaway,recallitquicklyandcompletelywhenyouneedit,anduseitasjustonestepinsomeothermentalprocess.Theinsightthatgoeswiththiscompressionisoneoftherealjoysofmathematics.”26

—WilliamThurston,winneroftheFieldsMedal,thetopawardinmathematics

Thechallengewithrepetitionandpractice,whichliebehindthemind’screationofsolidchunks,isthatitcanbeboring.Worseyet,inthehandsofapoorinstructor,likemyoldmathteacher,Mr.Crotchety,practicecanbecomeanunrelentinginstrumentoftorture.Despiteitsoccasionalmisuse,however,it’scritical.Everybodyknowsyoucan’teffectivelylearnthechunkedpatternsofchess,language,music,dance—justaboutanythingworthwhile—withoutrepetition.Goodinstructorscanexplainwhythepracticeandrepetitionisworththetrouble.

Ultimately,bothbottom-upchunkingandtop-downbig-pictureapproachesarevitalifyouaretobecomeanexpertwiththematerial.Welovecreativityandtheideaofbeingabletolearnbyseeingthebigpicture.Butyoucan’tlearnmathematicsorsciencewithoutalsoincludingahealthydoseofpracticeandrepetitiontohelpyoubuildthechunksthatwillunderpinyourexpertise.27

ResearchpublishedinthejournalScienceprovidedsolidevidencealongtheselines.28Studentsstudiedascientifictextandthenpracticeditbyrecallingasmuchoftheinformationastheycould.Thentheyrestudiedthetextandrecalledit(thatis,triedtorememberthekeyideas)oncemore.

Theresults?Inthesameamountoftime,bysimplypracticingandrecallingthematerial,studentslearned

farmoreandatamuchdeeperlevelthantheydidusinganyotherapproach,includingsimplyrereadingthetextanumberoftimesordrawingconceptmapsthatsupposedlyenrichedtherelationshipsinthematerialsunderstudy.Thisimprovedlearningcomeswhetherstudentstakeaformaltestorjustinformallytestthemselves.

Thisreinforcesanideawe’vealludedtoalready.Whenweretrieveknowledge,we’renotbeingmindlessrobots—theretrievalprocessitselfenhancesdeeplearningandhelpsusbeginformingchunks.29Evenmoreofasurprisetoresearcherswasthatthestudentsthemselvespredictedthatsimplyreadingandrecallingthematerialswasn’tthebestwaytolearn.Theythoughtconceptmapping(drawingdiagramsthatshowtherelationshipbetweenconcepts)wouldbebest.Butifyoutrytobuildconnectionsbetweenchunksbeforethebasicchunksareembeddedinthebrain,itdoesn’tworkaswell.It’sliketryingtolearnadvancedstrategyinchessbeforeyouevenunderstandthebasicconceptsofhowthepiecesmove.30

Practicingmathandscienceproblemsandconceptsinavarietyofsituationshelpsyoubuildchunks—solidneuralpatternswithdeep,contextualrichness.31Thefactis,whenlearninganynew

skillordiscipline,youneedplentyofvariedpracticewithdifferentcontexts.Thishelpsbuildtheneuralpatternsyouneedtomakethenewskillacomfortablepartofyourwayofthinking.

KEEPYOURLEARNINGATTHET IPOFYOURTONGUE

“Bychance,Ihaveusedmanyofthelearningtechniquesdescribedinthisbook.AsanundergraduateItookphysicalchemistryandbecamefascinatedwiththederivations.Igotintoahabitofdoingeveryprobleminthebook.Asaresult,Ihard-wiredmybraintosolveproblems.BytheendofthesemesterIcouldlookataproblemandknowalmostimmediatelyhowtosolveit.Isuggestthisstrategytomysciencemajorsinparticular,butalsotothenonscientists.Ialsotalkabouttheneedtostudyeveryday,notnecessarilyforlongperiodsoftimebutjustenoughtokeepwhatyouarelearningatthetipofyourtongue.Iusetheexampleofbeingbilingual.WhenIgotoFrancetowork,myFrenchtakesafewdaystokickin,butthenitisfine.WhenIreturntotheStatesandastudentorcolleagueasksmesomethingonmyfirstorseconddayback,IhavetosearchfortheEnglishwords!Whenyoupracticeeverydaytheinformationisjustthere—youdonothavetosearchforit.”

—RobertR.Gamache,AssociateVicePresident,AcademicAffairs,StudentAffairs,andInternationalRelations,UniversityofMassachusetts,Lowell

RecallMaterialWhileOutsideYourUsualPlaceofStudy:TheValueofWalking

Doingsomethingphysicallyactiveisespeciallyhelpfulwhenyouhavetroublegraspingakeyidea.Asmentionedearlier,storiesaboundofinnovativescientificbreakthroughsthatoccurredwhenthepeoplewhomadethemwereoutwalking.32

Inaddition,recallingmaterialwhenyouareoutsideyourusualplaceofstudyhelpsyoustrengthenyourgraspofthematerialbyviewingitfromadifferentperspective.Peoplesometimeslosesubconsciouscueswhentheytakeatestinaroomthatlooksdifferentfromwheretheystudied.Bythinkingaboutthematerialwhileyouareinvariousphysicalenvironments,youbecomeindependentofcuesfromanyonelocation,whichhelpsyouavoidtheproblemofthetestroombeingdifferentfromwhereyouoriginallylearnedthematerial.33

InternalizingmathandscienceconceptscanbeeasierthanmemorizingalistofChinesevocabularywordsorguitarchords.Afterall,you’vegottheproblemtheretospeaktoyou,tellingyouwhatyouneedtodonext.Inthatsense,problemsolvinginmathandscienceislikedance.Indance,youcanfeelyourbodyhintingatthenextmove.

Differenttypesofproblemshavedifferentreviewtimeframesthatarespecifictoyourownlearningspeedandstyle.34Andofcourse,youhaveotherobligationsinyourlifebesideslearningoneparticulartopic.Youhavetoprioritizehowmuchyou’reabletodo,alsokeepinginmindthatyoumustschedulesometimeofftokeepyourdiffusemodeinplay.Howmuchinternalizingcanyoudoatastretch?Itdepends—everyoneisdifferent.But,here’stherealbeautyofinternalizingproblemsolutionsinmathandscience.Themoreyoudoit,theeasieritbecomes,andthemoreusefulitis.

ORGANIZE,CHUNK—ANDSUCCEED

“ThefirstthingIalwaysdowithstudentswhoarestrugglingisasktoseehowtheyareorganizingtheirnotesfromclassandreading.Weoftenspendmostofthefirstmeetinggoingoverwaystheycanorganizeorchunktheirinformation

ratherthanwithmyexplainingconcepts.Ihavethemcomebackthenextweekwiththeirmaterialalreadyorganized,andtheyareamazedathowmuchmoretheyretain.”

—JasonDechant,Ph.D.,CourseDirector,HealthPromotionandDevelopment,SchoolofNursing,UniversityofPittsburgh

Ifyoudon’tpracticewithyourgrowingchunks,itishardertoputtogetherthebigpicture—thepiecesaresimplytoofaint.

Interleaving—DoingaMixtureofDifferentKindsofProblems—versusOverlearning

Onelastimportanttipinbecominganequationwhispererisinterleaving.35Interleavingmeanspracticebydoingamixtureofdifferentkindsofproblemsrequiringdifferentstrategies.

Whenyouarelearninganewproblem-solvingapproach,eitherfromyourteacherorfromabook,youtendtolearnthenewtechniqueandthenpracticeitoverandoveragainduringthesamestudysession.Continuingthestudyorpracticeafteritiswellunderstoodiscalledoverlearning.Overlearningcanhaveitsplace—itcanhelpproduceanautomaticitythatisimportantwhenyouareexecutingaserveintennisorplayingaperfectpianoconcerto.Butbewaryofrepetitiveoverlearningduringasinglesessioninmathandsciencelearning—researchhasshownitcanbeawasteofvaluablelearningtime.36(Revisitingtheapproachmixedwithotherapproachesduringasubsequentstudysession,however,isjustfine.)

Insummary,then,onceyou’vegotthebasicideadownduringasession,continuingtohammerawayatitduringthesamesessiondoesn’tnecessarilystrengthenthekindsoflong-termmemoryconnectionsyouwanttohavestrengthened.Worseyet,focusingononetechniqueisalittlelikelearningcarpentrybyonlypracticingwithahammer.Afterawhile,youthinkyoucanfixanythingbyjustbashingit.37

Therealityis,masteringanewsubjectmeanslearningtoselectandusethepropertechniqueforaproblem.Theonlywaytolearnthatisbypracticingwithproblemsthatrequiredifferenttechniques.

Onceyouhavethebasicideaofatechniquedownduringyourstudysession(sortoflikelearningtorideabikewithtrainingwheels),startinterleavingyourpracticewithproblemsofdifferenttypes.38Sometimesthiscanbealittletoughtodo.Agivensectioninabook,forexample,isoftendevotedtoaspecifictechnique,sowhenyoufliptothatsection,youalreadyknowwhichtechniqueyou’regoingtouse.39Still,dowhatyoucantomixupyourlearning.Itcanhelptolookaheadatthemorevariedproblemsetsthataresometimesfoundattheendofchapters.Oryoucandeliberatelytrytomakeyourselfoccasionallypickoutwhysomeproblemscallforonetechniqueasopposedtoanother.Youwantyourbraintobecomeusedtotheideathatjustknowinghowtouseaparticularproblem-solvingtechniqueisn’tenough—youalsoneedtoknowwhentouseit.

Considercreatingindexcardswiththeproblemquestionononeside,andthequestionandsolutionstepsontheother.Thatwayyoucaneasilyshufflethecardsandbefacedwitharandomvarietyoftechniquesyoumustcalltomind.Whenyoufirstreviewthecards,youcansitatadeskortableandseehowmuchofthesolutionyoucanwriteonablanksheetofpaperwithoutpeekingatthebackofthecard.Later,whenmasteryismorecertain,youcanreviewyourcardsanywhere,evenwhileoutforawalk.Usetheinitialquestionasacuetobringtomindthestepsoftheresponse,andflipthecardoverifnecessarytoverifythatyou’vegottheproceduralstepsallinmind.Youarebasicallystrengtheninganewchunk.Anotherideaistoopenthebooktoarandomlychosenpageandworkaproblemwhile,asmuchaspossible,hidingfromvieweverythingbuttheproblem.

EMPHASIZEINTERLEAVINGINSTEADOFOVERLEARNING

PsychologistDougRohreroftheUniversityofSouthFloridahasdoneconsiderableresearchonoverlearningandinterleavinginmathandscience.Henotes:

“Manypeoplebelieveoverlearningmeansstudyingorpracticinguntilmasteryisachieved.However,intheresearchliterature,overlearningreferstoalearningstrategyinwhichastudentcontinuestostudyorpracticeimmediatelyaftersomecriterionhasbeenachieved.Anexamplemightbecorrectlysolvingacertainkindofmathproblemandthenimmediatelyworkingseveralmoreproblemsofthesamekind.Althoughworkingmoreproblemsofthesamekind(ratherthanfewer)oftenboostsscoresonasubsequenttest,doingtoomanyproblemsofthesamekindinimmediatesuccessionprovidesdiminishingreturns.“Intheclassroomandelsewhere,studentsshouldmaximizetheamounttheylearnperunittimespentstudyingor

practicing—thatis,theyshouldgetthemostbangforthebuck.Howcanstudentsdothis?Thescientificliteratureprovidesanunequivocalanswer:Ratherthandevotealongsessiontothestudyorpracticeofthesameskillorconceptsothatoverlearningoccurs,studentsshoulddividetheireffortacrossseveralshortersessions.Thisdoesn’tmeanthatlongstudysessionsarenecessarilyabadidea.Longsessionsarefineaslongasstudentsdon’tdevotetoomuchtimetoanyoneskillorconcept.Oncetheyunderstand‘X,’theyshouldmoveontosomethingelseandreturnto‘X’onanotherday.”40

It’sbesttowritetheinitialsolution,ordiagram,orconcept,outbyhand.There’sevidencethatwritingbyhandhelpsgettheideasintomindmoreeasilythanifyoutypetheanswer.41Morethanthat,it’softeneasiertowritesymbolicmateriallike∑orΩbyhandthantosearchoutthesymbolandtypeit(unlessyouusethesymbolsoftenenoughtomemorizethealtcodes).42Butifyouthenwanttophotographorscanthequestionandyourhandwrittensolutiontoloaditintoaflashcardprogramforyoursmartphoneorlaptop,thatwillworkjustfine.Beware—acommonillusionofcompetenceistocontinuepracticingatechniqueyouknow,simplybecauseit’seasyanditfeelsgoodtosuccessfullysolveproblems.Interleavingyourstudies—makingapointtoreviewforatest,forexample,byskippingaroundthroughproblemsinthedifferentchaptersandmaterials—cansometimesseemto

makeyourlearningmoredifficult.Butinreality,ithelpsyoulearnmoredeeply.

AVOIDMIMICKINGSOLUTIONS—PRACTICECHANGINGMENTALGEARS

“Whenstudentsdohomeworkassignments,theyoftenhavetenidenticalproblemsinarow.Afterthesecondorthirdproblem,theyarenolongerthinking;theyaremimickingwhattheydidonthepreviousproblem.Itellthemthat,whendoingthehomeworkfromsection9.4,afterdoingafewproblems,gobackanddoaproblemfromsection9.3.Doacouplemore9.4problems,andthendoonefromsection9.1.Thiswillgivethempracticeinmentallyshiftinggearsinthesamewaythey’llneedtoswitchgearsonthetest.“Ialsobelievetoomanystudentsdohomeworkjusttogetitdone.Theyfinishaproblem,checktheiranswerinthe

backofthetext,smile,andgoontothenextproblem.Isuggestthattheyinsertastepbetweenthesmileandgoingontothenextproblem—askingthemselvesthisquestion:HowwouldIknowhowtodotheproblemthiswayifIsawitonatestmixedtogetherwithotherproblemsandIdidn’tknowitwasfromthissectionofthetext?Studentsneedtothinkofeveryhomeworkproblemintermsoftestpreparationandnotaspartofatasktheyaretryingtocomplete.”

—MikeRosenthal,SeniorInstructorofMathematics,FloridaInternationalUniversity

SUMMINGITUP

Practicehelpsbuildstrongneuralpatterns—thatis,conceptualchunksofunderstanding.Practicegivesyouthementalfluidityandagilityyouneedfortests.Chunksarebestbuiltwith:

Focusedattention.Understandingofthebasicidea.Practicetohelpyougainbig-picturecontext.

Simplerecall—tryingtorememberthekeypointswithoutlookingatthepage—isoneofthebestwaystohelpthechunkingprocessalong.

Insomesense,recallhelpsbuildneuralhooksthatyoucanhangyourthinkingon.

ENHANCEYOURLEARNING

1.Howisachunkrelatedtoamemorytrace?

2.Thinkofatopicyouarepassionateabout.Describeachunkinvolvingthattopicthatwasatfirstdifficultforyoutograspbutnowseemseasy.

3.Whatisthedifferencebetweentop-downandbottom-upapproachestolearning?Isoneapproachpreferabletotheother?

4.Isunderstandingenoughtocreateachunk?Explainwhyorwhynot.

5.Whatisyourownmostcommonillusionofcompetenceinlearning?Whatstrategycanyouusetohelpavoidfallingforthisillusioninthefuture?

PAUSEANDRECALL

Next t imeyouarewithafamilymember,friend,orclassmate,relatetheessenceofwhat youhavebeenlearning,eitherfromthisbookorinregardtoaclassyouaretaking.Retellingwhateveryouarelearningabout not onlyhelpsfuelandshareyourownenthusiasm,but alsoclarifiesandcementstheideasinyourmind,soyou’llrememberthembet terintheweeksandmonthstocome.Evenifwhat youarestudyingisveryadvanced,simplifyingsoyoucanexplaintootherswhodonot shareyoureducat ionalbackgroundcanbesurprisinglyhelpfulinbuildingyourunderstanding.

OVERCOMINGTRAUMATICBRAININJURYANDLEARNINGTOLEARNWITHLIMITEDTIME—PAULKRUCHKO’SSTORY

PaulKruchkowithhiswifeanddaughter,whohavehelpedprovidethemotivationforhimtoreshapehislife.

“Igrewuppoor,withalotofdomesticturmoil.Ibarelygraduatedfromhighschool.Afterward,Ienlistedinthearmy,whereIwasdeployedasaninfantrymantoIraq.Myvehiclewashiteightoutofthetwelvetimesourplatoonwasambushedwithroadsidebombs.“Duringmytour,throughluckychance,Imetmywonderfulwife.Meetingherconvincedmetoleavetheserviceandstarta

family.TheproblemwasIdidn’tknowwhattodo.Worseyet,afterreturninghomeIstartedtohaveproblemswithconcentration,lackofcognition,andirritabilitythatIhadneverexperiencedbefore.SometimesIcouldbarelyfinishasentence.ItwasonlylaterthatIreadaboutsoldiersreturninghomefromIraqandAfghanistanhavingissueswithundiagnosedtraumaticbraininjury(TBI).“Ienrolledinacomputerandelectronicsengineeringtechnologyprogram.MyTBIwassevereenoughthatatfirstIeven

struggledtocomprehendfractions.“Butitwasablessingindisguise:Thelearningwasdoingsomethingtomybrain.Itwasasifthementalconcentration—

difficultthoughitwas—wasretoolingmymindandhelpingmybrainheal.Tome,thisprocessseemedanalogoustohowIwouldapplyphysicaleffortinthegym,andbloodwouldbeforcedintomymusclestobuildstrength.Intimemymindhealed—Igraduatedwithhighhonorsandgotajobasacivilianelectronicstechnician.“Idecidedtogobacktoschoolagainforanengineeringdegree.Mathematics—especiallycalculus—isfarmoreimportant

whenstudyingengineeringthanitiswhentrainingasahands-ontechnician.Atthispoint,mylackoffoundationofmathematicsfromtheearliestyearsofgradeschoolstartedtocatchupwithme.“BythistimeIwasmarried,anewfather,andworkingfull-time.NowthechallengeIfacedwasnolongerjustbasiccognition,

buttimemanagement.IhadonlyafewhourseachdaytolearnadvancedconceptsatafardeeperlevelthanIeverhadtobefore.Itwasonlyafterafewhardknocks(IearnedaDinmydifferentialequationsclass—ouch!)thatIstartedtoapproachlearninginamorestrategicway.

“Eachsemester,Igetacopyofthesyllabifrommyprofessorsandbeginreadingthetextbooksatleasttwotothreeweeksbeforethecoursesbegin.Itrytostayatleastachapteraheadoftheclass,althoughbythemiddleofthesemesterthisisoftenimpossible.Practiceinproblemsolving—buildingchunks—iskey.Overmylearningcareer,Igraduallydevelopedthefollowingrules,whichhaveallowedmetosatisfactorilycompletemycourses.Myobjectiveisagoodcareerthatwillsupportmyfamily—thesetechniquesarehelpingmegetthere.”

Paul’sTechniquesforLimitedStudyTime1.Read(but don’t yet solve)assignedhomeworkandpract iceexams/quizzes.WiththisinitialstepIprime

mymentalpumpforlearningnewconcepts—newchunks.

2.Reviewlecturenotes(attendeverylectureasmuchaspossible).Onehouroflectureisworthtwohoursreadingthebook.IlearnfarmoreefficientlyifIamfaithfulinattendinglecturesandtakingdetailednotes—notjuststaringatmywatchandwaitingforittobeover.Ireviewmynotesthefollowingdaywhilethesubjectsarestillfreshinmymind.I’vealsofoundthatthirtyminuteswithaprofessoraskingquestionsiseasilyworththreehoursreadingthebook.

3.Reworkexampleproblemspresentedinlecturenotes.Itneverhelpedmetopracticeproblemsgivenbyeithertheinstructororthetextbookthatdidn’thavesolutionstoprovidefeedback.WiththeexampleproblemsIalreadyhadastep-by-stepsolutionavailableifnecessary.Reworkinghelpssolidifychunks.Iusedifferent-coloredpenswhenIstudy:blue,green,red—notjustblack.Ifoundthatithelpsmefocusonreadingmynotesbetter;thingspopoutmore,insteadofblendingtogetherintoaconfusingcollageofinexplicablemathematicalchaosonthepage.

4.Workassignedhomeworkandpracticeexam/quizquestions.Thisbuilds“musclememory”chunksforthemindinsolvingcertaintypesofproblems.

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preventingprocrastination:

EnlistingYourHabits(“Zombies”)asHelpers

orcenturies,arsenicwasapopularchoiceforkillers.Asprinkleonyourmorningtoastwouldcauseyourpainfuldeathwithinaday.Soyoucanimaginetheshockattheforty-eighthmeeting

oftheGermanAssociationofArtsandSciencesin1875,whentwomensatinfrontoftheaudienceandblithelydownedmorethandoubleadeadlydoseofarsenic.Thenextdaythemenwerebackattheconference,smilingandhealthy.Analysisofthemen’surineshoweditwasnotrick.Themenhadindeedingestedthepoison.1

Howisitpossibletotakesomethingsobadforyouandstayalive—andevenlookhealthy?Theanswerhasanuncannyrelationshiptoprocrastination.Understandingsomethingofthe

cognitivepsychologyofprocrastination,justlikeunderstandingthechemistryofpoison,canhelpusdevelophealthypreventatives.

Inthisandthenextchapter,I’mgoingtoteachyouthelazyperson’sapproachtotacklingprocrastination.Thismeansyou’llbelearningaboutyourinnerzombies—theroutine,habitualresponsesyourbrainfallsintoasaresultofspecificcues.Thesezombieresponsesareoftenfocusedonmakingthehereandnowbetter.Asyou’llsee,youcantricksomeofthesezombiesintohelpingyoutofendoffprocrastinationwhenyouneedto(notallprocrastinationisbad).2Thenwe’llinterleaveachapterwhereyou’lldeepenyourchunkingskills,beforewereturnwithafinalchapterofwrap-upcoverageonprocrastinationthatprovidestips,tricks,andhandytechnologicaltools.

Firstthingsfirst.Unlikeprocrastination,whichiseasytofallinto,willpowerishardtocomebybecauseitusesalotofneuralresources.Thismeansthatthelastthingyouwanttodointacklingprocrastinationistogoaroundsprayingwillpoweronitlikeit’scheapairfreshener.Youshouldn’twastewillpoweronprocrastinationexceptwhenabsolutelynecessary!Bestofall,asyouwillsee,youdon’tneedto.

Poison.Zombies.Coulditgetanybetter?Ahyes—there’sexperimentation!Bwahhahhah—whatcouldbemorefun?

DISTRACTIONANDPROCRASTINATION

“Procrastinationisoneofourgeneration’sbiggestproblems.Wehavesomanydistractions.Iamalwaysthinking,‘BeforeIstartmyhomework,letmejustcheckmyFacebook,Twitter,Tumblr,ande-mail.’BeforeIevenrealizeit,Ihavewastedatleastanhour.EvenafterIfinallystartmyhomework,Ihavethosedistractingwebsitesopeninthe

background.“Ineedtofindawayjusttofocusonmystudyingandhomework.Ithinkitdependsalotonmyenvironmentandthe

time.Ishouldnotbewaitinguntilthelastminutetodoeverything.”

—Acalculusstudent

ProcrastinationandDiscomfort

Imaginehowyourcalfmuscleswouldscreamifyoupreparedforabigracebywaitingtillmidnightthenightbeforeyourfirstmarathontodoyourfirstpracticerun.Injustthesameway,youcan’tcompeteinmathandscienceifyoujustcramatthelastminute.

Formostpeople,learningmathandsciencedependsontwothings:briefstudysessionswheretheneural“bricks”arelaid,andtimeinbetweenforthementalmortartodry.Thismeansthatprocrastination,aterriblycommonproblemformanystudents,3isparticularlyimportantformathandsciencestudentstomaster.

Weprocrastinateaboutthingsthatmakeusfeeluncomfortable.4Medicalimagingstudieshaveshownthatmathphobes,forexample,appeartoavoidmathbecauseevenjustthinkingaboutitseemstohurt.Thepaincentersoftheirbrainslightupwhentheycontemplateworkingonmath.5

Butthere’ssomethingimportanttonote.Itwastheanticipationthatwaspainful.Whenthemathphobesactuallydidmath,thepaindisappeared.ProcrastinationexpertRitaEmmettexplains:“Thedreadofdoingataskusesupmoretimeandenergythandoingthetaskitself.”6

Avoidingsomethingpainfulseemssensible.Butsadly,thelong-termeffectsofhabitualavoidancecanbenasty.Youputoffstudyingmath,anditbecomesevenmorepainfultothinkaboutstudyingit.YoudelaypracticingfortheSATorACT,andonthecriticalexamday,youchokebecauseyouhaven’tlaidthefirmneuralfoundationsyouneedtofeelcomfortablewiththematerial.Youropportunityforscholarshipsevaporates.

Perhapsyou’dloveacareerinmathandscience,butyougiveupandsettleonadifferentpath.Youtellothersyoucouldn’thackthemath,whentherealitywasthatyouhadsimplyletprocrastinationgetthebestofyou.

Procrastinationisasingle,monumentallyimportant“keystone”badhabit.7Ahabit,inotherwords,thatinfluencesmanyimportantareasofyourlife.Changeit,andamyriadofotherpositivechangeswillgraduallybegintounfold.

Andthere’ssomethingmore—somethingcruciallyimportant.It’seasytofeeldistasteforsomethingyou’renotgoodat.Butthebetteryougetatsomething,themoreyou’llfindyouenjoyit.

HowtheBrainProcrastinates

Beepbeepbeep...It’stenA.M.onSaturday,andyouralarmclockpullsyoufromluscioussleep.Anhourlateryou’refinallyup,coffeeinhand,poisedoveryourbooksandyourlaptop.You’vebeenmeaningtoputinasoliddayofstudyingsoyoucanwrapupthatmathhomeworkthat’sdueonMonday.Youalsoplantogetastartonthehistoryessay,andtolookatthatconfusingchemistry

section.Youlookatyourmathtextbook.There’sasubtle,barelydetectableouch.Yourbrain’spain

centerslightupasyouanticipatelookingattheconfusinggraphsandtangleofstrangeverbiage.Youreallydon’twanttobedoingmathhomeworknow.Thethoughtofspendingthenextseveralhoursstudyingmath,asyou’dplanned,makestheideaofopeningthebookevenlesspleasant.

Youshiftyourfocusfromyourtextbooktoyourlaptop.Hmm,that’smorelikeit.Nopainfulfeelingsthere,justalittledollopofpleasureasyouflipopenthescreenandcheckyourmessages.LookatthatfunnypictureJessesent...

Twohourslater,youhaven’tevenstartedyourmathhomework.

Thisisatypicalprocrastinationpattern.Youthinkaboutsomethingyoudon’tparticularlylike,andthepaincentersofyourbrainlightup.Soyoushiftandnarrowyourfocusofattentiontosomethingmoreenjoyable.8Thiscausesyoutofeelbetter,atleasttemporarily.

Procrastinationislikeaddiction.Itofferstemporaryexcitementandrelieffromboringreality.It’seasytodeludeyourselfthatthemostprofitableuseofanygivenmomentissurfingthewebforinformationinsteadofreadingthetextbookordoingtheassignedproblems.Youstarttotellyourselfstories.Forexample,thatorganicchemistryrequiresspatialreasoning—yourweakness—soofcourseyou’redoingpoorlyatit.Youdeviseirrationalexcusesthatsoundsuperficiallyreasonable:IfIstudytoofaraheadofatest,I’llforgetthematerial.(Youconvenientlyforgetthetestsinothercoursesyou’llbetakingduringexamtime,makingitimpossibletolearnallthematerialatonce.)Onlywhenthesemesterisendingandyoustartyourdesperatecrammingforthefinalexamdoyourealizethattherealreasonyouaredoingsobadlyinorganicchemistryisthatyouhavebeencontinuallyprocrastinating.

Researchershavefoundthatprocrastinationcanevenbecomeasourceofprideaswellasanexcusefordoingpoorly.“Icrammedforthequizlastnightafterfinishingthelabreportandthemarketinginterview.OfcourseIcouldhavedonebetter.Butwithsomanythingsonmyplate,whatdoyouexpect?”9Evenwhenpeopleworkhardattheirstudies,theysometimesliketofalselyclaimtheyprocrastinatedbecauseitmakesthemseemcoolandsmart:“Ifinallymademyselfcramlastnightforthemidterm.”

Likeanyhabit,procrastinationissomethingyoucansimplyfallinto.Yougetyourprocrastinationcueandunthinkinglyrelaxintoyourcomfortableprocrastinationresponse.Over

time,yourhabitual,zombielikeresponseinobtainingthosetemporarydollopsofpleasurecangraduallyloweryourself-confidence,leavingyouwithevenlessofadesiretolearnhowtoworkeffectively.Procrastinatorsreporthigherstress,worsehealth,andlowergrades.10Astimegoeson,thehabitcanbecomeentrenched.Atthatpoint,fixingitcanfeelhopeless.11

CHANGEISPOSSIBLE

“IusedtobeaprocrastinatorbutI’vechanged.IhadanAPclassinhighschoolthatreallyhelpedgetmeintogear.MyteacherassignedfourtosixhoursofAmericanhistoryhomeworkanight.WhatIlearnedistotakeitonetaskatatime.I’vefoundthatifIfeellikeI’veaccomplishedsomething,it’seasiertokeepmovingforwardandstayontrack.”

—PaulaMeerschaert,freshman,creativewriting

Occasionallyyoucanpullanall-nighterinyourstudiesandstillgetadecentgrade.Youcanevenfeelasortofhighwhenyou’vefinished.Muchaswithgambling,thisminorwincanserveasarewardthatpromptsyoutotakeachanceandprocrastinateagain.Youmayevenstarttellingyourselfthatprocrastinationisaninnatecharacteristic—atraitthatisasmuchapartofyouasyourheightorthecolorofyourhair.Afterall,ifprocrastinationwereeasilyfixable,wouldn’tyouhavefixeditbynow?

Thehigheryougoinmathandscience,however,themoreimportantitistotakecontrolofprocrastination.Habitsthatworkedinearlieryearscanturnaroundandbiteyou.WhatI’llshowyouinthesenextfewchaptersishowyoucanbecomethemasterofyourhabits.Youshouldbemakingyourdecisions,notyourwell-meaning,butunthinking,zombies—yourhabits.Asyouwillsee,thestrategiesfordealingwithprocrastinationaresimple.It’sjustthattheyaren’tintuitivelyobvious.

Let’sreturntothestorythatbeganthischapter.Thearseniceatersstartedwithtinydosesofarsenic.Intinydoses,arsenicdoesn’tseemharmful.Youcanevenbuildupanimmunitytoitseffects.Thiscanallowyoutotakelargedosesandlookhealthyevenasthepoisonisslowlyincreasingyourriskofcancerandravagingyourorgans.

Inasimilarway,procrastinatorsputoffjustthatonelittlething.Theydoitagainandagain,graduallygrowingusedtoit.Theycanevenlookhealthy.Butthelong-termeffects?

Notsogood.

ALITTLEGOESALONGWAY

“Whenastudentcomplainsoffailingandtellsmehestudiedfortenwholehoursthedaybeforetheexam,Ianswer,‘That’swhyyoufailed.’Whenthestudentlooksatmeindisbelief,Isay,‘Youshouldhavebeenstudyingalittlebitallalong.’”

—RichardNadel,SeniorInstructorofMathematics,FloridaInternationalUniversity,Miami,Florida

SUMMINGITUP

Weprocrastinateaboutthingsthatmakeusfeeluncomfortable.Butwhatmakesusfeelgoodtemporarilyisn’tnecessarilygoodforusinthelongrun.

Procrastinationcanbeliketakingtinyamountsofpoison.Itmaynotseemharmfulatthetime.Butthelong-termeffectscanbeverydamaging.

PAUSEANDRECALL

Inchapter4,welearnedthat it canhelptorecallmaterialwhenyouareinaphysicallydifferent locat ionfromwhereyouoriginallylearnedit .Thishelpsyoubecomeindependent oflocat ioncues.Later,youwillfindyourselfthinkingmorecomfortablyabout thematerialnomat terwhereyouare—thisisoftenimportant whenyouarebeingtested.Let ’st rythisideanow.What werethemainideasofthischapter?Youcanrecallthem

whereyouarecurrent lysit t ing,but thent ryrecallingtheideasagaininadifferent room,orbet teryet ,whenyouareoutside.

ENHANCEYOURLEARNING

1.Havehabitsofprocrastinationhadanimpactonyourlife?Ifso,how?

2.Whattypesofstorieshaveyouheardotherpeopletellaboutwhytheyprocrastinate?Canyouseetheholesinsomeofthesestories?Whatholesareinyourownstoriesaboutprocrastination?

3.Listsomespecificactionsyoucouldtakethatwouldhelpyoucurbhabitsofprocrastinationwithoutrelyingverymuchonwillpower.

ACTIVELYSEEKGOODADVICE!INSIGHTSFROMNORMANFORTENBERRY,ANATIONALLEADERINENGINEERINGEDUCATION

“WhenIwasafirst-yearcollegestudent,IalreadyknewIwantedtobeanengineer,soIsignedupforCalculuswithApplicationsinsteadoftheregularcalculusbeingtakenbymostofmyclassmates.Thiswasamistake.Manyofthestudentsinthisclasshadalreadytakencalculusinhighschoolandwereexpandingtheirknowledgebase.SoIwasatacompetitivedisadvantage.“Morecritical,sincefarfewerstudentswereintheversionofcalculusthatIwas

taking,therewerefewpotentialstudypartners.Unlikeinhighschool,thereisnopremium(indeedthereisapenalty)forgoingitaloneincollege.Professorsinengineering,afieldwhereteamworkisanimportantprofessionaltrait,oftenassumethatyou’reworkingwithothersanddesignhomeworkaccordingly.IsqueakedthroughwithaBbutalwaysfeltthatIhadaninadequateconceptualandintuitiveunderstandingofthefundamentalsofcalculusandofthesubsequentcoursesthatdependedonit.Ididlotsofstudyingonmyowninajust-in-timefashionforthecalculusportionsofsubsequentclasses.Butthatcostmealotoftimethatcouldhavebeendevotedtootherpursuits.“IamluckythatImadeitthroughtograduationwithabachelor’sdegreeinmechanical

engineering,andwiththeencouragementandmentorshipofsomepeersandmyfacultyadvisor,continuedontograduateschoolandmydoctorateinmechanicalengineering.Butapointtotaketoheartfromallofthisistoaskyourpeersandteachersforgoodadviceasyouchooseyourclasses.Theircollectivewisdomwillserveyouwell.”

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zombieseverywhere:

DiggingDeepertoUnderstandtheHabitofProcrastination

ntheinsightfulbookThePowerofHabit,authorCharlesDuhiggdescribesalostsoul—LisaAllen,amiddle-agedwomanwhohadalwaysstruggledwithherweight,whohadbegundrinkingand

smokingwhenshewassixteen,andwhosehusbandhadleftherforanotherwoman.Lisahadneverheldajobformorethanayearandhadfallendeeplyintodebt.

Butinafour-yearspan,Lisaturnedherlifearoundcompletely.Shelostsixtypounds,wasworkingtowardamaster ’sdegree,stoppeddrinkingandsmoking,andwassofitthatsheranamarathon.

TounderstandhowLisamadethesechanges,weneedtounderstandhabit.Habitscanbegoodandbad.Habit,afterall,issimplywhenourbrainlaunchesintoa

preprogrammed“zombie”mode.Youwillprobablynotbesurprisedtolearnthatchunking,thatautomaticallyconnectedneuralpatternthatarisesfromfrequentpractice,isintimatelyrelatedtohabit.1Habitisanenergysaverforus.Itallowsustofreeourmindforothertypesofactivities.Anexampleofthisisbackingyourcaroutofthedriveway.Thefirsttimeyoudothis,youareonhyper-alert.Thedelugeofinformationcomingatyoumadethetaskseemalmostimpossiblydifficult.Butyouquicklylearnedhowtochunkthisinformationsothatbeforeyouknewit,allyouhavetodowasthinkLet’sgo,andyouwerebackingoutofthedriveway.Yourbraingoesintoasortofzombiemode,whereitisn’tconsciouslyawareofeverythingitisdoing.

Yougointothishabitualzombiemodefarmoreoftenthanyoumightthink.That’sthepointofthehabit—youdon’tthinkinafocusedmanneraboutwhatyouaredoingwhileyouareperformingthehabit.Itsavesenergy.

Habitualactionscanvaryinlength.Theycanbebrief:seconds-longintervalswhereyousmileabsentlyatapasserbyorglanceatyourfingernailstoseewhethertheyareclean.Habitscanalsotakesometime—forexample,whenyougoforarunorwatchtelevisionforafewhoursafteryougethomefromwork.

Habitshavefourparts:

1.TheCue:Thisisthetriggerthatlaunchesyouinto“zombiemode.”Thecuemaybesomethingassimpleasseeingthefirstitemonyourto-dolist(timetostartnextweek’shomework!)orseeingatextmessagefromafriend(timetodawdle!).Acuebyitselfisneitherhelpfulnorharmful.It’stheroutine—whatwedoinreactiontothatcue—thatmatters.

2.TheRoutine:Thisisyourzombiemode—theroutine,habitualresponseyourbrainisusedtofallingintowhenitreceivesthecue.Zombieresponsescanbeharmless,useful,or,intheworstcase,sodestructivethattheydefycommonsense.

3.TheReward:Habitsdevelopandcontinuebecausetheyrewardus—giveusadollopofpleasure.Procrastinationisaneasyhabittodevelopbecausethereward—movingyourmind’sfocustosomethingmorepleasant—happenssoquickly.Butgoodhabitscanalsoberewarded.Findingwaystorewardgoodstudyhabitsinmathandscienceisvitaltoescapingprocrastination.

4.TheBelief:Habitshavepowerbecauseofyourbeliefinthem.Forexample,youmightfeelthatyou’llneverbeabletochangeyourhabitofputtingoffyourstudiesuntillateintheday.Tochangeahabit,you’llneedtochangeyourunderlyingbelief.

“IoftenfindthatwhenIcannotbringmyselftostartsomething,ifIgoforaquickrunordosomethingactivefirst,whenIcomebacktoit,itismucheasiertostart.”

—KatherineFolk,freshman,industrialandsystemsengineering

HarnessingYourHabits(Your“Zombies”)toHelpYou

Inthissection,we’regoingtogetintothespecificsofharnessingyourzombiepowersofhabittohelpyouavoidprocrastinationwhileminimizingyouruseofwillpower.Youdon’twanttodoafull-scalechangeofoldhabits.Youjustwanttooverwritepartsofthemanddevelopafewnewones.Thetricktooverwritingahabitistolookforthepressurepoint—yourreactiontoacue.Theonlyplaceyouneedtoapplywillpoweristochangeyourreactiontothecue.

Tounderstandthat,ithelpstogobackthroughthefourcomponentsofhabitandreanalyzethemfromtheperspectiveofprocrastination.

1.TheCue:Recognizewhatlaunchesyouintoyourzombie,procrastinationmode.Cuesusuallyfallintooneofthefollowingcategories:location,time,howyoufeel,reactionstootherpeople,orsomethingthatjusthappened.2Doyoulooksomethinguponthewebandthenfindyourselfwebsurfing?Doesatextmessagedisturbyourreverie,takingyoutenminutestogetbackintotheflowofthingsevenwhenyoutrytokeepyourselfontask?Theissuewithprocrastinationisthatbecauseit’sanautomatichabit,youareoftenunawarethatyouhavebeguntoprocrastinate.

Studentsoftenfindthatdevelopingnewcues,suchasstartinghomeworkassoonastheygethomefromschoolorrightaftertheirfirstbreakfromclass,arehelpful.AsprocrastinationexpertPiersSteel,authorofTheProcrastinationEquation,pointsout,“Ifyouprotectyourroutine,eventuallyitwillprotectyou.”3

YoucanpreventthemostdamagingcuesbyshuttingoffyourcellphoneorkeepingyourselfawayfromtheInternetforbriefperiodsoftime,aswhenyouareworkingonhomeworkduringatwenty-five-minutestudysession.FreshmanactuarialstudentYusraHasanlikestogiveherphoneandlaptoptohersisterto“watchover,”whichisdoublycleverbecauseapubliccommitmenttostudyismadeintheveryactofremovingtemptation.Friendsandfamilycanbehelpfulifyouenlistthem.

2.TheRoutine:Let’ssaythatinsteadofdoingyourstudies,youoftendivertyourattentiontosomethinglesspainful.Yourbrainwantstoautomaticallygointothisroutinewhenyou’vegottenyourcue,sothisisthepressurepointwhereyoumustactivelyfocusonrewiringyouroldhabit.Thekeytorewiringistohaveaplan.Developinganewritualcanbehelpful.Somestudentsmakeitahabittoleavetheirsmartphoneintheircarwhentheyheadinforclass,whichremovesapotentdistraction.Manystudentsdiscoverthevalueofsettlingintoaquietspotinthelibraryor,closertohome,theproductiveeffectsofsimplysittinginafavoritechairatthepropertimewithallInternetaccessdisconnected.Yourplanmaynotworkperfectlyatfirst,butkeepatit.Adjusttheplanifnecessaryandsavorthevictorieswhenyourplanworks.Don’ttrytochangeeverythingatonce.ThePomodorotechnique—thetwenty-five-minutetimer—canbeespeciallyhelpfulinshiftingyourreactiontocues.

Also,ithelpstohavesomethinginyourstomachwhenstartingparticularlydifficulttasks.Thisensuresthatyouhavementalenergyforthatmomentarydollopofwillpowerasyouaregettingstarted.4ItalsoavoidsthepotentialdistractionofI’lljustgograbsomethingtoeat....

3.TheReward:Thiscansometimesrequireinvestigation.Whyareyouprocrastinating?Can

yousubstituteinanemotionalpayoff?Afeelingofprideforaccomplishingsomething,evenifitissmall?Asenseofsatisfaction?Canyouwinasmallinternalbetorcontestinsomethingyou’veturnedintoapersonalgame?Allowyourselftoindulgeinalatteorreadafavoritewebsite?Provideyourselfwithaneveningofmindlesstelevisionorwebsurfingwithoutguilt?Andwillyougiveyourselfabiggerrewardforabiggerachievement—movietickets,asweater,oranutterlyfrivolouspurchase?

“MyboyfriendandIlovemovies,soasarewardforcompletingspecifictasksoncertaindays,hetakesmetothemovies.Thisnotonlyismotivationtostudyorgethomeworkdone,butalsohasledmetodevelopnewhabitsofstudyingbyreinforcingthecue/routine/rewardsystem.”

—CharleneBrisson,psychologymajor,acceleratedsecond-degreenursingprogram

Remember,habitsarepowerfulbecausetheycreateneurologicalcravings.Ithelpstoaddanewrewardifyouwanttoovercomeyourpreviouscravings.Onlyonceyourbrainstartsexpectingtherewardwilltheimportantrewiringtakeplacethatwillallowyoutocreatenewhabits.

It’sparticularlyimportanttorealizethatgivingyourselfevenasmall“attaboy”or“attagirl”jump-startstheprocessofrewiringyourbrain.Thisrewiring,sometimescalledlearnedindustriousness,helpsbrightentasksyouoncethoughtwereboringanduninteresting.5Asyouwillfind,simplygettingintotheflowofyourworkcanbecomeitsownreward,givingyouasenseofproductivenessyoumightnothaveimaginedwaspossiblewhenyoufirstsatdowntobeginworking.Manypeoplefindthatsettingarewardataspecifictime—forexample,breakingforlunchwithafriendatthedeliatnoon,orstoppingthemaintasksatfiveP.M.,givesasolidmini-deadlinethatcanhelpspurwork.

Don’tfeelbadifyoufindthatyouhavetroublegettingintoa“flow”stateatfirst.IsometimesfindittakesafewdaysofdrudgerythroughafewcyclesofthePomodorotechniquebeforeflowbeginstounfoldandIfindmyselfstartingtoenjoyworkinaverynewarea.Alsorememberthatthebetteryougetatsomething,themoreenjoyableitcanbecome.

4.TheBelief:Themostimportantpartofchangingyourprocrastinationhabitisthebeliefthatyoucandoit.Youmayfindthatwhenthegoinggetsstressful,youlongtofallbackintoold,morecomfortablehabits.Beliefthatyournewsystemworksiswhatcangetyouthrough.Partofwhatcanunderpinyourbeliefistodevelopanewcommunity.Hangoutwithclassmateswhohavethe“cando”philosophythatyouwanttodevelop.Developinganencouragingculturewithlike-mindedfriendscanhelpusrememberthevaluesthat,inmomentsofweakness,wetendtoforget.

Apowerfulapproachismentalcontrasting.6Inthistechnique,youthinkaboutwhereyouarenowandcontrastitwithwhatyouwanttoachieve.Ifyou’retryingtogetintomedicalschool,forexample,imagineyourselfasadoctor,helpingothersevenasyou’repreparingforagreatvacationthatyoucanactuallyafford.Onceyou’vegotthatupbeatimageinmind,contrastitwithimagesofyourcurrentlife.Imagineyourclunkerofacar,yourmacaroniandcheesedinners,andyourmountainofstudentdebts.Yetthere’shope!

Inmentalcontrasting,it’sthecontrastofwhereyouwanttobewithwhereyouarenow,orwhereyouhavebeen,thatmakesthedifference.Placingpicturesaroundyourworkandlivingspacesthatremindyouofwhereyouwanttobecanhelpprimeyourdiffuse-modepump.Justremembertocontrastthosegreatimageswiththereal,moremundanelifethatcurrentlysurroundsyou,orthatyouareemergingfrom.Youcanchangeyourreality.

ONEBADDAYCANSPURMANYBETTERONES

“Mentalcontrastingisgreat!I’vebeenusingthissinceIwasakid—it’ssomethingthatpeoplecouldlearntoapplytomanydifferentsituations.“IoncewasstuckformonthsinMarylandworkinginachickensupplierfactoryinthemiddleofahotsummer.Imade

upmymindrighttherethatIwasgoingtoschooltogetmydegree.ThisexperienceiswhatIuseasmymentalcontrast.Ibelievethatsometimesallittakesisonebaddaytosparkanimportantrealization.Afterthat,keepingyourfocustofindthewayoutofyourcurrentsituationismucheasier.”

—MikeOrrell,junior,electricalengineering

NOWYOUTRY!

Pract icingYourZombieWrangling

Doyouliketocheckyoure-mailorFacebookrightwhenyouwakeupinthemorning?Setatimerfortenminutesofworkfirstthinginstead—thenrewardyourselfwithonlinetime.Youwillbesurprisedtoseethatthistinyexerciseinself-controlwillhelpempoweryouoveryourzombiesthroughtheday.Warning:Whenyoufirstsitdowntotrythis,someofyourzombieswillscreamasiftheywanttoeatyourbrain.Tune

themout!Partofthepointofthisexerciseislearningtolaughatyourzombies’anticsastheypredictablytellyou,“Justthisonceit’sokaytocheckFacebookrightnow.”

GetintotheFlowbyFocusingonProcess,NotProduct

Ifyoufindyourselfavoidingcertaintasksbecausetheymakeyouuncomfortable,thereisagreatwaytoreframethings:Learntofocusonprocess,notproduct.

Processmeanstheflowoftimeandthehabitsandactionsassociatedwiththatflowoftime—asin,“I’mgoingtospendtwentyminutesworking.”Productisanoutcome—forexample,ahomeworkassignmentthatyouneedtofinish.

Topreventprocrastination,youwanttoavoidconcentratingonproduct.Instead,yourattentionshouldbeonbuildingprocesses—habits—thatcoincidentallyallowyoutodotheunpleasanttasksthatneedtobedone.

Forexample,let’ssayyoudon’tlikedoingyourmathhomework.Soyouputoffworkingonthehomework.It’sonlyfiveproblems,youthink.Howhardcouldthatbe?

Deepdown,yourealizethatsolvingfiveproblemscouldbeadauntingtask.It’seasiertoliveinafantasyworldwherethefivehomeworkproblems(orthetwenty-pagereport,orwhatever)canbedoneatthelastminute.

Yourchallengehereistoavoidfocusingontheproduct—thesolvedhomeworkproblems.Theproductiswhattriggersthepainthatcausesyoutoprocrastinate.Instead,youneedtofocusontheprocess,thesmallchunksoftimeyouneedoverdaysorweeks,tosolvethehomeworkproblemsorpreparefortests.Whocareswhetheryoufinishedthehomeworkorgraspedkeyconceptsinanyonesession?Thewholepointinsteadisthatyoucalmlyputforthyourbesteffortforashortperiod—theprocess.

Theessentialideahereisthatthezombie,habitualpartofyourbrainlikesprocesses,becauseitcanmarchmindlesslyalong.It’sfareasiertoenlistafriendlyzombiehabittohelpwithaprocessthantohelpwithaproduct.

XMARKSTHESPOT!

“It’sagoodideatomarktheobjectiveofyourdailyreadingassignmentwithabookmark(orPost-itnote).Thisgivesimmediatefeedbackonprogress—youaremoremotivatedwhenyoucanseethefinishline!”

—ForrestNewman,ProfessorofAstronomyandPhysics,SacramentoCityCollege

BreakYourWorkintoBite-SizedPieces—ThenWorkIntently,butBriefly

The“Pomodoro”isatechniquethat’sbeendevelopedtohelpyoufocusyourattentionoverashortperiodoftime.PomodoroisItalianfor“tomato”—FrancescoCirillo,whooriginallydevelopedthistime-managementsysteminthe1980s,usedatomato-shapedtimer.InthePomodorotechnique,yousetatimerfortwenty-fiveminutes.(Youwereintroducedearliertothisideainoneofthe“NowYouTry!”challengesinchapter2.)Oncethetimerstartsticking,you’reontheclock.Nosneakingofftowebsurf,chatonthephone,orinstant-messageyourbuddies.What’sniceaboutdoingaPomodoroisthatif

you’reworkingaroundfriendsorfamily,youcantellthemaboutthetechnique.Then,iftheyhappentointerruptyou,allyouneedtodoismentionthatyou’re“doingaPomodoro”or“ontheclock,”anditgivesafriendlyreasonforthemtoleaveyoualone.

Youmayobjectthatitisstressfulbeingunderthetimer.Butresearchershavefoundsomethingfascinatingandcounterintuitive.Ifyoulearnundermildstress,youcanhandlegreaterstressmuchmoreeasily.Forexample,asresearcherSianBeilockdescribesinherbookChoke,golferswhopracticeputtinginfrontofothersaren’tfazedlateronwhentheyhavetoperformbeforeanaudienceincompetitions.Inthesameway,ifyougetusedtofiguringthingsoutunderamildtimecrunch,youaremuchlesslikelytochokelater,whenyouareinahigh-pressuretest-takingsituation.7Timeaftertime,topperformersinfieldsasdifferentassurgeryandcomputerprogrammingdeliberatelyseekcoacheswhoplacethemunderstressbychallengingthemanddrivingthemtoperformbetter.8

Focusingonprocess,notproduct,isimportantinavoidingprocrastination.Itistheconsistent,dailyt imeyouspendgettingintotheflowofyourstudiesthatmattersmost.FocusondoingaPomodoro—atwenty-five-minutet imedworksession—not oncomplet ingatask.Inasimilarway,noticehow,inthispicture,physicistandsurferdudeGarretLisiisfocusedonthemoment—notontheaccomplishmentofhavingsurfedawave.

WhenyoufirsttryusingthePomodoro,youwillprobablybeamazedathowoftentheurgearisestotakeaquickpeekatsomethingnon-work-related.Butatthesametime,youwillalsobepleasedathoweasyitistocatchyourselfandturnyourattentionbacktoyourwork.Twenty-fiveminutesissuchabriefperiodthatalmostanyadultornear-adultcanfocushisattentionforthatlong.Andwhenyouaredone,youcanleanbackandsavorthefeelingofaccomplishment.

START!

“Onehelpfultipistojustgetstarted.Thisadvicesoundsrelativelysimple,butonceyougetofftoagoodstartitismucheasiertoaccomplishsomething.Iliketogotothequietfloorinthelibrarybecauseyoucanoftenseeotherpeopleinthesamesituation.Ilearnbestbyvisualizing.IfIcanseeotherpeopleworkingonhomework,thenIammoreinclinedtodothatmyself.”

—JosephCoyne,junior,history

Thekeyis,whenthedistractionarises,whichitinevitablywill,youwanttotrainyourselftoignoreit.OneofthesinglemostimportantpiecesofadviceIcangiveyouondealingwithprocrastinationistoignoredistractions!Ofcourse,settingyourselfupsothatdistractionsareminimalisalsoagoodidea.

Manystudentsfindthateitheraquietspaceornoise-cancelingheadphones—orboth—areinvaluablewhentheyarereallytryingtoconcentrate.

OFFWITHDISTRACTIONS!

“Iwasbornwithoutauditorycanalsandthusamdeaf(I’maTreacher-Collinsmutant).So,whenIstudy,offgoesthehearingaid,andIcanREALLYfocus!Ilovemyhandicap!ItookanIQtestattheendoffirstgrade.MyIQwas90—wellbelowaverage.Mymomwasdismayed.IwaselatedsinceIthoughtImadeanAgrade.IhavenoideawhatmycurrentIQis.NowthatIcanhear,it’sprobablydroppedafewnotches.ThankGodforon/offswitches.”

—BillZettler,ProfessorofBiology,codiscovererofseveralviruses,andwinneroftheTeacheroftheYearAward,UniversityofFlorida

Howsoonshouldyoustartagainonceyou’vedoneaPomodoro?Itdependswhatyou’redoing.Ifyou’retryingtogetyourselfstartedonsomethingthat’sdueinmanyweeks,youmayrewardyourselfwithahalfhourofguilt-freewebsurfing.Ifyou’reunderstressandhavealotdue,atwo-tofive-minutebreathermayhavetodo.YoumaywanttoalternateyourPomodorosessionswithworkingsessionsthatdon’tmakeuseofatimer.Ifyoufindyourselflaggingandnotworkingwithfocus,youcanputyourselfbackonthetimer.

InPomodoro-typetimersystems,theprocess,whichinvolvessimplefocusedeffort,movestotheforefront.Youdisconnectfrombeingstuckonanyoneitemandcangetintoastateofautomaticitywithoutconcernsabouthavingtofinishanything.9Thisautomaticityappearstoallowyoutomoreeasilyaccessdiffuse-modecapabilities.Byfocusingonprocessratherthanproduct,youallowyourselftobackawayfromjudgingyourself(AmIgettingclosertofinishing?)andallowyourselftorelaxintotheflowofthework.Thishelpspreventtheprocrastinationthatcanoccurnotonlywhenyouarestudyingmathandscience,butwhenyouaredoingthewritingthatissoimportantformanydifferentcollegeclasses.

Multitaskingislikeconstantlypullingupaplant.Thiskindofconstantshiftingofyourattentionmeansthatnewideasandconceptshavenochancetotakerootandflourish.Whenyoumultitaskwhiledoingschoolwork,yougettiredmorequickly.Eachtinyshiftbackandforthofattentionsiphonsoffenergy.Althougheachattentionswitchitselfseemstiny,thecumulativeresultisthatyouaccomplishfarlessforyoureffort.Youalsodon’trememberaswell,youmakemoremistakes,andyouarelessabletotransferwhatlittleyoudolearnintoothercontexts.Atypicalnegativeexampleofmultitaskingisthatonaverage,studentswhoallowthemselvestomultitaskwhilestudyingorsittinginclasshavebeenfoundtoreceiveconsistentlylowergrades.10

Procrastinationofteninvolvesbecomingsidetrackedonlessessentiallittletasks,suchaspencilsharpening,inpartbecauseyoucanstillfeelthethrillofaccomplishment.Yourmindistrickingyou.Thatiswhykeepinganexperimentalnotebookissoimportant;we’lltalkaboutthatsoon.

NOWYOUTRY!

IgnoranceIsBliss

Nexttimeyoufeeltheurgetocheckyourmessages,pauseandexaminethefeeling.Acknowledgeit.Thenignoreit.Practiceignoringdistractions.Itisafarmorepowerfultechniquethantryingtowillyourselftonotfeelthose

distractionsinthefirstplace.

SUMMINGITUP

Alittlebitofworkonsomethingthatfeelspainfulcanultimatelybeverybeneficial.Habitssuchasprocrastinationhavefourparts:

ThecueTheroutineTherewardThebelief

Changeahabitbyrespondingdifferentlytoacue,orevenavoidingthatcuealtogether.Rewardandbeliefmakethechangelong-lasting.Focusontheprocess(thewayyouspendyourtime)insteadoftheproduct(whatyouwanttoaccomplish).Usethetwenty-five-minutePomodorotostayproductiveforbriefperiods.Thenrewardyourselfaftereachsuccessfulperiodoffocusedattention.Besuretoschedulefreetimetonurtureyourdiffusemode.Mentalcontrastingisapowerfulmotivatingtechnique—thinkabouttheworstaspectsofyourpresentorpastexperiencesandcontrastthesewiththeupbeatvisionofyourfuture.Multitaskingmeansthatyouarenotabletomakefull,richconnectionsinyourthinking,becausethepartofyourbrainthathelpsmakeconnectionsisconstantlybeingpulledawaybeforeneuralconnectionscanbefirmedup.

PAUSEANDRECALL

Ifyoufeelmuzzyorfeatherbrainedasyou’ret ryingtolookawayandrecallakeyidea,oryoufindyourselfrereadingthesameparagraphsoverandoveragain,t rydoingafewsitups,pushups,orjumpingjacks.Alit t lephysicalexert ioncanhaveasurprisinglyposit iveeffect onyourabilit ytounderstandandrecall.Trydoingsomethingact ivenow,beforerecallingtheideasofthischapter.

ENHANCEYOURLEARNING

1.Whydoyouthinkthezombie-like,habitualpartofyourbrainmightpreferprocesstoproduct?Whatcanyoudotoencourageaprocessorientationeventwoyearsfromnow,longafteryou’vefinishedthisbook?

2.Whatkindofsubtlechangecouldyoumakeinoneofyourcurrenthabitsthatcouldhelpyouavoidprocrastination?

3.Whatkindofsimpleandeasynewhabitcouldyouformthatwouldhelpyouavoidprocrastination?

4.Whatisoneofyourmosttroublesomecuesthatspinsyouoffintoaprocrastinationresponse?Whatcouldyoudotoreactdifferentlytothatcue,ortoavoidreceivingthecue?

MATHPROFESSORORALDO“BUDDY”SAUCEDOONHOWFAILURECANFUELSUCCESS

Oraldo“Buddy”SaucedoisahighlyrecommendedmathprofessoronRateMyProfessors.com;heisafull-timemathinstructorfortheDallasCountyCommunityCollegeDistrictinTexas.Oneofhisteachingmottosis“Iofferopportunitiesforsuccess.”Here,Buddyprovidesinsightintoafailurethatfueledhissuccess.“Everyonceinawhile,astudentasksmeifIhavealwaysbeensmart—thismakesmelaugh.IthenproceedtotellthemaboutmyinitialGPAatTexasA&MUniversity.“Whilewriting‘4.0’onthewhiteboard,IsaythatIwasclosetohavinga4.0myfirst

semester.‘Soundsgreat,right?’Iask,pausingfortheirreaction.ThenItakemyeraserandmovethedecimalpointovertotheleft.Itendsuplookinglikethis:‘0.4.’“Yes.It’strue.Ifailedmiserablyandwaskickedoutoftheuniversity.Shocking,right?

ButIdidreturnandeventuallyreceivedbothmybachelor’sandmaster’s.“Therearealotoffailure-to-successtypesouttherewithsimilarstories.Ifyou’vefailed

inthepast,youmaynotrealizehowimportantthatitcanbeinfuelingyoursuccess.“HerearesomeoftheimportantlessonsI’velearnedinmyclimbtosuccess:

Youarenotyourgrade;youarebetterthanthat.Gradesareindicatorsoftimemanagementandarateofsuccess.Badgradesdonotmeanyouareabadperson.Procrastinationisthedeathofsuccess.Focusingontakingsmall,manageablestepsforwardandtimemanagementarekey.Preparationiskeytosuccess.Weallhaveafailurerate.Youwillfail.Socontrolyourfailures.Thatiswhywedohomework—toexhaustourfailurerate.Thebiggestlieeveristhatpracticemakesperfect.Nottrue—practicemakesyoubetter.Practiceiswhereyouaresupposedtofail.Practiceathome,inclass,anytimeandanywhere—exceptontheTEST!Crammingandpassingarenotsuccess.Crammingfortestsistheshortgamewithlesssatisfactionandonlytemporaryresults.Learningisthelonggamewithlife’sbiggestrewards.WeshouldALWAYSbeperpetuallearners.AlwaysinALLWAYS.Embracefailure.Celebrateeachfailure.ThomasEdisonrenamedhisfailures:“1,000waystoNOTcreatealightbulb.”Renameyourownfailures.Evenzombiesgetupandtryagain!

“Theysayexperienceisthebestteacher.Instead,itshouldbethatfailureisthebestteacher.I’vefoundthatthebestlearnersaretheoneswhocopebestwithfailureanduseitasalearningtool.”

N

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chunkingversuschoking:

HowtoIncreaseYourExpertiseandReduceAnxiety

ewinventionsalmostneverinitiallyappearintheirfullyformedglory.Rather,theygothroughmanyiterationsandareconstantlybeingimproved.Thefirst“mobile”phoneswereaboutas

portableasbowlingballs.Thefirstclumsyrefrigeratorswerecrankydevicesusedbybreweries.Theearliestengineswereoverbuiltmonstrositieswithaboutasmuchpowerastoday’sgo-karts.

Enhancementscomeonlyafteraninventionhasbeenoutforawhileandpeoplehavehadachancetomesswithit.Ifyouhaveaworkingengineonhand,forexample,it’saloteasiertoimproveanyparticularfeatureoraddnewones.That’showcleverinnovationssuchasengineturbochargingarose.Engineersrealizedtheycouldgetmorepowerandbangforthebuckbystuffingmoreairandfuelintothecombustionchamber.German,Swiss,French,andAmericanengineers,amongmanyothers,racedtotweakandimprovethebasicidea.

Didyouremembertoskimaheadandcheckthequestionsattheendofthechaptertohelptohelpyoustartbuildingchunksofunderstanding?

HowtoBuildaPowerfulChunk

Inthischapter,muchaswithenhancingandrefininginventions,we’regoingtolearntoenhanceandrefineourchunkingskills.Creatingalittlelibraryofthesechunkswillhelpyouperformbetterontestsandsolveproblemsmorecreatively.Theseprocesseswilllaythegroundworkforyoutobecomeanexpertatwhateveryou’reworkingon.1(Incaseyouarewondering,ourjumpinthischapterfromprocrastinationbacktochunkingisanexampleofinterleaving—varyingyourlearningbyhoppingbackafterabreaktostrengthenanapproachyou’velearnedearlier.)

Here’sakeyidea:Learningfundamentalconceptsofmathandsciencecanbealoteasierthanlearningsubjectsthatrequirealotofrotememorization.Thisisnottotrivializethedifficultyorimportanceofmemorization.Askanymedicalschoolstudentpreparingforboardexams!

Onereasonthatstatementistrueisthatonceyoustartworkingonamathorscienceproblem,you’llnoticethateachstepyoucompletesignalsthenextsteptoyou.Internalizingproblem-solving

techniquesenhancestheneuralactivitythatallowsyoutomoreeasilyhearthewhispersofyourgrowingintuition.Whenyouknow—reallyknow—howtosolveaproblemjustbylookingatit,you’vecreatedacommandingchunkthatsweepslikeasongthroughyourmind.Alibraryofthesechunksgivesyouanunderstandingoffundamentalconceptsinawaynothingelsecan.

Sowiththat,herewego:

STEPSTOBUILDINGAPOWERFULCHUNK

1.Workakeyproblemallthewaythroughonpaper.(Youshouldhavethesolutiontothisproblemavailable,eitherbecauseyou’vealreadyworkeditorbecauseit’sasolvedproblemfromyourbook.Butdon’tlookatthesolutionunlessyouabsolutelyhaveto!)Asyouworkthroughthisproblem,thereshouldbenocheating,skippingsteps,orsaying,“Yeah,I’vegotit”beforeyou’vefullyworkeditout.Makesureeachstepmakessense.

2.Doanotherrepet it ionoftheproblem,payingat tent iontothekeyprocesses.Ifitseemsalittleoddtoworkaproblemagain,keepinmindthatyouwouldneverlearntoplayasongontheguitarbyplayingitonlyonce,orworkoutbyliftingaweightasingletime.

3.Takeabreak.Youcanstudyotheraspectsofthesubjectifyouneedto,butthengodosomethingdifferent.Workatyourpart-timejob,studyadifferentsubject,2orgoplaybasketball.Youneedtogiveyourdiffusemodetimetointernalizetheproblem.

4.Sleep.Beforeyougotosleep,worktheproblemagain.3Ifyougetstuck,listentotheproblem.Letyoursubconscioustellyouwhattodonext.

5.Doanotherrepet it ion.Assoonasyoucanthenextday,worktheproblemagain.Youshouldseethatyouareabletosolvetheproblemmorequicklynow.Yourunderstandingshouldbedeeper.Youmayevenwonderwhyyoueverhadanytroublewithit.Atthispoint,youcanstartlighteninguponcomputingeachstep.Keepyourfocusonthepartsoftheproblemthatarethemostdifficultforyou.Thiscontinuedfocusonthehardstuffiscalled“deliberatepractice.”Althoughitcansometimesbetiring,itisoneofthemostimportantaspectsofproductivestudying.Analternativeorsupplementatthispointistoseewhetheryoucandoasimilarproblemwithease.)

6.Addanewproblem.Pickanotherkeyproblemandbeginworkingonitinthesamewaythatyoudidthefirstproblem.Thesolutiontothisproblemwillbecomethesecondchunkinyourchunkedlibrary.Repeatstepsonethroughfiveonthisnewproblem.Andafteryoubecomecomfortablewiththatproblem,moveontoanother.Youwillbesurprisedhowevenjustafewsolidchunksinyourlibrarycangreatlyenhanceyourmasteryofthematerialandyourabilitytosolvenewproblemsefficiently.

7.Do“act ive”repet it ions.Mentallyreviewkeyproblemstepsinyourmindwhiledoingsomethingactive,suchaswalkingtothelibraryorexercising.Youcanalsousespareminutestoreviewasyouarewaitingforabus,sittinginthepassengerseatofacar,ortwiddlingyourthumbsuntilaprofessorarrivesintheclassroom.Thistypeofactiverehearsalhelpsstrengthenyourabilitytorecallkeyideaswhenyouaresolvinghomeworkproblemsortakingatest.

That’sit.Thosearethekeystepstobuildingachunkedlibrary.Whatyouaredoingisbuildingandstrengtheninganincreasinglyinterconnectedwebofneurons—enrichingandstrengtheningyourchunks.4Thismakesuseofwhatisknownasthegenerationeffect.Generating(thatis,recalling)thematerialhelpsyoulearnitmuchmoreeffectivelythansimplyrereadingit.

Thisisusefulinformation,butIcanalreadyhearwhatyou’rethinking:“I’mspendinghourseveryweekjustsolvingallmyassignedproblemsonce.HowamIsupposedtodoitfourtimesforoneproblem?”

Inresponse,Iwouldaskyou:Whatisyourrealgoal?Toturninhomework?Ortoperformwellontheteststhatdemonstratemasteryofthematerialandformthebasisformostofyourcoursegrade?Remember,justsolvingaproblemwiththebookopeninfrontofyoudoesn’tguaranteeyoucouldsolvesomethinglikeitagainonatest,and,moreimportant,itdoesn’tmeanthatyoutruly

understandthematerial.Ifyouarepressedfortime,usethistechniqueonafewkeyproblemsasaformofdeliberate

practicetospeedandstrengthenyourlearningandtohelpyouspeedyourproblem-solvingskills.

THELAWOFSERENDIPITY

Remember,LadyLuckfavorstheonewhotries.Sodon’tfeeloverwhelmedwitheverythingyouneedtolearnaboutanewsubject.Instead,focusonnailingdownafewkeyideas.You’llbesurprisedathowmuchthatsimpleframeworkcanhelp.

Thewayinwhichmusiciansimprovetheirabilitytoplayaninstrumentcanalsobeappliedtolearningmathinthissense:Amasterviolinist,forexample,doesn’tjustplayamusicalpiecefrombeginningtoend,overandoveragain.Instead,shefocusesonthehardestpartsofthepiece—thepartswherethefingersfumbleandthemindbecomesconfused.5Youshouldbelikethatinyourowndeliberatepractice,focusingandbecomingquickeratthehardestpartsofthesolutionproceduresyouaretryingtolearn.6

Remember,researchhasshownthatthemoreeffortyouputintorecallingmaterial,thedeeperitembedsitselfintoyourmemory.7Recall,notsimplerereading,isthebestformofdeliberatepracticeinstudy.Thisstrategyisalsosimilartothatusedbychessmasters.Thesementalwizardsinternalizeboardconfigurationsaschunksassociatedwiththebestnextmovesintheirlong-termmemory.Thosementalstructureshelpthemselecttheirbestoptionforeachmoveintheircurrentgame.8Thedifferencebetweenlesser-rankedplayersandgrandmastersisthatgrandmastersdevotefarmoretimetofiguringoutwhattheirweaknessesareandworkingtostrengthenthoseareas.9It’snotaseasyasjustsittingaroundandplayingchessforfun.Butintheend,theresultscanbefarmoregratifying.

Remember,retrievalpracticeisoneofthemostpowerfulformsoflearning.Itisfarmoreproductivethansimplyrereadingmaterial.10Buildingachunkedlibraryofwaystosolveproblemsiseffectivepreciselybecauseitisbuiltonmethodsofretrievalpractice.Donotbefooledbyillusionsofcompetence.Remember,juststaringatmaterialthat’salreadyonthepageinfrontofyoucanfoolyouintothinkingyouknowitwhenyouactuallydon’t.

Whenyoufirststartpracticingthisway,itmayfeelawkward—asifyou’reathirty-year-oldsittingdownforyourfirstpianolesson.Butasyoupractice,you’llfinditgraduallycomingtogethermoreeasilyandswiftly.Bepatientwithyourself—asyoureasewiththematerialbeginstogrow,you’llfindyourselfenjoyingitmoreandmore.Isitwork?Sure—andsoislearningtoplaythepianowithverveandstyle.Butthepayoffiswellworththeeffort!

“CHUNK-PUTERS”AREGREAT!

“Betweenbeingafull-timeengineeringstudentandalsoworkingafull-timejobasanengineeringtech,Ihavetoomuchacademicworktokeepitallintheforefrontofmymind.Somymentaltrickistocreatebigchunksfordifferentareas—thermoclass,machinedesign,programming,etcetera.WhenIneedtorecallanindividualproject,Isetmycurrentfocusasideandreferencethedesiredchunk,whichislikealinkonmycomputerdesktop.Icaneitherfocusinonaspecificareaor,indiffusemode,Icanlookatthecompletedesktopandfindconceptuallinksbetweenchunks.WhenIhaveacleanandorganizedmentaldesktop,Icanmakeconnectionsmoreeasily.Itincreasesmymentalagilityandalsoallowsmetoboredeeperintoanyonetopicmoreeasily.”

—MikeOrrell,junior,electricalengineering

HittingtheWall—WhenYourKnowledgeSuddenlySeemstoCollapse

Learningdoesn’tprogresslogicallysothateachdayjustaddsanadditionalneatpackettoyourknowledgeshelf.Sometimesyouhitawallinconstructingyourunderstanding.Thingsthatmadesensebeforecansuddenlyseemconfusing.11

Thistypeof“knowledgecollapse”seemstooccurwhenyourmindisrestructuringitsunderstanding—buildingamoresolidfoundation.Inthecaseoflanguagelearners,theyexperienceoccasionalperiodswhentheforeignlanguagesuddenlyseemsascomprehensibleasKlingon.

Remember—ittakestimetoassimilatenewknowledge.Youwillgothroughsomeperiodswhenyouseemtotakeanexasperatingstepbackwardinyourunderstanding.Thisanaturalphenomenonthatmeansyourmindiswrestlingdeeplywiththematerial.You’llfindthatwhenyouemergefromtheseperiodsoftemporaryfrustration,yourknowledgebasewilltakeasurprisingstepforward.

GettingYourActTogether—OrganizingYourMaterials

Inpreparationforatest,haveyourproblemsandsolutionsneatlyorganizedsoyoucangooverthemquickly.Somestudentstapehandwrittensolutionstoproblemsontherelevantpagesoftheirtextbooksoeverythingisreadilyavailable.(Usepainter ’smaskingtapeorstickynotesifyouplantolaterreturnabook.)Thehandwrittensolutionisimportantbecausewritingbyhandincreasestheoddsthatwhatiswrittenwillberetainedinmemory.Alternatively,keepabinderhandywithimportantproblemsandsolutionsfromtheclassandthebook,soyoucangooverthemagainbeforetests.

WORDSOFWISDOMABOUTREMEMBERINGFROMONEOFHISTORY’SGREATESTPSYCHOLOGISTS

“Acuriouspeculiarityofourmemoryisthatthingsareimpressedbetterbyactivethanbypassiverepetition.Imeanthatinlearningbyheart(forexample),whenwealmostknowthepiece,itpaysbettertowaitandrecollectbyaneffortfromwithin,thantolookatthebookagain.Ifwerecoverthewordsintheformerway,weshallprobablyknowthemthenexttime;ifinthelatterway,weshallverylikelyneedthebookoncemore.”

—WilliamJames,writingin189012

TestingIsaPowerfulLearningExperience—GiveYourselfLittleMini-TestsConstantly

Here’soneofthemostimportantreasonstohavewell-chunkedsolutionmethodsreadilyinmind:Theyhelppreventchokingontests.Choking—panickingtothepointwhereyoufreeze—can

happenwhenyourworkingmemoryisfilledtocapacity,yetyoustilldon’thaveenoughroomfortheadditionalcriticalpiecesyouneedtosolveaproblem.Chunkingcompressesyourknowledgeandmakesroominyourworkingmemoryforthosepiecessoyoudon’tgointomentaloverloadsoeasily.Also,bymakingmoreroominyourworkingmemory,youhaveabetterchanceofrememberingimportantproblem-solvingdetails.13

Practicinglikethisisaformofmini-testing.Researchhasshownthattestingisn’tjustameansofmeasuringhowmuchyouknow.Testinginitselfisapowerfullearningexperience.Itchangesandaddstowhatyouknow,alsomakingdramaticimprovementsinyourabilitytoretainthematerial.14Thisimprovementinknowledgebecauseoftesttakingiscalledthetestingeffect.Itseemstooccurbecausetestingstrengthensandstabilizestherelatedneuralpatternsinyourbrain.Thisispreciselywhatwesawinchapter4,inthe“PracticeMakesPermanent”section,withthepictureofthedarkeningpatternsinthebrainthatoccurswithrepetition.15

Improvementbecauseofthetestingeffectoccursevenwhenthetestperformanceisbadandnofeedbackisgiven.Whenyouareself-testingwhileyouarestudying,however,youwanttodoyourbesttogetfeedbackandcheckyouranswersusingsolutionsmanuals,thebackofthebook,orwhereverthesolutionmaylie.Also,aswe’lldiscusslater,interactionwithpeersaswellasinstructorshelpswiththelearningprocess.16

Onereasonwhybuildingsolidchunksissohelpfulisthatyougetplentyofmini-testsinwhileyouarecreatingthosechunks.Studieshaveshownthatstudents,andeveneducators,areoftenshockinglyunawareofthebenefitsofthiskindofmini-testingthroughretrievalpractice.17

Studentsthinktheyarejustcheckinghowwellthey’redoingwhentheydoamini-testoftheirrecall.Butthisactivetestofrecallisoneofthebestlearningmethods—betterthanjustsittingpassivelyandrereading!Bybuildingyourlibraryofchunks,withplentyofactivepracticingatretrievingmaterialoverandoveragain,andtestingyourrecall,youareusingsomeofthebestmethodspossibleforlearningdeeplyandwell.

NOWYOUTRY!

BuildaMentalSolut ionLibrary

Akeytobuildingmentalflexibilityandexpertiseistobuildyourlibraryofchunkedsolutionpatterns.Thisisyourrapid-accessdatabank—alwayshandyinapinch.Thisideaisn’tjustusefulformathandscienceproblems—itappliestomanyareasinlife.That’swhy,forexample,it’salwaysagoodstrategytolookatwheretheemergencyexitsarerelativetoyourseatonanairplaneoryourroominahotel.

SUMMINGITUP

Chunkingmeansintegratingaconceptintoonesmoothlyconnectedneuralthoughtpattern.Chunkinghelpsincreasetheamountofworkingmemoryyouhaveavailable.Buildingachunkedlibraryofconceptsandsolutionshelpsbuildintuitioninproblemsolving.Whenyouarebuildingachunkedlibrary,it’simportanttokeepdeliberatefocusonsomeofthetoughestconceptsandaspectsofproblemsolving.Occasionallyyoucanstudyhardandfatedealsabadhand.ButremembertheLawof

Serendipity:Ifyoupreparewellbypracticingandbuildingagoodmentallibrary,youwillfindthatluckwillbeincreasinglyonyourside.Inotherwords,youguaranteefailureifyoudon’ttry,butthosewhoconsistentlygiveitagoodeffortwillexperiencemanymoresuccesses.

PAUSEANDRECALL

What werethemainideasofthischapter?Almost noonecanrememberalot ofdetails,andthat ’sokay.You’llbesurprisedtoseehowfast yourlearningprogressesifyoubegintoencapsulateideasrelatedtowhat youarelearningintoafewkeychunks.

ENHANCEYOURLEARNING

1.Whatdoeschunkinghavetodowithworkingmemory?

2.Whydoyouneedtosolveaproblemyourselfaspartofthechunkingprocess?Whycan’tyoujustlookatthesolutioninthebackofthebook,understandit,andthenmoveon?Whataresomeadditionalthingsyoucandotohelpsmoothyourchunksrightbeforeatest?

3.Whatisthetestingeffect?

4.Onceyou’vepracticedaproblemafewtimes,pauseandseeifyoucansensethefeelingofrightnessthatoccurswhenyourealizewhatthenextstepinthesolutionprocessis.

5.WhatistheLawofSerendipity?Thinkofanexamplefromyourownexperiencesthattypifiesthisidea.

6.Howdoeschokingdifferfromknowledgecollapse?

7.Studentsfoolthemselvesintothinkingthattheyarelearningbestbyrereadingthematerialinsteadofbytestingthemselvesthroughrecall.Howcanyoukeepyourselffromfallingintothiscommontrap?

NEELSUNDARESAN,SENIORDIRECTOROFEBAYRESEARCHLABS,ONINSPIRATIONANDTHEPATHTOSUCCESSINMATHANDSCIENCE

Dr.NeelSundaresanisthecreatoroftheInspire!programtohelpstudentssucceedinscience,engineering,math,andtechnology.SomeInspire!scholars—agroupoffreshmenfromdisadvantagedbackgrounds—recentlyfiledtheirfirstpatent,whichprovidedacriticalintellectualpropertyassetformobilecommerceforeBay.Dr.Sundaresan’sownstoryprovidesinsightintohispathtosuccess.“IdidnotgotoaneliteschoolwhenIwasgrowingup.Infact,myschoolwasbelowaverage—wedidn’thavetheproperteachersformanysubjects.ButIfocusedonfindingsomethinggoodinwhateverteacherscamemyway,whetheritwasanexcellentmemoryorsimplyaneasysmile.Thiskindofpositiveattitudehelpedmeappreciatemyteachersandkeepanopen-mindedapproachtowardmyclasses.“Thissameattitudealsohelpedmelaterinmycareer.Today,Ialwaysactivelyseek

inspirationfromthepeopleIworkwithandfor.WheneverIfindmyspiritbendinglow,IdiscoveritisbecauseIhavestoppedlookingforpeople’spositiveattributes.Thismeansitistimeformetolookwithinandmakechanges.“Iknowthissoundsclichéd,butmymaininspirationhasalwaysbeenmymother.She

wasnotallowedtostudybeyondmiddleschoolbecauseshewouldhavehadtoleavehersmalltowntocompletehighschool.ShegrewupduringanexcitingbutdangeroustimeinIndia’sstruggleforindependence.Thedoorsthatshutformymotherhavemade

medeterminedtoopendoorsforothers,tohelpthemrealizetheenormousopportunitiesthatcanbesoclosetotheirgrasp.“Oneofmymother’sGoldenRuleswasthat‘writingisthefoundationoflearning.’Fromgradeschoolthroughdoctoralstudies,

IhavefoundimmensepowerinsystematicallyunderstandingandwritingeachstepofwhatIreallywantedtolearn.“WhenIwasagraduatestudent,Iusedtoseeotherstudentsvigorouslyhighlightingstepsinproofsorsentencesinapassage

ofabook.Ineverunderstoodthis.Onceyouhighlight,insomesense,youhavedestroyedtheoriginalwithoutanyguaranteethatyouhaveplaceditinsideyou,whereitcanflower.“Myownexperiences,then,echotheresearchfindingsyouarelearningaboutinthisbook.Highlightingshouldbeavoided

because,atleastinmyexperience,itprovidesonlyanillusionofcompetence.Retrievalpracticeisfarmorepowerful.Trytogetthemainideasofeachpageyouarereadingcementedinyourmindbeforeyouturnthepage.“Igenerallylikedtoworkonmymoredifficultsubjects,likemath,inthemorning,whenIwasfresh.Istillpracticethisapproach

today.Ihavesomeofmybestmentalbreakthroughsinthebathroomandshower—it’swhenItakemymindoffthesubjectthatthediffusemodeisabletoworkitsmagic.”

A

{8}

tools,tips,andtricks

snotedmanagementspecialistDavidAllenpointsout,“Wetrickourselvesintodoingwhatweoughttobedoing....Toagreatdegree,thehighest-performingpeopleIknowarethosewho

haveinstalledthebesttricksintheirlives...Thesmartpartofussetsupthingsforustodothatthenot-so-smartpartrespondstoalmostautomatically,creatingbehaviorthatproduceshigh-performanceresults.”1

Allenisreferringtotrickslikewearingexerciseclothestohelphimgetintothemoodforexercisingorplacinganimportantreportbythefrontdoorsohecan’tmissit.OneconstantrefrainIhearfromstudentsisthatputtingthemselvesinnewsurroundings—suchasthequietsectionofalibrary,whichhasfewinterruptingcues—workswonderswithprocrastination.Researchhasconfirmedthataspecialplacedevotedjusttoworkingisparticularlyhelpful.2

Anothertrickinvolvesusingmeditationtohelpyoulearntoignoredistractingthoughts.3(MeditationisnotjustforNewAgetypes—alotofsciencehasrevealeditsvalue.4)Ashort,helpfulguidetogettingstartedwithmeditationisBuddhainBlueJeansbyTaiSheridan.It’sfreeasanelectronicbookandissuitableforpeopleofanyfaith.Andofcoursetherearemanymeditationapps—justGooglearoundtoseewhatlooksworkableforyou.

Alastimportanttrickistoreframeyourfocus.Onestudent,forexample,isabletogethimselfupatfourthirtyeachweekdaymorning,notbythinkingabouthowtiredheiswhenhewakesbutabouthowgoodbreakfastwillbe.

OneofthemostextraordinarystoriesofreframingisthatofRogerBannister,thefirstpersontorunamileinlessthanfourminutes.Bannisterwasamedicalschoolstudentwhocouldn’taffordatraineroraspecialrunner ’sdiet.Hedidn’tevenhavetimetorunmorethanthirtyminutesaday,squeezedinaroundhismedicalstudies.YetBannisterdidnotfocusonallthereasonswhyhelogicallyhadnochanceofreachinghisgoal.Heinsteadrefocusedonaccomplishinghisgoalinhisownway.Onthemorninghemadeworldhistory,hegotup,atehisusualbreakfast,didhisrequiredhospitalrounds,andthencaughtabustothetrack.

It’snicetoknowthattherearepositivementaltricksyoucanusetoyouradvantage.Theymakeupforsomeofthenegativetricksyoucanplaythateitherdon’tworkormakethingsmoredifficultforyou,liketellingyourselfthatyoucanpolishoffyourhomeworkjustbeforeit’sdue.

It’snormaltositdownwithafewnegativefeelingsaboutbeginningyourwork.It’showyouhandlethosefeelingsthatmatters.Researchershavefoundthatthedifferencebetweenslowandfaststartersisthatthenonprocrastinatingfaststartersputtheirnegativethinkingaside,sayingthingstothemselveslike,“Quitwastingtimeandjustgetonwithit.Onceyougetitgoing,you’llfeelbetteraboutit.”5

APOSITIVEAPPROACHTOPROCRASTINATION

“Itellmystudentstheycanprocrastinateaslongastheyfollowthreerules:

1.Nogoingontothecomputerduringtheirprocrastinationtime.It’sjusttooengrossing.

2.Beforeprocrastinating,identifytheeasiesthomeworkproblem.(Nosolvingisnecessaryatthispoint.)

3.Copytheequationorequationsthatareneededtosolvetheproblemontoasmallpieceofpaperandcarrythepaperarounduntiltheyarereadytoquitprocrastinatingandgetbacktowork.

“Ihavefoundthisapproachtobehelpfulbecauseitallowstheproblemtolingerindiffusemode—studentsareworkingonitevenwhiletheyareprocrastinating.”

—ElizabethPloughman,LecturerofPhysics,CamosunCollege,Victoria,BritishColumbia

Self-Experimentation:TheKeytoaBetterYou

Dr.SethRobertsisaprofessoremeritusofpsychologyattheUniversityofCalifornia,Berkeley.Whilelearningtoperformexperimentsasagraduatestudent,hebegantoexperimentonhimself.Roberts’sfirstself-experimentinvolvedhisacne.Adermatologisthadprescribedtetracycline,soRobertssimplycountedthenumberofpimpleshehadonhisfacewithvaryingdosesoftetracycline.Theresult?Thetetracyclinemadenodifferenceonthenumberofpimpleshehad!

Robertshadstumbledacrossafindingthatwouldtakemedicineanotherdecadetodiscover—thatseeminglypowerfultetracycline,whichhasunsafesideeffects,doesn’tnecessarilyworkonacne.Ontheotherhand,benzoylperoxidecreamdidwork,contrarytowhatRobertshadoriginallythought.AsRobertsnoted,“FrommyacneresearchIlearnedthatself-experimentationcanbeusedbynon-expertsto(a)seeiftheexpertsarerightand(b)learnsomethingtheydon’tknow.Ihadn’trealizedsuchthingswerepossible.”6Overtheyears,Robertshasusedhisself-experimentationeffortstostudyhismood,controlhisweight,andtoseetheeffectsofomega-3onhowwellhisbrainfunctioned.

Overall,Robertshasfoundthatself-experimentationisextremelyhelpfulintestingideasaswellasingeneratinganddevelopingnewhypotheses.Ashenotes:“Byitsnature,self-experimentationinvolvesmakingsharpchangesinyourlife:youdon’tdoXforseveralweeks,thenyoudoXforseveralweeks.This,plusthefactthatwemonitorourselvesinahundredways,makesiteasyforself-experimentationtorevealunexpectedsideeffects....Moreover,dailymeasurementsofacne,sleep,oranythingelse,supplyabaselinethatmakesiteveneasiertoseeunexpectedchanges.”7

Yourownself-experimentation,atleasttobeginwith,shouldbeonprocrastination.Keepnotesonwhenyoudon’tcompletewhatyouhadintendedtocomplete,whatthecuesare,andyourzombie-modehabitualreactiontoprocrastinationcues.Byloggingyourreaction,youcanapplythesubtlepressureyouneedtochangeyourresponsetoyourprocrastinationcuesandgraduallyimproveyourworkinghabits.InhisexcellentbookTheNowHabit,authorNeilFioresuggestskeepingadetaileddailyscheduleofyouractivitiesforaweekortwotogetahandleonwhereyourproblemareasareforprocrastination.8Therearemanydifferentwaystomonitoryourbehavior.Themostimportantideahereisthatkeepingawrittenhistoryoverseveralweeksappearstobecriticalinhelpingyoumakechanges.Also,differentpeoplefunctionbetterincertainenvironments—someneedabusycoffeeshop,whileothersneedaquietlibrary.Youneedtofigureoutwhat’sbestforyou.

ISOLATIONVERSUSGROUPWORK—TREATINGPROCRASTINATIONDIFFERENTLYTHANSIMPLYSTRUGGLINGTOUNDERSTAND

“AtipIhavetoaddressprocrastinationistoisolateyourselffromthingsyouknowwilldistractyou,includingpeople.Gotoaroomallalone,orthelibrarysoyoudonothaveanythingtodistractyou.”

—AukuryCowart,sophomore,electricalengineering

“IfI’mstrugglinginasubject,Ifindithelpfultostudywithotherpeoplefromthesameclass.ThatwayIcanaskquestionsandwecanworktogethertofigureoutwhatweareconfusedon.ChancesareImightknowwhatheorsheisconfusedaboutandviceversa.”

—MichaelPariseau,junior,mechanicalengineering

UltimateZombieAlliance:ThePlanner-JournalasYourPersonalLabNotebook

Thebestwayforyoutogaincontrolofyourhabitsissimple:Onceaweek,writeabriefweeklylistofkeytasks.Then,eachday,writealistofthetasksthatyoucanreasonablyworkonoraccomplish.Trytowritethisdailytasklisttheeveningbefore.

Whythedaybefore?Researchhasshownthishelpsyoursubconscioustograpplewiththetasksonthelistsoyoufigureouthowtoaccomplishthem.9Writingthelistbeforeyougotosleepenlistsyourzombiestohelpyouaccomplishtheitemsonthelistthenextday.

Mostpeopleusetheirphoneoranonlineorpapercalendartokeeptrackofimportantduedates—youareprobablyusingsuchasystem.Fromyour“duedate”calendar,writedownaweeklyto-dolistoftwentyorfewerkeyitems.Eachnight,createthenextday’sdailyto-dolistfromtheitemsontheweeklyto-dolist.Keepittofivetotenitems.Trynottoaddtothedailylistonceyou’vemadeitunlessitinvolvessomeunanticipatedbutimportantitem(youdon’twanttostartcreatingendlesslists).Trytoavoidswappingoutitemsonyourlist.

Ifyoudon’twriteyourtasksdowninalist,theylurkattheedgeofthefour-or-soslotsinyourworkingmemory,takingupvaluablementalrealestate.

Butonceyoumakeatasklist,itfreesworkingmemoryforproblemsolving.Yay!Butremember,youmustabsolutelytrustthatyouwillcheckyourplanner-journal.Ifyoursubconsciousdoesn’ttrustyoutodothat,taskswillbeginswirlingbackup,blockingyourworkingmemory.

Onemorething.AswritingcoachDaphneGray-Grantrecommendstoherwritingclients:“Eatyourfrogsfirstthinginthemorning.”Dothemostimportantandmostdislikedjobsfirst,assoonasyouwakeup.Thisisincrediblyeffective.

ThefollowingisadaysampleIdrewupfrommyownplanner-journal.(Youcancreateyourownweeksample.)Notethatthereareonlysixitems—someofthemareprocessoriented.Forexample,Ihaveapaperduetoajournalinseveralmonths,soIspendalittlefocusedtimeonmostdaysworkingtowardcompletingit.Afewitemsareproductoriented,butthatisonlybecausetheyaredoablewithinalimitedperiodoftime.

NOV.30

PNASpaper(1hour)GoforawalkBook(1section)ISE150:demoprepEGR260:prepare1questionforfinalexamFinalizeupcomingtalk

Focus,fun!Goalfinishtimeforday:5:00P.M.

Notemyreminders:IwanttokeepmyfocusoneachitemwhenIamworkingonit,andIwanttohavefun.I’mwellalongmylisttoday.IdidcatchmyselfgettingsidetrackedbecauseIforgottoshutdownmye-mail.Togetmyselfbackintogear,Isetatwenty-two-minutePomodorochallengeusingatimeronmycomputerdesktop.(Whytwenty-twominutes?Well,whynot?Idon’thavetodothesamethingeachtime.Andnotice,too,thatbymovingtoPomodoromode,I’veswitchedtoaprocessorientation.)Noneoftheitemsonmylististoobig,becauseI’vegototherthingsgoingoninmyday—meetingstogoto,alecturetogive.SometimesIsprinkleafewtasksthatinvolvephysicalmotiononmylist,likepullingweedsorsweepingthekitchen.Thesearen’tgenerallymyfavoritekindsoftasks,butsomehow,becauseI’musingthemasdiffuse-modebreaks,Ioftenlookforwardtothem.Mixingothertasksupwithyourlearningseemstomakeeverythingmoreenjoyableandkeepsyoufromprolongedandunhealthyboutsofsitting.

Overtime,asI’vegainedmoreexperience,I’vegottenmuchbetteratgauginghowlongittakestodoanygiventask.Youwillfindyourselfimprovingquicklyasyoubecomemorerealisticaboutwhatyoucanreasonablydoinanygiventime.Somepeopleliketoplaceanumberfromonetofivebesideeachtask,withonebeingthehighestpriorityandfivebeinganitemthatwouldbeokaytodelayuntilthenextday.Othersliketoputastarbesidehigh-prioritytasks.Somepeopleliketoputaboxinfrontofeachitemsotheycancheckitoff.IpersonallyliketoputabigblacklinethrougheachitemwhenIfinishit.Whateverfloatsyourboat.You’llbedevelopingasystemthatworksforyou.

THEFREEDOMOFASCHEDULE

“Tocombatprocrastination,ImakeascheduleofeverythingIhavetodo.Forexample,Itellmyself,‘Friday,IneedtostartmypaperandthenfinishitonSaturday.Also,onSaturday,Ineedtodomymathhomework.OnSunday,IneedtostudyformyGermantest.’Itreallyhelpsmestayorganizedandpracticallystress-free.IfIdon’tfollowmyschedule,thenIhavetwicetheamountoftheworktodothenextday,andthat’sreallynotsomethingIlookforwardto.”

—RandallBroadwell,mechanicalengineeringstudentwithaGermanminor

Incidentally,ifyou’vetriedstartingaplannerorjournalbeforeandnothaditworkforyou,youmighttryarelatedtechniquethathasamoreobviousreminderfunctionbuiltin:Keepyourtasklistonachalkboardorwhiteboardbyyourdoor.Andofcourse,youcanstillfeelthatvisceralthrillofpleasureeverytimeyouchecksomethingoffyourlist!

Noticemygoalfinishtimefortheday:5:00P.M.Doesn’tseemright,doesit?Butitisright,anditisoneofthemostimportantcomponentsofyourdailyplanner-journal.Planningyourquittingtimeisasimportantasplanningyourworkingtime.Generally,Iaimtoquitat5:00P.M.,althoughwhenI’mlearningsomethingnew,itcansometimesbeapleasuretolookatitagainafterI’vetakenaneveningbreak,justbeforeIgotosleep.AndoccasionallythereisamajorprojectthatI’mwrappingup.The5:00P.M.quittingtimecomesaboutbecauseIhaveafamilyIenjoyhangingwith,andIliketohaveplentyoftimeforawidevarietyofreadingintheevening.Ifthisseemsliketooeasyaschedule,keepinmindthatIriseearlyanddothissixdaysaweek,obviouslynotsomethingyouneedtobedoingunlessyourstudyandworkloadisextraheavy.

Youmightthink,Well,yeah,butyou’reaprofessorwhoispastyouryouthfulstudydays—ofcourseanearlyquittingtimeisfineforyou!However,oneofmymostadmiredstudyexperts,CalNewport,useda5:00P.M.quittingtimethroughmostofhisstudentcareer.10HeendedupgettinghisPh.D.fromMIT.Inotherwords,thismethod,implausiblethoughitmayseemforsome,canworkforundergraduateandgraduatestudentsinrigorousacademicprograms.Timeaftertime,thosewhoarecommittedtomaintaininghealthyleisuretimealongwiththeirhardworkoutperformthosewhodoggedlypursueanendlesstreadmill.11

Onceyou’vefinishedyourdailylist,you’redonefortheday.Ifyoufindyourselfconsistentlyworkingbeyondyourplannedquittingtime,ornotfinishingtheitemsyou’velaidoutforyourself,yourplanner-journalwillhelpyoucatchitandallowyoutostartmakingsubtleshiftsinyourworkingstrategy.Youhaveanimportantgoaleachday:tojotafewbriefnotesintoyourplanner-journalforthenextday,andafewcheckmarks(hopefully)onyourcurrentday’saccomplishments.

Ofcourse,yourlifemaynotlenditselftoaschedulewithbreaksandleisuretime.Youmayberunningonfumeswithtwojobsandtoomanyclasses.Buthoweveryourlifeisgoing,trytosqueezealittlebreaktimein.

It’simportanttotransformdistantdeadlinesintodailyones.Attackthembitbybit.Bigtasksneedtobetranslatedintosmalleronesthatshowuponyourdailytasklist.Theonlywaytowalkajourneyofathousandmilesistotakeonestepatatime.

NOWYOUTRY!

PlanningforSuccess

Pickasmallportionofataskyouhavebeenavoiding.Planwhereandwhenyouwilltacklethatportionofthetask.Willyougotothelibraryintheafternoon,leavingyourcellphoneonairplanemode?Willyougointoadifferentroominyourhousetomorrowevening,leavingyourlaptopbehindandwritingbyhandtogetastart?Whateveryoudecide,justplanninghowyouwillimplementwhatyouneedtodomakesitfarmorelikelythatyouwillsucceedinthetask.12

Youmaybesousedtoprocrastinationandguiltasmotivatorsthatitishardtobringyourselftobelievethatanothersystemcouldwork.Morethanthat,itmaytakeyouawhiletofigureouthowtoproperlybudgetyourtimebecauseyou’veneverbeforehadtheluxuryofknowinghowmuchtimeittakestodoagoodjobwithoutrushing.Chronicprocrastinators,asitturnsout,tendtoseeeachactofprocrastinationasaunique,unusualact,a“justthisonetime”phenomenonthatwon’tberepeatedagain.Eventhoughitisn’ttrue,itsoundsgreat—sogreatthatyouwillbelieveitagainandagain,becausewithoutyourplanner-journal,there’snothingtocounteryourthoughts.AsChicoMarxoncesaid,“Whoyougonnabelieve,meoryourowneyes?”

AVOIDINGPROCRASTINATION—INSIGHTSFROMINDUSTRIALENGINEERINGSTUDENTJONATHONMCCORMICK

1.Iwritedownassignmentsinmyplannerasbeingdueonedaybeforetheyarereallydue.Thatway,Ineverrushtofinishatthelastminute,andIstillhaveonefulldaytothinkmyassignmentthroughbeforeturningitin.

2.ItellmyfriendsthatI’mworkingonmyhomework.Thatway,wheneveroneofthemcatchesmeliveonFacebook,they’llholdmeaccountabletothefactthatI’msupposedtobedoinghomework.

3.Ihaveaframedpieceofpaperwiththestartingsalaryofanindustrialengineeronmydesk.WheneverIcan’tfocusonmytaskathand,Ilookatthatandremindmyselfthatit’llpayoffinthelongrun.

Alittleprocrastinationhereandthereisunavoidable.Buttobeeffectiveinlearningmathandscience,youmustmasteryourhabits.Yourzombiesmustbeunderyourcontrol.Yourplanner-journalservesasyoureyestokeeptrackofwhatworks.Whenyoufirststartusingatasklist,youwilloftenfindthatyou’vebeentooambitious—there’snowaytoaccomplishitall.Butasyoufine-tune,youwillquicklylearnhowtosetsensible,doablegoals.

Youmaythink,Yes,butwhataboutatimemanagementsystem?AndhowdoIknowwhatismostimportantformetobeworkingon?That’swhattheweeklyto-dolistisallabout.Ithelpsyoucalmlystepback,lookatthebigpicture,andsetpriorities.Settingoutyourdailylisttheeveningbeforecanalsohelppreventyoufrommakinglast-minutedecisionsthatcancostyouinthelongrun.

Doyouneedtosometimesmakechangesinyourplansbecauseofunforeseenevents?Ofcourse!ButremembertheLawofSerendipity:LadyLuckfavorstheonewhotries.Planningwellispartoftrying.Keepyoureyeonthegoal,andtrynottogettoounsettledbyoccasionalroadblocks.

ENLISTINGLISTSANDTHEIMPORTANCEOFSTARTING

“Istayorganizedduringtheweekbymakingalistofthingsthatneedtobedoneforeachday.ThelistisusuallyonalinedsheetofpaperthatIjustfoldandstickinmypocket.Everyday,acoupleoftimesaday,I’llpullitoutanddouble-checkthatI’vedoneoramgoingtodowhateverisontheagendaforthatday.It’snicetobeabletocrossstuffoffthelist,especiallywhenit’ssuperlong.Ihaveadrawerjustfullofthesefolded-uppiecesofpaper.“Ifindit’seasiertostartonething,orevenafewthingsatatime,andknowthatthenexttimeIgotodothem,they

arealreadypartlydone,sothereislesstoworryabout.”

—MichaelGashaj,sophomore,industrialengineering

TechnologyTips:TheBestAppsandProgramsforStudying

Asimpletimerpluspenandpaperareoftenthemoststraightforwardtoolstoavoidprocrastination,butyoucanalsomakeuseoftechnology.Here’sarundownofsomeofthebeststudent-orientedtools.

NOWYOUTRY!

Best AppsandProgramstoKeeponTask(freeversionsavailableunlessotherwisenoted)

TimersThePomodorotechnique(variedpricesandresources):http://pomodorotechnique.com/

Tasks,Planning,andFlashCards30/30—combinestimerswithatasklist:http://3030.binaryhammer.com/StudyBlue—combinesflashcardsandnoteswithtextmessageswhenit’stimetostudyagain,alongwithadirectlinktothematerial:http://www.studyblue.com/Evernote—oneofmypersonalfavorites;verypopularfornotingtasklistsandrandompiecesofinformation(replacesthelittlenotebookwritershavelongcarriedtokeeptrackoftheirideas):http://evernote.com/Anki—oneofthebestpureflashcardsystems,withanexcellentspacedrepetitionalgorithm;manyexcellentpremadedecksareavailableforavarietyofdisciplines:http://ankisrs.net/Quizlet.com—allowsyoutoinputyourownflashcards;youcanworkwithclassmatestodivideuptheduties(free):http://quizlet.com/GoogleTasksandCalendar:http://mail.google.com/mail/help/tasks/

LimitingYourTimeonTime-WastingWebsitesFreedom—manypeopleswearbythisprogram,availableforMacOS,Windows,andAndroid($10):http://macfreedom.com/StayFocusd—forGoogleChrome:https://chrome.google.com/webstore/detail/stayfocusd/laankejkbhbdhmipfmgcngdelahlfoji?hl=enLeechBlock—forFirefox:https://addons.mozilla.org/en-us/firefox/addon/leechblock/MeeTimer—forFirefox;tracksandlogswhereyouspendyourtime:https://addons.mozilla.org/en-us/firefox/addon/meetimer/

CheeringYourselfandOthersOn43Things—agoal-settingsite:http://www.43things.com/StickK—agoal-settingsite:http://www.stickk.com/Coffitivity—modestbackgroundnoisesimilartoacoffeeshop:http://coffitivity.com/

EasiestBlockofAllDisablesoundnotificationsonyourcomputerandsmartphone!

SUMMINGITUP

Mentaltrickscanbepowerfultools.Thefollowingaresomeofthemosteffective:Putyourselfinaplacewithfewinterruptions,suchasalibrary,tohelpwithprocrastination.Practiceignoringdistractingthoughtsbysimplylettingthemdriftpast.Ifyourattitudeistroubled,reframeyourfocustoshiftattentionfromthenegativetothepositive.

Realizeit’sperfectlynormaltositdownwithafewnegativefeelingsaboutbeginningyourwork.

Planningyourlifefor“playtime”isoneofthemostimportantthingsyoucandotopreventprocrastination,andoneofthemostimportantreasonstoavoidprocrastination.Attheheartofprocrastinationpreventionisareasonabledailyto-dolist,withaweeklyonce-overtoensureyou’reontrackfromabig-pictureperspective.Writeyourdailytasklisttheeveningbefore.Eatyourfrogsfirst.

PAUSEANDRECALL

Closethebookandlookaway.What werethemainideasofthischapter?Remembertocongratulateyourselfforhavingfinishedreadingthissect ion—everyaccomplishmentdeservesamentalpat ontheback!

ENHANCEYOURLEARNING

1.Ifit’snormalforstudentstofirstsitdownwithafewnegativefeelingsaboutbeginningtheirwork,whatcanyoudotohelpyourselfgetoverthishurdle?

2.Whatisthebestwayforyoutogaincontrolofhabitsofprocrastination?

3.Whywouldyouwanttowriteatasklistdowntheeveningbeforeyouintendtoaccomplishthetasks?

4.Howmightyoureframesomethingyouarecurrentlyperceivinginanegativeway?

5.Explainwhyhavingadailyquittingtimetoworktowardissoimportant.

NOWYOUTRY!

Set t ingReasonableGoals

Iwouldliketheendofthischaptertobethebeginningofyourown.Forthenexttwoweeks,writeyourweeklygoalsdownatthebeginningofeachweek.Then,eachday,writeoutfivetotensmall,reasonabledailygoalsbasedonyourweeklygoals.Crossoffeachitemasyoucompleteit,andmentallysavoreachcompleteditemthatyoucrossoffyourlist.Ifyouneedto,breakagiventaskoutintoa“minitasklist”ofthreesmallsubtaskstohelpkeepyourselfmotivated.Remember,partofyourmissionistofinishyourdailytasksbyareasonabletimesothatyouhavesomeguilt-free

leisuretimeforyourself.Youaredevelopinganewsetofhabitsthatwillmakeyourlifemuchmoreenjoyable!Youcanusepaperoranotebook,oryoucangetachalkboardorwhiteboardtopostbyyourdoor.Whateveryou

thinkwillworkbest,that’swhatyouneedtodotogetstarted.

COPINGWITHLIFE’STOUGHESTCHALLENGESUSINGMAGICALMATHMARINATION—MARYCHA’SSTORY

“MyfatherabandonedmyfamilywhenIwasthreeweeksold,andmymotherdiedwhenIwasnine.Asaresult,Ididterriblyinmiddleandhighschool,andwhilestillateenager,Ileftmyadoptedparents’housewith$60tomyname.“Iamcurrentlya3.9GPAbiochemistrymajor,andIamworkingtowardmygoalof

goingtomedicalschool.Iwillapplynextyear.“Whatdoesthishavetodowithmath?Gladyouasked!“WhenIjoinedthearmyatagetwenty-five,itwasbecausemylifehadbecome

financiallyunmanageable.Joiningthearmywasthebestdecisionofmylife—althoughthat’snottosayarmylifewaseasy.ThemostdifficultperiodwasinAfghanistan.Iwashappywithmywork,butIhadlittleincommonwithmycoworkers.Thisoftenleftmefeelingalienatedandalone,soIstudiedmathinmysparetimetokeeptheideasfreshin

mymind.“Mymilitaryexperiencehelpedmedevelopgoodstudyhabits.Notasinstareintentlyforhours,butasinonlygotafew

minuteshere,gottafigureoutwhatIcan!Someissueorotherwasalwaysarising,whichmeantthatIhadtodomyworkinshortbursts.“That’swhenIaccidentallydiscovered‘magicalmathmarination’—theequivalentofdiffuse-modeprocessing.I’dbestuckon

someproblems—reallystuck,withnoclueaboutwhatwasgoingon.ThenI’dgetcalledouttorespondtosomeexplosionoranother.WhileIwasoutleadingtheteam,orevenjustsittingquietly,waiting,thebackofmymindwassimultaneouslymusingovermathproblems.I’dcomebacktomyroomlaterthatnightandeverythingwouldbesolved!“AnothertrickI’vediscoverediswhatIcallactivereview.I’llbestraighteningmyhairorshowering,butI’msimultaneously

reviewinginmyheadproblemsthatIhavealreadysolved.ThisallowsmetokeepproblemsintheforefrontofmymindsoIwon’tforgetthem.“Myprocessforstudyingisasfollows:

1.Doalltheoddproblemsinasection(oratleastenoughofeach‘type’tocompleteyourunderstanding).

2.Lettheproblemsmarinate.

3.Makesheetswithalltheimportantconceptsandoneexampleofeachtypeofproblemyou’dliketoaddtoyourtoolbox.

4.Beforeanexam,beabletolisteverythingonyoursheets:thesubjects,thetypesofproblemswithinthesections,andthetechniques.You’dbesurprisedbywhatjustbeingabletolistthesectionsandsubjectswilldoforyou,letalonethetypesofproblemsandtoolboxtricks.Thistypeofverbalrecallallowsyoutorecognizetypesofproblemsmorequicklyandhavemoreconfidencebeforeyougointotheexam.

“WhenIwasyounger,IthoughtthatifIdidn’tgetsomethingimmediately,itmeantIwouldneverbeabletogetit,orIwasn’tsmart.Thatisn’ttrueatall,ofcourse.NowIunderstandthatit’sreallyimportanttogetstartedonsomethingearly,leavingtimeforittodigest.Thisleadstostress-freeunderstandingthatmakeslearningalotmoreenjoyable.”

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procrastinationzombiewrap-up

e’vesweptthroughanumberofissuesrelatedtoprocrastinationintheselastfewchapters.Buthereareafewfinalthoughtsthatcanshednewinsightintoprocrastination.

ThePlusesandMinusesofWorkingUnrelentinglyin“TheZone”

AchancemeetingoftwoMicrosofttechiesataFriday-nightpartyin1988resultedinanexcitingsolutiontoamajorsoftwarestumblingblockthatMicrosofthadbasicallygivenupon.Thepairleftthepartytogivetheideaashot,firingupacomputerandgoingthroughtheproblematiccodelinebyline.Laterthatevening,itwasclearthattheywereontosomething.Thatsomething,asFransJohanssondescribesinhisfascinatingbookTheClickMoment,turnedthenearlyabandonedsoftwareprojectintoWindows3.0,whichhelpedturnMicrosoftintotheglobaltechnologytitanitistoday.1Therearetimeswheninspirationseemstoeruptfromnowhere.

Thesekindsofrarecreativebreakthroughs—relaxedmomentsofinsightfollowedbymentallystrenuous,all-out,late-nightlabor—areverydifferentfromatypicaldayofstudyingmathandscience.It’sratherlikesports:Everyonceinawhile,youhaveadayofcompetitionwhenyouneedtogiveeverythingyouhaveunderconditionsofextraordinarystress.Butyoucertainlywouldn’ttraineverysingledayunderthosekindsofconditions.

Ondayswhenyouaresuperproductiveandkeepworkingawaylongintothenight,youmaygetalotdone—butinsubsequentdays,ifyoulookatyourplanner-journal,youmaynotethatyouarelessproductive.Peoplewhomakeahabitofgettingtheirworkdoneinbingesaremuchlessproductiveoverallthanthosewhogenerallydotheirworkinreasonable,limitedstints.2Stayinginthezonetoolongwillsendyoutowardburnout.3

Animpendingdeadlinecanratchetupstresslevels,movingyouintoazonewherethestresshormonescankickinandassistinthinking.Butrelyingonadrenalinecanbeadangerousgame,becauseoncestressgoestoohigh,theabilitytothinkclearlycandisappear.Moreimportant,learningmathandscienceforanupcomingexaminationisverydifferentfromfinishingawrittenreportbyagivenduedate.Thisisbecausemathandsciencedemandthedevelopmentofnewneuralscaffoldsthataredifferentfromthesocial,pictorial,andlanguage-orientedscaffoldsthatourbrainshaveevolvedtoexcelat.Formanypeople,math-andscience-relatedscaffoldsdevelopslowly,alternatingfocused-modeanddiffuse-modethinkingasthematerialisabsorbed.Especiallywhenitcomestolearningmathandscience,thebingeingexcuse,“Idomybestworkunderdeadlines,”issimplynottrue.4

Rememberthearseniceatersatthebeginningofthesechaptersonprocrastination?Backinthe1800s,whenarseniceatingtookholdinonetinyAustrianpopulation,peopleignoredhowharmfulitwaslong-term,eveniftolerancecouldbebuiltup.It’salittlelikenotrecognizingthedangersofprocrastination.

Gettingagriponhabitsofprocrastinationmeansacknowledgingthatsomethingthatfeelspainfulatthemomentcanultimatelybehealthy.Overcomingyoururgetoprocrastinatesharesmuchincommonwithotherminorstressorsthatareultimatelybeneficial.

“WhenIamnotworking,Imustrelax—notworkonsomethingelse!”

—PsychologistB.F.Skinner,reflectingonacrucialrealizationthatbecameaturningpointinhiscareer5

WiseWaiting

We’velearnedthatseeminglygoodtraitscanhavebadconsequences.Einstellunginchess—beingblockedfromseeingabettermovebecauseofpreviouslyconceivednotions—isafineexample.Yourfocusedattention,normallydesirable,keepsyourmindpreoccupiedsothatitdoesn’tseebettersolutions.

Justasfocusedattentionisn’talwaysgood,seeminglynastyhabitsofprocrastinationaren’talwaysbad.Wheneveryoumakeupato-dolist,forexample,youcouldbeaccusedofprocrastinatingonwhateverisn’tfirstonyourlist.Ahealthyformofprocrastinationentailslearningtopauseandreflectbeforejumpinginandaccomplishingsomething.Youarelearningtowaitwisely.Thereisalwayssomethingtobedone.Prioritizingallowsyoutogainbig-picturecontextforyourdecisionmaking.Sometimeswaitingallowsasituationtoresolveitself.

Pausingandreflectingarekey,notonlyinstoppingprocrastinationbutinmathandscienceproblemsolvingingeneral.Youmaybesurprisedtolearnthatthedifferenceinthewaythatmathexperts(professorsandgraduatestudents)andmathnovices(undergraduatestudents)solvephysicsproblemsisthatexpertsareslowertobeginsolvingaproblem.6Expertstookanaverageofforty-fivesecondstofigureouthowtheywouldcategorizeaproblemaccordingtoitsunderlyingphysicsprinciples.Undergraduates,ontheotherhand,simplyrushedrightin,takingonlythirtysecondstodeterminehowtheyshouldproceed.

Unsurprisingly,theconclusionsdrawnbytheundergraduateswereoftenwrongbecausetheirchoiceswerebasedonsuperficialappearancesratherthanunderlyingprinciples.It’sasifexpertstooktheirtimetoconcludethatbroccoliisavegetableandlemonisafruit,whilenovicesbargedintosaythatbroccoliisatinytreewhilelemonsareclearlyeggs.Pausinggivesyoutimetoaccessyourlibraryofchunksandallowsyourbraintomakeconnectionsbetweenaparticularproblemandthebiggerpicture.

Waitingisalsoimportantinabroadercontext.Whenyouhavedifficultypuzzlingoutaparticularmathorscienceconcept,itisimportantnottoletfrustrationtakecontrolanddismissthoseconceptsastoodifficultorabstract.InhisaptlytitledbookStallingforTime,FBIhostagenegotiatorGaryNoesnernotesthatwecouldalllearnfromthesuccessesandfailuresofhostagenegotiation.7Atthebeginningofsuchsituations,emotionsrunhigh.Effortstospeedmattersalongoftenleadtodisaster.

Stavingoffnaturaldesirestoreactaggressivelytoemotionalprovocationsallowstimeforthemoleculesofemotiontograduallydissipate.Theresultingcoolerheadssavelives.

Emotionsthatgoadyoubysaying,“Justdoit,itfeelsright,”canbemisleadinginotherways.Inchoosingyourcareer,forexample,“Followyourpassion”maybelikedecidingtomarryyourfavoritemoviestar.Itsoundsgreatuntilrealityrearsitshead.Theproofisintheoutcome:Overthepastdecades,studentswhohaveblindlyfollowedtheirpassion,withoutrationalanalysisofwhethertheirchoiceofcareertrulywaswise,havebeenmoreunhappywiththeirjobchoicesthanthosewhocoupledpassionwithrationality.8

Allofthisrelatestomyownlife.Ioriginallyhadnopassion,talent,orskillinmath.Butasaresultofrationalconsiderations,Ibecamewillingtogetgoodatit.Iworkedhardtogetgoodatit.AndIknewthatworkinghardwasn’tenough—Ialsohadtoavoidfoolingmyself.

Ididgetgoodatmath.Thatopenedthedoortoscience.AndIgraduallygotgoodatthat,too.AsIgotgood,thepassionalsocame.

Wedevelopapassionforwhatwearegoodat.Themistakeisthinkingthatifwearen’tgoodatsomething,wedonothaveandcanneverdevelopapassionforit.

ProcrastinationFAQs

I’msooverwhelmedbyhowmuchI’vegottodothatIavoidthinkingaboutit,eventhoughitonlymakesmybadsituationworse.WhatcanIdowhenIfeelparalyzedbytheenormityoftheworkIneedtodo?

Writedownthree“microtasks”thatyoucandowithinafewminutes.RememberhowLadyLuckfavorsthosewhotry—justdoyourbesttofocusonsomethingworthwhile.

Atthispoint,closeyoureyesandtellyourmindthatyouhavenothingelsetoworryabout,nootherconcerns,justyourfirstmicrotask.(I’mnotkiddingaboutthe“closeyoureyes”part—remember,thatcanhelpdisengageyoufromyourpreviousthoughtpatterns.9)YoumaywanttoplayaPomodorogamewithyourself.Canyougetastartonthefirstfewpagesofthechapterintwenty-fiveminutes?

Accomplishingalotofdifficulttasksislikeeatingasalami.Yougoslicebyslice—bitbybit.Cheereveryaccomplishment,eventhetiniestones.You’removingahead!

Howlongwillittaketochangemyprocrastinationhabits?

Althoughyouwillprobablyseesomeresultsrightaway,itmaytakeaboutthreemonthsofadjustmenttogetinplaceanewsetofworkinghabitsthatyoulikeandarecomfortablewith.Bepatientandusecommonsense—don’tattempttomakedrasticchangesimmediatelybecausetheymaynotbesustainableandthatmayonlydiscourageyoumore.

Myattentiontendstohopallovertheplace,soit’sdifficultformetostayfocusedonthetaskathand.AmIdoomedtobeaprocrastinator?

Ofcoursenot!ManyofmymostcreativeandsuccessfulstudentshaveovercomeADHDandrelatedattentiondifficultiesusingthetypesoftoolsI’veoutlinedinthisbook.Youcan,too.

Ifyourattentioniseasilydivided,youespeciallywillbenefitfromtoolsthathelpkeepyoufocusedonaspecifictaskforashortperiodoftime.Thesetoolsincludeaplanner-journal,awhiteboardbyyourdoor,atimer,andschedulingandtimingappsandprogramsonyoursmartphoneorcomputer.Allofthesetoolscanhelpyouturnyourzombieprocrastinationhabitsintozombie“takecharge”habits.

INSIGHTSFROMASTUDENTWITHATTENTIONDEFICIT DISORDER

“Asastudentwithattentiondeficitdisorder,Istrugglewithprocrastinationonadailybasis,andstructureistheonlyfoolproofwaytopreventprocrastination.Forme,thismeanswritingEVERYTHINGdowninmyplannerornotebook—thingslikeassignmentduedates,workhours,andtimestohangoutwithfriends.ItalsomeansstudyinginthesameareaeverydayandremovingALLdistractions—forexample,turningmycellphoneoff.“Inowalsodothingsatthesamegeneraltimeeveryweek—mybodylikesstructureandroutine;that’swhyitwasso

hardatthebeginningtobreakoutofmyprocrastinationhabits,butitisalsowhyithasbeensoeasytokeepupwithnewhabitsafteramonthofforcingmyselfintoit.”

—WestonJeshurun,sophomore,undeclaredmajor

You’vetoldmetouseaslittleaspossibleofmywillpowerindealingwithprocrastination.Butshouldn’tIbeusingmywillpoweralotsothatIcanstrengthenit?

Willpowerisalotlikemuscle.Youhavetouseyourmusclestostrengthenanddevelopthemovertime.Butatanygiventime,yourmuscleshaveonlysomuchenergyavailable.Developingandusingwillpowerisabitofabalancingact.10Thisiswhyit’softenimportanttopickonlyonedifficultthingatatimethatrequiresself-disciplineifyouaretryingtomakechanges.

It’seasytogetmyselftositdownandstartmyschoolwork.ButassoonasIstart,IfindmyselftakingquickpeeksatFacebookormye-mail.BeforeIknowit,it’stakenmeeighthourstodoathree-hourtask.

ThePomodorotimerisyourall-purposezombiedistracter.Nooneeversaidyouhavetobeperfectaboutovercominghabitsofprocrastination.Allyouneedtodoiskeepworkingtoimproveyourprocess.

Whatdoyousaytothestudentwhoprocrastinatesbutrefusestoaccepthisownroleandinsteadblameseveryoneandeverythingexcepthimself?Orthestudentwhoflunkseverytestbutthinkssheknowsthematerialsbetterthanherscoresshow?

Ifyoufindyourselfconstantlyfallingintosituationswhereyouthink,“It’snotmyfault,”somethingiswrong.Ultimately,youarethecaptainofyourfate.Ifyouaren’tgettingthegradesyou’dlike,youneedtostartmakingchangestosteeryourselftowardbettershores,ratherthanblamingothers.

Anumberofstudentshavetoldmeovertheyearsthatthey“reallyknewthematerial.”Theyprotestthattheyflunkedbecausetheydon’ttestwell.Often,thestudent’steammatestellmetherealstory:Thestudentdoeslittletonostudying.It’ssadtosaythatmisplacedself-confidenceinone’sabilitiescansometimesreachalmostdelusionallevels.I’mconvincedthisispartofwhyemployersliketohirepeoplewhoaresuccessfulinmathandscience.Goodgradesinthosedisciplinesareoftenbasedonobjectivedataaboutastudent’sabilitytograpplewithdifficultmaterial.

It’sworthreemphasizingthatworld-classexpertsinavarietyofdisciplinesrevealthattheirpathtoexpertisewasn’teasy.Theysloggedthroughsometedious,difficulttimestogettotheircurrentlevelofexpertisewheretheycanglidebyandmakeitalllookeasy.11

NOWYOUTRY!

Pract icingYourZombieWrangling

Thinkofachallengethatyouhavebeenputtingoff.Whatkindofthoughtswouldhelpyouactuallydoit?Forexample,youmightthink:“It’snotreallysodifficult;itwillgeteasieronceIgetstarted;sometimesit’sgoodtodothingsthatIdon’tenjoy;therewardsareworthit.”12

SUMMINGITUP

Procrastinationissuchanimportanttopicthatthissummaryincludeskeytakeawaypointsfromallthisbook’schaptersonovercomingprocrastination:

Keepaplanner-journalsoyoucaneasilytrackwhenyoureachyourgoalsandobservewhatdoesanddoesn’twork.Commityourselftocertainroutinesandtaskseachday.Writeyourplannedtasksoutthenightbefore,soyourbrainhastimetodwellonyourgoalstohelpensuresuccess.Arrangeyourworkintoaseriesofsmallchallenges.Alwaysmakesureyou(andyourzombies!)getlotsofrewards.Takeafewminutestosavorthefeelingsofhappinessandtriumph.Deliberatelydelayrewardsuntilyouhavefinishedatask.Watchforprocrastinationcues.Putyourselfinnewsurroundingswithfewprocrastinationcues,suchasthequietsectionofalibrary.Obstaclesarise,butdon’tmakeapracticeofblamingallyourproblemsonexternalfactors.Ifeverythingisalwayssomebodyelse’sfault,it’stimetostartlookinginthemirror.Gaintrustinyournewsystem.Youwanttoworkhardduringtimesoffocusedconcentration—andalsotrustyoursystemenoughthatwhenitcomestimetorelax,youactuallyrelaxwithoutfeelingsofguilt.Havebackupplansforwhenyoustillprocrastinate.Nooneisperfect,afterall.Eatyourfrogsfirst.

Happyexperimenting!

PAUSEANDRECALL

Closethebookandlookaway.What werethemainideasofthischapter?Whenyougotobedthisevening,t ryrecallingthemainideasagain—just beforesleepoftenseemstobeapart icularlypowerfult imeforset t ingideasmentallyinmind.

ENHANCEYOURLEARNING

1.Ifyouhaveproblemswithbeingeasilydistracted,whataresomegoodapproachestohelpyoupreventprocrastination?

2.Howwouldyoudecidewhenprocrastinationisusefulandwhenitisharmful?

3.Wherehaveyounoticedthatpausingandreflectingbeforechargingforwardhasbeenbeneficialinyourlife?

4.Ifyousitdowntoworkbutfindyourselffritteringawayyourtime,whataresomeactionsyoucantaketoquicklygetyourselfbackontask?

5.Reflectonyourwayofreactingtosetbacks.Doyoutakeactiveresponsibilityforyourpartinthosesetbacks?Ordoyouassumeavictim’srole?Whatwayofrespondingisultimatelymosthelpful?Why?

6.Whywouldthosewhofollowedtheirpassioninchoosingtheircareers,withoutbalancingtheirdecisionwithrationalanalysisoftheirchoice,belesslikelytobehappyinthosecareers?

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enhancingyourmemory

oshuaFoerwasanormalguy.Butsometimesnormalpeoplecandoveryunusualthings.Arecentcollegegrad,Foer(pronounced“four”),livedwithhisparentswhiletryingtomake

agoofbeingajournalist.Hedidn’thaveagreatmemory;heregularlyforgotimportantdateslikehisgirlfriend’sbirthday,couldn’trecallwherehe’dputhiscarkeys,andforgothehadfoodintheoven.Andinhiswork,nomatterhowhardhetriedtocatchhimself,hestillwroteitsinsteadofit’s.

ButFoerwasamazedtofindthatsomepeopleseemedverydifferent.Theycouldmemorizetheorderofashuffleddeckofplayingcardsinonlythirtyseconds,orcasuallyabsorbdozensofphonenumbers,names,faces,events,ordates.Givethesepeopleanyrandompoem,andinminutes,theycouldreciteittoyoufrommemory.

Foerwasjealous.Thesebrilliantmastersofmemory,hethought,musthavesomeunusualwaytheirbrainswerewiredthathelpedthemeasilyrememberprodigiousamountsofdata.

JournalistJoshFoerashepreparestocompeteintheU.S.MemoryChampionships.TheearmufflersandthepinholesinJosh’seyemaskhelphimavoiddistraction,whichisthecompetitivememorizer’sgreatestenemy.Thisisafirmreminderthatit’sbesttofocuswithoutdistractionifyoureallywanttoputsomethingintomemory.

ButthememoryacesFoertalkedtoeachinsistedthattheirprevious,untrainedabilitytorememberwasperfectlyaverage.Improbablethoughitseemed,thesepeopleclaimedthatancientvisualizingtechniqueswerewhatenabledthemtoremembersoquicklyandeasily.Anybodycandoit,Foerheardrepeatedly.Evenyoucoulddoit.1

Andthatgoadingishow,inoneofthemostunlikelyscenariosFoercouldhaveimagined,hefoundhimselfstaringatadeckofcardsasatopfinalistattheU.S.MemoryChampionships.

“Aseducators,inourzealtoencouragestudentstoformchunksratherthansimplymemorizeisolatedfacts,wesometimesgivetheimpressionthatmemorizationisunimportant.(‘WhyshouldImemorizeanequationthatIcanlookup?’)Butmemorizationofkeyfactsisessentialsinceitisthesefactsthatformtheseedsforthecreativeprocessofchunking!Theimportantlessonisthatwemustcontinuejigglingandplayingmentallywiththingswehavememorizedinordertoformchunks.”

—ForrestNewman,professorofastronomyandphysics,SacramentoCityCollege

CanYouRememberWhereYourKitchenTableIs?YourSupersizedVisuospatialMemory

Itmaysurpriseyoutolearnthatwehaveoutstandingvisualandspatialmemorysystems.Whenyouusetechniquesthatrelyonthosesystems,you’renotjustrelyingonrawrepetitiontoburninformationintoyourbrain.Instead,you’reusingfun,memorable,creativeapproachesthatmakeiteasiertosee,feel,orhearwhatyouwanttoremember.Evenbetter,thesetechniquesfreeupyourworkingmemory.Bygroupingthingsinasometimeswackyyetlogicallyretrievablefashion,youeasilyenhanceyourlong-termmemory.Thiscanreallyhelptakethestressoffduringtests.

Here’swhatImeanaboutyourgoodvisualandspatialmemory.Ifyouwereaskedtolookaroundahouseyou’dnevervisitedbefore,youwouldsoonhaveasenseofthegeneralfurniturelayout,wheretheroomswere,thecolorscheme,thepharmaceuticalsinthebathroomcupboard(whoa!).Injustafewminutes,yourmindwouldacquireandretainthousandsofnewpiecesofinformation.Evenweekslater,you’dstillholdfarmoreinyourmindthanifyou’dspentthesameamountoftimestaringatablankwall.Yourmindisbuilttoretainthiskindofgeneralinformationaboutaplace.

Thememorytricksusedbybothancientandmodernmemoryexpertstapsintothesenaturallysupersizedvisuospatialmemorizationabilities.Ourancestorsneverneededavastmemoryfornamesornumbers.Buttheydidneedamemoryforhowtogetbackhomefromthethree-daydeerhunt,orforthelocationoftheplumpblueberriesontherockyslopestothesouthofcamp.Theseevolutionaryneedshelpedlockinsuperior“wherethingsareandhowtheylook”memorysystems.

ThePowerofMemorableVisualImages

Tobegintappingintoyourvisualmemorysystem,trymakingaverymemorablevisualimagerepresentingonekeyitemyouwanttoremember.2Forexample,hereisapictureyoucouldusetorememberNewton’ssecondlaw:f=ma.(Thisisafundamentalrelationshiprelatingforcetomassandaccelerationthatonlytookhumansacouplehundredthousandyearstofigureout.)Theletterfintheformulacouldstandforflying,mformule,anda,well,that’suptoyou.Partofthereasonanimageissoimportanttomemoryisthatimagesconnectdirectlytoyourrightbrain’svisuospatialcenters.3Theimagehelpsyouencapsulateaseeminglyhumdrumandhard-to-remember

conceptbytappingintovisualareaswithenhancedmemoryabilities.

Acreativememorydevice—themonthswiththeprojectingknucklesonhandshavethirty-onedays.Asonecollegecalculusstudentnoted:“Oddlyenough,withthatsimplememorytoolIdoubtIwilleverforgetwhichmonthshavethirty-onedays—whichamazesme.TensecondstolearnsomethingI’vejustavoidedlearningfortwentyyearsbecauseIthoughtitwouldbetootedioustositthereandmemorizeitthroughrepetition.”

Themoreneuralhooksyoucanbuildbyevokingthesenses,theeasieritwillbeforyoutorecalltheconceptandwhatitmeans.Beyondmerelyseeingthemule,youcansmellthemuleandfeelthesamewindypressurethemuleisfeeling.Youcanevenhearthewindwhistlingpast.Thefunnierandmoreevocativetheimages,thebetter.

TheMemoryPalaceTechnique

Thememorypalacetechniqueinvolvescallingtomindafamiliarplace—likethelayoutofyourhouse—andusingitasasortofvisualnotepadwhereyoucandepositconcept-imagesthatyouwanttoremember.Allyouhavetodoiscalltomindaplaceyouarefamiliarwith:yourhome,yourroutetoschool,oryourfavoriterestaurant.Andvoilà!Intheblinkofanimaginativeeye,thisbecomesthememorypalaceyou’lluseasyournotepad.

Thememorypalacetechniqueisusefulforrememberingunrelateditems,suchasagrocerylist

(milk,bread,eggs).Tousethetechnique,youmightimagineagiganticbottleofmilkjustinsideyourfrontdoor,thebreadploppedonthecouch,andacrackedeggdribblingofftheedgeofthecoffeetable.Inotherwords,you’dimagineyourselfwalkingthroughaplaceyouknowwell,coupledwithshockinglymemorableimagesofwhatyoumightwanttoremember.

Let’ssayyouaretryingtorememberthemineralhardnessscale,whichrangesfrom1to10(talc1,gypsum2,calcite3,fluorite4,apatite5,orthoclase6,quartz7,topaz8,corundum9,diamond10).Youcancomeupwithamemorysentencemnemonic:TerribleGiantsCanFindAlligatorsorQuaintTrollsConvenientlyDigestible.Theproblemisthatitcanstillbedifficulttorememberthesentence.Butthingsbecomeeasierifyouthenaddthememorypalace.Atyourfrontdoor,thereisaterriblegiantthere,holdingacan.Onceinside,youfindanalligator....Yougettheidea.Ifyouarestudyingfinance,economics,chemistry,orwhat-have-you,you’dusethesameapproach.

Walkthroughyourmemorypalaceanddeposityourmemorableimages.It’sahelpfulwaytorememberlistssuchasthefiveelementsofastoryorthesevenstepsofthescientificmethod.

Thefirsttimeyoudothis,itwillbeslow.Ittakesabittoconjureupasolidmentalimage.Butthemoreyoudoit,thequickeritbecomes.Onestudyshowedthatapersonusingthememorypalacetechniquecouldremembermorethan95percentofaforty-to-fifty-itemlistafteronlyoneortwo

practicemental“walks”wheretheitemswereplacedonthegroundsofthelocaluniversity.4Inusingthemindthisway,memorizationcanbecomeanoutstandingexerciseincreativitythatsimultaneouslybuildsneuralhooksforevenmorecreativity.What’snottolike?(Well,maybethere’sonethingnottolike:Becausethismethodhooksintoyourvisuospatialsystem,youdonotwanttousethememorypalacetechniquewhenyouaredoingotherspatialtasks,suchasdriving.5Thedistractioncouldprovedangerous.)

NOWYOUTRY!

UsetheMemoryPalace

TopanatomyprofessorTraceyMagrannappliesthememorypalacetechniquetolearningthefivelayersoftheepidermis:“Theepidermishasfivelayers.Fromdeeptosuperficial,theyarethestratumbasale,stratumspinosum,stratumgranulosum,stratumlucidum,andstratumcorneum.Torememberwhichoneisthedeepestlayer,visualizeyourbasement.Thatisthestratumbasale.Togetfromyourbasement(deepestlayer)totheroof(superficiallayer),walkupyourbasementstairs...becareful!Theyarecoveredwithcactusspines(stratumspinosum).Thatleadsyoutothekitchen,wheresomeonehasspilledgranulatedsugaralloverthefloor(stratumgranulosum).Thenyougoupstairsandstoptoputonsuntanlotionbeforeyougototheroof.ThestratumlucidumislikealayerofsuntanlotionbecauseitprotectsyoufromUVraysbutispresentonlyonthepalmsandsoles,sothat’swhereyoupictureyourselfapplyingthelotion.Nowyouarereadytogototheroofandenjoyanicecornonthecob(stratumcorneum).”Canyouthinkofawaytousethememorypalaceinyourstudies?

Songsthathelpcementideasinyourmindarerelatedtothememorypalacetechniqueinthattheyalsomakepreferentialuseofthebrain’srighthemisphere.Therearetunestohelpyourememberthequadraticformula,volumeformulasforgeometricfigures,andmanyothertypesofequations.JustGoogle“quadraticformula”and“song”forexamples,ormakeupyourown.Manynurseryrhymesuseactionsalongwithsongtohelpembedthelyrics(thinkof“LittleBunnyFooFoo”).Usingmeaningfulmotions,fromaprancetoajiggletoanitty-bittyhop,canofferevenmoreneuralhookstoholdideasinmemorybecausemovementproducessensationsthatbecomepartofthememory.

Thesekindsoftechniquescanbehelpfulformanythingsbeyondequations,concepts,andgrocerylists.Evenspeechesandpresentations—thoseoccasionallypetrifyingdo-or-dieexperiences—canbecomemucheasierwhenyourealizethatpotentiallymemorableimagescanhelpthekeyconceptsyouwanttospeakaboutstayinmind.Allyouneedtodoistietheessentialideasyouwanttotalkabouttomemorableimages.SeeJoshuaFoer ’smasterfulTEDtalkforademonstrationofthememorypalacetechniqueforrememberingspeeches.6Ifyou’dliketoseehowtoapplytheseideasdirectlytomemorizingformulas,tryouttheSkillsToolbox.comwebsiteforalistofeasy-to-remembervisualsformathematicalsymbols.7(Forexample,thedividesymbol“/”isachildren’sslide.)

Memoryaids—whethermemorableimages,stickysongs,oreasilyimagined“palaces”—areusefulbecausetheyhelpyoufocusandpayattentionwhenyourmindwouldratherskitteroffanddosomethingelse.Theyhelpremindyouthatmeaningisimportantforremembering,eveniftheinitialmeaningiswacky.Inshort,memorizationtechniquesremindyoutomakewhatyoulearninyourlifemeaningful,memorable,andfun.

MIND-JOGGINGJINGLES

“Inmytenth-gradechemistryclass,wewereintroducedtoAvogadro’snumber—6.02214×107—andnoneofuscouldrememberit.SooneofmyfriendsmadeupasongaboutitwithatuneborrowedfromaGoldenGrahamscerealcommercial(thatturnedouttobeamucholdersongcalled‘Oh,ThemGoldenSlippers’).Sonow,thirtyyearslaterasanolderstudent,IstillrememberAvogadro’snumberbecauseofthatsong.”

—MalcolmWhitehouse,senior,computerengineering

TOPTEACHERTRACEY’SMEMORYTIPS

“Pacingbackandforth,andevenhavingabitofasnackbeforehand,canbehelpfulwhenyouarememorizingbecausethebrainusesalotofenergyduringmentalactivities.Itisalsoimportanttomakeuseofmultipleareasofthebrainwhenlearning.Weusethevisualcortexofthebraintorememberwhatwesee,theauditorycortexforthingswehear,thesensorycortexforthingswefeel,andthemotorcortexforthingswepickupandmove.Byusingmoreareasofthebrainwhilelearning,webuildstrongermemorypatterns,weavingatighterwebthatislesslikelytobeforgottenduringthestressofanexam.Forexample,inanatomylab,studentsshouldpickuptheanatomymodels,closetheireyes,feeleachstructure,andsaythenameofeachpartoutloud.Youcanskipthesensesofsmellandtaste...gottadrawthelinesomewhere!”

—TraceyMagrann,ProfessorofBiologicalSciences,SaddlebackCollege

SUMMINGITUP

Thememorypalacetechnique—placingmemorablenudgesinascenethatisfamiliartoyou—allowsyoutodipintothestrengthofyourvisualmemorysystem.Learningtouseyourmemoryinamoredisciplined,yetcreativemannerhelpsyoulearntofocusyourattention,evenasyoucreatewild,diffuseconnectionsthatbuildstrongermemories.Bymemorizingmaterialyouunderstand,youcaninternalizethematerialinaprofoundway.Andyouarereinforcingthementallibraryyouneedtobecomeagenuinemasterofthematerial.

PAUSEANDRECALL

Closethebookandlookaway.What werethemainideasofthischapter?Tomorrowmorning,asyouareget t ingupandbeginningyourdaily“get t ingout ofbed”rout ine,t rytoseewhatyoucanrecallofthesekeyideas.

ENHANCEYOURLEARNING

1.Describeanimageyoucouldusetohelpyourememberanimportantequation.

2.Pickanylistingoffourormorekeyideasorconceptsfromanyofyourclasses.Describe

howyouwouldencodethoseideasasmemorableimagesandtellwhereyouwoulddeposittheminyourmemorypalace.(Foryourteacher ’ssake,youwillwanttocensorsomeofyourmorememorableimages.AsawittyBritishactressoncesaid,“Idon’tcarewhattheydo,aslongastheydon’tdoitinthestreetandfrightenthehorses.”)

3.Explainthememorypalacetechniqueinawaythatyourgrandmothercouldunderstand.

SPATIALABILIT IESCANBELEARNED—VISIONARYENGINEERINGPROFESSORSHERYLSORBY

SherylSorbyisanaward-winningengineerwhoseresearchinterestsincludedesigning3-Dcomputergraphicsforvisualizingcomplexbehaviors.Hereshetellsherstory.8“Manypeopleerroneouslybelievethatspatialintelligenceisafixedquantity—youeitherhaveitoryoudon’t.Iamheretosayemphaticallythatthisisnotthecase.Infact,Iamlivingproofthatspatialabilitiescanbelearned.Ialmostleftmychosenprofessionofengineeringduetopoorlydevelopedspatialskills,butIworkedatit,developedtheskills,andsuccessfullycompletedmydegree.BecauseIstruggledwithspatialskillsasastudent,Idedicatedmycareertohelpingstudentsdeveloptheirs.VirtuallyallofthestudentsIworkedwithwereabletoimprovethroughpractice.“Humanintelligencetakesmanyforms,rangingfrommusicaltoverbalto

mathematicalandbeyond.Animportantformisspatialthinking.Peoplewithhighspatialintelligencecanimaginewhatobjectswilllooklikefromadifferentvantagepoint,oraftertheyhavebeenrotatedorslicedintwo.Insomecases,spatialintelligencemightbetheabilitytofigureoutthepathyouwouldtaketogetfromoneplacetoanother,armedonlywithamap.“Theabilitytothinkinspatialtermshasbeenshowntobeimportantforsuccessin

careerssuchasengineering,architecture,computerscience,andmanyothers.Thinkaboutthejobofairtrafficcontrollerswhomustimaginetheflightpathsofseveralaircraftatagiventime,ensuringtheirpathsdon’tcross.Imaginealsothespatialskillsrequiredbyanautomechanictofitpartsbackintoanengine.Inrecentstudies,spatialintelligence

hasbeenlinkedtocreativityandinnovation.Inotherwords,thebetteryouareatspatialthinking,themorecreativeandinnovativeyouwillbe!“Wehavefoundthereasonsomestudentshaveweakspatialskillsisthattheylikelyhaven’thadmanychildhoodexperiences

tohelpdeveloptheseskills.Childrenwhospentagooddealoftimetakingthingsapartandbuildingthemagaintypicallyhavegoodspatialability.Somechildrenwhoplayedcertaintypesofsportshavegoodspatialability.Thinkofbasketball.Playershavetoimaginethearcnecessaryfortheballtogointothebasketfromanyplaceonthecourt.“However,evenifsomeonedidn’tdothesekindsofthingsasachild,it’snottoolate.Spatialskillscanbedevelopedwellinto

adulthood—itjusttakespracticeandpatience.“Whatcanyoudo?Tryaccuratelysketchinganobject,andthentrysketchingitfromadifferentviewpoint.Play3-Dcomputer

games.Puttogether3-Dpuzzles(youmayhavetostartwith2-Dpuzzlesfirst!).PutawayyourGPSandtrytonavigatewithamapinstead.Aboveallelse,don’tgiveup—instead,justkeepworkingonit!”

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morememorytips

CreateaLivelyVisualMetaphororAnalogy

Oneofthebestthingsyoucandotonotonlyrememberbutunderstandconceptsinmathandscienceistocreateametaphororanalogyforit—often,themorevisual,thebetter.1Ametaphorisjustawayofrealizingthatonethingissomehowsimilartoanother.Simpleideaslikeonegeographyteacher ’sdescriptionofSyriaasshapedlikeabowlofcerealandJordanasaNikeAirJordansneakercanstickwithastudentfordecades.

Ifyou’retryingtounderstandelectricalcurrent,itcanhelptovisualizeitaswater.Similarly,electricalvoltagecan“feellike”pressure.Voltagehelpspushtheelectricalcurrenttowhereyouwantittogo,justlikeamechanicalpumpusesphysicalpressuretopushrealwater.Asyouclimbtoamoresophisticatedunderstandingofelectricity,orwhatevertopicyouareconcentratingon,youcanreviseyourmetaphors,ortossthemawayandcreatemoremeaningfulones.

Ifyouaretryingtounderstandtheconceptoflimitsincalculus,youmightvisualizearunnerheadingforthefinishline.Theclosertherunnergets,theslowerhegoes.It’soneofthoseslo-mocamerashotswheretherunnerisneverquiteabletoreachtheribbon,justaswemightnotquitebeabletogettotheactuallimit.Incidentally,thelittlebookCalculusMadeEasy,bySilvanusThompson,hashelpedgenerationsofstudentsmasterthesubject.Sometimestextbookscangetsofocusedonallthedetailsthatyoulosesightofthemostimportant,big-pictureconcepts.LittlebookslikeCalculusMadeEasyaregoodtodipintobecausetheyhelpusfocusinasimplewayonthemostimportantissues.

It’softenhelpfultopretendyouaretheconceptyouaretryingtounderstand.Putyourselfinanelectron’swarmandfuzzyslippersasitburrowsthroughaslabofcopper,orsneakinsidethexofanalgebraicequationandfeelwhatit’sliketopokeyourheadoutoftherabbithole(justdon’tletitgetexplodedwithaninadvertent“dividebyzero”).

MOONBEAMSANDSCHOOLDREAMS

“IalwaysstudybeforeIgotobed.Forsomereason,IusuallydreamaboutthematerialIjuststudied.Mosttimesthese‘schooldreams’arequitestrangebuthelpful.Forinstance,whenIwastakinganoperationsresearchclass,IwoulddreamIwasrunningbackandforthbetweennodes,physicallyactingouttheshortestpathalgorithm.PeoplethinkI’mcrazy,butIthinkit’sgreat;itmeansIdon’thavetostudyasmuchasotherpeopledo.Iguessthesedreamsinvolvemysubconsciouslymakingmetaphors.”

—AnthonySciuto,senior,industrialandsystemsengineering

Inchemistry,compareacationwithacatthathaspawsandistherefore“pawsitive,”andananionwithanonionthatisnegativebecauseitmakesyoucry.

Metaphorsareneverperfect.Butthen,allscientificmodelsarejustmetaphors,whichmeanstheyalsobreakdownatsomepoint.2Butnevermindthat—metaphors(andmodels!)arevitallyimportantingivingaphysicalunderstandingofthecentralideabehindthemathematicalorscientificprocessorconceptthatyouaretryingtounderstand.Interestingly,metaphorsandanalogiesareusefulforgettingpeopleoutofEinstellung—beingblockedbythinkingaboutaprobleminthewrongway.Forexample,tellingasimplestoryofsoldiersattackingafortressfrommanydirectionsatoncecanopencreativepathsforstudentstointuithowmanylow-intensityrayscanbeeffectivelyusedtodestroyacanceroustumor.3

Metaphorsalsohelpglueanideainyourmind,becausetheymakeaconnectiontoneuralstructuresthatarealreadythere.It’slikebeingabletotraceapatternwithtracingpaper—metaphorsatleasthelpyougetasenseofwhat’sgoingon.Ifthere’satimewhenyoucan’tthinkofametaphor,justputapenorpencilinyourhandandasheetofpaperinfrontofyou.Whetherusingwordsorpictures,youwilloftenbeamazedatwhatjustnoodlingaboutforaminuteortwowillbring.

METAPHORSANDVISUALIZATIONINSCIENCE

Metaphorsandvisualization—beingabletoseesomethinginyourmind’seye—havebeenuniquelypowerfulinhelpingthescientificandengineeringworldmoveforward.4Inthe1800s,forexample,whenchemistsbegantoimagineandvisualizetheminiatureworldofmolecules,dramaticprogressbegantobemade.Hereisadelightfulillustrationof

monkeysinabenzeneringfromaninsiderspoofofGermanacademicchemicallife,printedin1886.5Notethesinglebondswiththemonkeys’handsandthedoublebondswiththeirtinytails.

SpacedRepetitiontoHelpLodgeIdeasinMemory

Focusingyourattentionbringssomethingintoyourtemporaryworkingmemory.Butforthat“something”tomovefromworkingmemorytolong-termmemory,twothingsshouldhappen:theideashouldbememorable(there’sagiganticflyingmulebrayingf=maonmycouch!),anditmustberepeated.Otherwise,yournaturalmetabolicprocesses,liketinyvampires,simplysuckawayfaint,newlyformingpatternsofconnections.Thisvampiricremovaloffaintpatternsisactuallyagoodthing.Muchofwhatgoesonaroundyouisbasicallytrivial—ifyouremembereditall,you’denduplikeahoarder,trappedinanimmensecollectionofuselessmemories.

Ifyoudon’tmakeapointofrepeatingwhatyouwanttoremember,your“metabolicvampires”cansuckawaytheneuralpatternrelatedtothatmemorybeforeitcanstrengthenandsolidify.

Repetitionisimportant;evenwhenyoumakesomethingmemorable,repetitionhelpsgetthatmemorableitemfirmlylodgedinlong-termmemory.Buthowmanytimesshouldyourepeat?Howlongshouldyouwaitbetweenrepetitions?6Andisthereanythingyoucandotomaketherepetitionprocessmoreeffective?

Researchhasgivenushelpfulinsight.Let’stakeapracticalexample.Sayyouwanttorememberinformationrelatedtotheconceptofdensity—namelythatitissymbolizedbyafunny-lookingsymbol,ρ,whichispronounced“row,”andthatitismeasuredinstandardunitsof“kilogramspercubicmeter.”

Howcanyouconvenientlyandeffectivelycementthisinformationintomemory?(Youknownowthatplacingsmallchunksofinformationlikethisinyourlong-termmemoryhelpsgraduallybuildyourbig-pictureunderstandingofasubject.)

Youmighttakeanindexcardandwrite“ρ”ononesideandtheremaininginformationontheother.Writingappearstohelpyoutomoredeeplyencode(thatis,convertintoneuralmemory

structures)whatyouaretryingtolearn.Whileyouarewritingout“kilogramspercubicmeter,”youmightimagineashadowykilogram(justfeelthatmass!)lurkinginanoversizedpieceofluggagethathappenstobeameteroneachside.Themoreyoucanturnwhatyouaretryingtorememberintosomethingmemorable,theeasieritwillbetorecall.Youwillwanttosaythewordanditsmeaningaloud,tostartsettingauditoryhookstothematerial.

Next,justlookatthesideofthecardwiththe“ρ”onitandseewhetheryoucanrememberwhat’sontheothersideofthecard.Ifyoucan’t,flipitoverandremindyourselfofwhatyouaresupposedtoknow.Ifyoucanremember,putthecardaway.

Nowdosomethingelse—perhapsprepareanothercardandtestyourselfonit.Onceyouhaveseveralcardstogether,tryrunningthroughthemalltoseeifyoucanrememberthem.(Thishelpsyouinterleaveyourlearning.)Don’tbesurprisedifyoustruggleabit.Onceyou’vegivenyourcardsagoodtry,putthemaway.Waitandtakethemoutagainbeforeyougotosleep.Rememberthatsleepiswhenyourmindrepeatspatternsandpiecestogethersolutions.

Brieflyrepeatwhatyouwanttorememberoverseveraldays;perhapsforafewminuteseachmorningoreachevening,changetheorderofyourcardssometimes.Graduallyextendthetimesbetweenrepetitionsasthematerialfirmsitselfintoyourmind.Byincreasingyourspacingasyoubecomemorecertainofmastery,youwilllockthematerialmorefirmlyintoplace.7(GreatflashcardsystemslikeAnkihavebuiltinalgorithmsthatrepeatonascalerangingfromdaystomonths.)

Interestingly,oneofthebestwaystorememberpeople’snamesistosimplytrytoretrievethepeople’snamesfrommemoryatincreasingtimeintervalsafterfirstlearningthename.8Materialthatyoudonotreviewismoreeasilydiscountedorforgotten.Yourmetabolicvampiressuckawaythelinkstothememories.Thisiswhyit’swisetobecarefulaboutwhatyoudecidetoskipwhenreviewingfortests.Yourmemoryforrelatedbutnonreviewedmaterialcanbecomeimpaired.9

SPACEDREPETIT ION—USEFULFORBOTHSTUDENTSANDPROFESSORS!

“Ihavebeenadvisingmystudentstodospacedrepetitionoverdaysandweeks,notjustinmyanalyticcourses,butalsoinmyHistoryofAncientEngineeringcourse.Whenmemorizingstrangenamesandterms,it’salwaysbesttopracticeoverseveraldays.Infact,that’spreciselywhatIdowhenI’mpreparingforlectures—repeatthetermsoutloudoveraperiodofseveraldays,sotheyrolleasilyoffmytonguewhenIsaytheminclass.”

—FabianHadiprionoTan,ProfessorofCivilEngineering,TheOhioStateUniversity

NOWYOUTRY!

CreateaMetaphortoHelpYouLearn

Thinkofaconceptyouarelearningnow.Isthereanotherprocessorideainacompletelydifferentfieldthatsomehowseemssimilartowhatyouarestudying?Seeifyoucancomeupwithahelpfulmetaphor.(Bonuspointsifthere’satouchofsilliness!)

CreateMeaningfulGroups

Anotherkeytomemorizationistocreatemeaningfulgroupsthatsimplifythematerial.Let’ssayyouwantedtorememberfourplantsthathelpwardoffvampires—garlic,rose,hawthorn,andmustard.ThefirstlettersabbreviatetoGRHM,soallyouneedtodoisremembertheimageofaGRAHAMcracker.(Retrieveyourcrackerfromthekitchentableofyourmemorypalace,dustoffthevowels,andyou’regoodtogo.)

It’smucheasiertoremembernumbersbyassociatingthemwithmemorableevents.Theyear1965mightbewhenoneofyourrelativeswasborn,forexample.Oryoucanassociatenumberswithanumericalsystemthatyou’refamiliarwith.Forexample,11.0secondsisagoodrunningtimeforthe100-meterdash.Or75mightbethenumberofknittingstitchescastontoaneedlefortheskihatsyouliketomake.Personally,IliketoassociatenumberswiththefeelingsofwhenIwasorwillbeatagivenage.Thenumber18isaneasyone—that’swhenIwentoutintotheworld.Byage104,Iwillbeanoldbuthappygreat-granny!

Manydisciplinesusememorablesentencestohelpstudentsmemorizeconcepts;thefirstletterofeachwordinthesentenceisalsothefirstletterofeachwordinalistthatneedstobememorized.Medicine,forexample,isladenwithmemorablemnemonics,amongthecleanerofwhichare“SomeLoversTryPositionsthatTheyCan’tHandle”(tomemorizethenamesofthecarpalbonesofthehand)and“OldPeoplefromTexasEatSpiders”(forthecranialbones).

Anotherexampleisfortheincreases-by-tenstructureofthedecimalsystem:KingHenrydiedwhiledrinkingchocolatemilk.Thistranslatestokilo—1,000;hecto—100;deca—10;“while”represents1;deci—0.1;centi—0.01;milli—0.001.

Timeaftertime,thesekindsofmemorytricksprovehelpful.Ifyou’rememorizingsomethingcommonlyused,seewhethersomeone’scomeupwithaparticularlymemorablememorytrickbysearchingitoutonline.Otherwise,trycomingupwithyourown.

BEWAREOFMISTAKINGAMEMORYTRICKFORACTUALKNOWLEDGE

“Inchemistrywehavethephraseskittivicermanfeconikuzin,whichhasthecadenceofarapsong.Itrepresentsthefirstrowofthetransitionmetalsontheperiodictable(Sc,Ti,V,Cr,Mn,Fe,Co,Ni,Cu,Zn).Then,therestofthetransitionmetalscanbeplacedonablankperiodictablebyothermemorytricks.Forexample,studentsremembertoplaceAg(silver)andAu(gold)inthesameverticalgroupasCu(copper)sincecopper,silver,andgoldareallusedtomakecoins.“Unfortunately,somestudentscomeawaythinkingthat’sthereasonthesemetalsareinthesameverticalcolumn—

becausetheyareusedtomakecoins.Therealreasonhastodowithsimilaritiesinchemicalpropertiesandvalences.“Thisisanexampleofhowstudentssometimesmistakeamemorytrickforactualknowledge.Alwaysbewaryof

confusingwhatistrulygoingonwiththemetaphoryouareusingtohelpyourmemory.”

—WilliamPietro,ProfessorofChemistry,YorkUniversity,Toronto,Ontario

CreateStories

Noticethatthegroupsmentionedpreviouslyoftencreatemeaningthroughstory,eventhoughthestorymightbeshort.PoorKingHenryshouldn’thavedrunkthatchocolatemilk!Storytellingingeneralhaslongbeenavitallyimportantwayofunderstandingandretaininginformation.ProfessorVeraPavri,ahistorianofscienceandtechnologyatYorkUniversity,tellsherstudentsnottothinkof

lecturesaslecturesbutasstorieswherethereisaplot,characters,andoverallpurposetothediscussion.Thebestlecturesinmathandscienceareoftenframedlikethrillers,openingwithanintriguingproblemthatyoujusthavetofigureout.Ifyourinstructororbookdoesn’tpresentthematerialwithaquestionthatleavesyouwantingtofindtheanswer,seeifyoucanfindthatquestionyourself—thensetaboutansweringit.10Anddon’tforgetthevalueofstoryasyoucreatememorytricks.

WRITEON!

“ThenumberonethingIstresswhenstudentscometoseemeisthatthereisadirectconnectionbetweenyourhandandyourbrain,andtheactofrewritingandorganizingyournotesisessentialtobreakinglargeamountsofinformationdownintosmallerdigestiblechunks.IhavemanystudentswhoprefertotypetheirnotesinaWorddocumentoronslides,andwhenthesestudentsarestruggling,thefirstthingIrecommendistoquittypingandstartwriting.Ineverycase,theyperformbetteronthenextsectionofmaterial.”

—JasonDechant,Ph.D.,CourseDirector,HealthPromotionandDevelopment,SchoolofNursing,UniversityofPittsburgh

MuscleMemory

We’vealreadymentionedthatwritingoutacardbyhandappearstohelpcementideasinthemind.Althoughthereislittleresearchinthisarea,11manyeducatorshaveobservedthatthereseemstobeamusclememoryrelatedtowritingbyhand.Forexample,whenyoufirststareatanequation,itcanappearutterlymeaningless.Butifyouthoughtfullywritetheequationoutseveraltimesonasheetofpaper,youwillbestartledbyhowtheequationwillbegintotakelifeandmeaninginyourmind.Inarelatedvein,somelearnersfindthatreadingproblemsorformulasaloudhelpsthemunderstandbetter.Justbewaryofexerciseslikewritinganequationoutahundredtimesbyhand.Thefirstfewtimesmaygiveyouvalue,butafterawhile,itsimplybecomesaroteexercise—thetimecouldbebetterspentelsewhere.

TALKTOYOURSELF

“Ioftentellmystudentstotalktothemselvesinsteadofjusthighlightingandrereading.Theylookatmequizzically,likeIamabsolutelyinsane(whichcouldbetrue).ButIhavehadmanystudentscomebacktomelaterandsaythatitreallyworksandthatthisisnowoneoftheirstudytools.”

—DinaMiyoshi,AssistantProfessorofPsychology,SanDiegoMesaCollege

RealMuscleMemory

Ifyoureallywanttoboostyourmemoryaswellasyourgeneralabilitytolearn,itseemsoneofthe

bestwaystodoitistoexercise.Severalrecentexperimentsinbothanimalsandhumanshavefoundthatregularexercisecanmakeasubstantiveimprovementinyourmemoryandlearningabilities.Exercise,itseems,helpscreatenewneuronsinareasthatrelatetomemory.Italsocreatesnewsignalingpathways.12Itseemsthatdifferenttypesofexercise—runningorwalking,forexample,versusstrengthtraining—mayhavesubtlydifferentmoleculareffects.Butbothaerobicandresistanceexerciseexertsimilarlypowerfulresultsonlearningandmemory.

MemoryTricksHelpYouBecomeanExpertMoreQuickly

Here’sthebottomline.Byusingmentalpicturesinsteadofwordstorememberthings,youcanleapmoreeasilyintoexpertstatus.Inotherwords,learningtoprocessideasvisuallyinmathandscienceisapowerfulwaytobecomeamasterofthematerial.13Andusingothermemorytrickscangreatlyenhanceyourabilitytolearnandretainthematerial.

Puristsmightsniffthatusingoddballmemorizationgimmicksisn’treallylearning.Butresearchhasshownthatstudentswhousethesetypesoftricksoutperformthosewhodon’t.14Inaddition,imagingresearchonhowpeoplebecomeexpertsshowsthatsuchmemorytoolsspeeduptheacquisitionofbothchunksandbig-picturetemplates,helpingtransformnovicestosemiexpertsmuchmorequickly—eveninamatterofweeks.15Memorytricksallowpeopletoexpandtheirworkingmemorywitheasyaccesstolongtermmemory.

What’smore,thememorizationprocessitselfbecomesanexerciseincreativity.Themoreyoumemorizeusingtheseinnovativetechniques,themorecreativeyoubecome.Thisisbecauseyouarebuildingwild,unexpectedpossibilitiesforfutureconnectionsearlyon,evenasyouarefirstinternalizingtheideas.Themoreyoupracticeusingthistypeof“memorymuscle,”themoreeasilyyouwillbeabletoremember.Whereatfirstitmaytakefifteenminutestobuildanevocativeimageforanequationandembeditin,say,thekitchensinkofyourmemorypalace,itcanlatertakeonlyminutesorsecondstoperformasimilartask.

Youwillalsorealizethatasyoubegintointernalizekeyaspectsofthematerial,takingalittletimetocommitthemostimportantpointstomemory,youcometounderstanditmuchmoredeeply.Theformulaswillmeanfarmoretoyouthantheywouldifyousimplylookedthemupinabook.Andyou’llbeabletoslingthoseformulasaroundmoreproficientlyontestsandinreal-worldapplications.

Onestudyofhowactorsmemorizetheirscriptsshowedthattheyavoidverbatimmemorization.Instead,theydependonanunderstandingofthecharacters’needsandmotivationsinordertoremembertheirlines.16Similarly,themostimportantpartofyourmemorizationpracticesistounderstandwhattheformulasandsolutionstepsreallymean.Understandingalsohelpsalotwiththememorizationprocess.

Youmayobjectandsaythatyou’renotcreative—thatanequationortheorycouldhardlyhaveitsowngrandiosemotivationsorpersnicketyemotionalneedstohelpyouunderstandandrememberit.Butrememberthatinnertwo-year-old.Yourchildlikecreativityisstillthere—youjustneedtoreachouttoit.

MEMORYTRICKSWORK

“Ontopofworkingtowardmyengineeringdegree,Iamintheprocessofgettingmyparamediclicense(onlytwomonthsleft!)andhavetomemorizealargeselectionofdrugsanddosagesforbothadultandpediatricpatients.Atfirst,thisseemedoverwhelming,especiallysincetherewillbelivesatstake.ButIquicklyfoundlittletricksthatmadelearningeasy.Take,forexample,thedrugfurosemide,alsocalledLasix,whichdrawsfluidoutofthebody.ThedoseIneededtorememberwas40milligrams.Thistomewasagodsend,asthenumbers4–0appearedtomeintheword(4–0semide=furosemide).Itisthingslikethisthattrulycancementideasandknowledgeinourheads.Inowdon’teverhavetoeventhinktwiceaboutit.Trulyremarkable.”

—WilliamKoehler,sophomore,mechanicalengineering

NOWYOUTRY!

SongstoHelpYouLearn

Makeupasongtorememberanidentity,integral,orscientificformulathatyouneedforclass.Havingsomeoftheseimportantconceptsmemorized,throughwhatevertrickyouneed,willmakemorecomplicatedproblemseasierandfastertosolve.

SUMMINGITUP

Metaphorscanhelpyoulearndifficultideasmorequickly.Repetitioniscriticalinallowingyoutofirmupwhatyouwanttorememberbeforetheideasfadeaway.Meaningfulgroupsandabbreviationscanallowyoutosimplifyandchunkwhatyouaretryingtolearnsoyoucanstoreitmoreeasilyinmemory.Stories—eveniftheyarejustusedassillymemorytricks—canallowyoutomoreeasilyretainwhatyouaretryingtolearn.Writingandsayingwhatyouaretryingtolearnseemstoenhanceretention.Exerciseispowerfullyimportantinhelpingyourneuronstogrowandmakenewconnections.

PAUSEANDRECALL

Rememberhowimportant it canbetosomet imesthinkofwhat youarelearninginaplacedifferent fromwhereyoulearnedit .Trythat techniqueagainasyourecallthekeyideasofthischapter.Peoplesomet imesrecollect thefeeloftheplacewheretheywerestudying—eventhecushionyfeelofthearmchair,orthepart icularmusicorpictureonthewallinthecoffeeshopwheretheyweresit t ing—tohelpcueamemory.

ENHANCEYOURLEARNING

1.Takeapieceofpaperanddoodletocreateavisualorverbalmetaphorforaconceptyouaretryingtounderstandnowinmathorscience.

2.Lookatachapterinabookyouarereadinginmathorscience.Createaquestionaboutthatmaterialthatwouldmakeyouwanttolearnmoreaboutit.

3.Justbeforeyoutogosleep,reviewsomethingmentallythatyouaretryingtolearn.Toboostthisprocess,reviewityetagainwhenyoufirstwakeup.

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learningtoappreciateyourtalent

WorktowardanIntuitiveUnderstanding

Wecanlearnalotabouthowtodomathandsciencefromsports.Inbaseball,forexample,youdon’tlearnhowtohitinoneday.Instead,yourbodyperfectsyourswingfromplentyofrepetitionoveraperiodofyears.Smoothrepetitioncreatesmusclememory,sothatyourbodyknowswhattodofromasinglethought—onechunk—insteadofhavingtorecallallthecomplexstepsinvolvedinhittingaball.1

Inthesameway,onceyouunderstandwhyyoudosomethinginmathandscience,youdon’thavetokeepreexplainingthehowtoyourselfeverytimeyoudoit.It’snotnecessarytogoaroundwith100beansinyourpocketandtolayout10rowsof10beansagainandagainsothatyougetthat10×10=100.Atsomepoint,youjustknowitfrommemory.Forexample,youmemorizetheideathatyousimplyaddexponents—thoselittlesuperscriptnumbers—whenmultiplyingnumbersthathavethesamebase(104×105=109).Ifyouusetheprocedurealot,bydoingmanydifferenttypesofproblems,youwillfindthatyouunderstandboththewhyandthehowbehindtheprocedurefarbetterthanyoudoaftergettingaconventionalexplanationfromateacherorbook.Thegreaterunderstandingresultsfromthefactthatyourmindconstructedthepatternsofmeaning,ratherthansimplyacceptingwhatsomeoneelsehastoldyou.Remember—peoplelearnbytryingtomakesenseoutofinformationtheyperceive.Theyrarelylearnanythingcomplexsimplybyhavingsomeoneelsetellittothem.(Asmathteacherssay,“Mathisnotaspectatorsport.”)

Chessmasters,emergencyroomphysicians,fighterpilots,andmanyotherexpertsoftenhavetomakecomplexdecisionsrapidly.Theyshutdowntheirconscioussystemandinsteadrelyontheirwell-trainedintuition,drawingontheirdeeplyingrainedrepertoireofchunks.2Atsomepoint,self-consciously“understanding”whyyoudowhatyoudojustslowsyoudownandinterruptsflow,resultinginworsedecisions.

Teachersandprofessorscaninadvertentlygettoocaughtupinfollowingrules.Inanintriguingstudythatillustratesthis,sixpeoplewerefilmeddoingCPR,onlyoneofwhomwasaprofessionalparamedic.3Professionalparamedicswerethenaskedtoguesswhowastherealparamedic.Ninetypercentofthese“realdeal”expertparamedicschosecorrectly,remarkingalongthelinesof“heseemedtoknowwhathewasdoing.”4CPRinstructors,ontheotherhand,couldpicktherealparamedicoutofthelineuponly30percentofthetime.Theseoverlypickytheoreticianscriticizedtherealexpertsinthefilmsforissuessuchasnottakingthetimetostopandmeasurewheretoputtheirhands.Preciserulefollowinghadcometomeanmoretotheinstructorsthanpracticality.

Onceyouunderstandwhyyoudosomethinginmathandscience,youshouldn’tkeepreexplainingthehow.Suchoverthinkingcanleadtochoking.

NoNeedforGeniusEnvy

JustasOlympicathletesdon’tbuildtheirathleticprowesssimplybyspendingafewhoursjoggingontheweekendsorliftingafewweightsintheirsparetime,chessgrandmastersdon’tconstructtheirneuralstructuresthroughlast-minutecramming.Instead,theirknowledgebaseisgraduallybuiltovertimeandwithplentyofpracticethatbuildstheirunderstandingofbig-picturecontext.Practicelikethisplacesthememorytracesprominentlyinthewarehouseoflong-termmemory,wheretheneuralpatterncanbequicklyandeasilyaccessedwhenneeded.5

Let’sreturntochessmasterMagnusCarlsen—thatfast-thinkinggeniusofspeedchessaswellasregularchess.Carlsenhasanextraordinarygraspofthepatternsofthousandsofpreviouslyplayedchessgames—hecanlookatthearrangementofanendgameonachessboardandinstantlytellyouwhichofmorethantenthousandgamesofpastcenturiesitwasdrawnfrom.Inotherwords,Carlsenhascreatedavastchunkedlibraryofpotentialsolutionpatterns.Hecanquicklyrifflethroughthechunkstoseewhatothershavedonewhenfacedwithsituationssimilartowhatheisfacing.6

Carlsenisn’tunusualinwhatheisdoing,althoughhedoesitbetterthanallbutaveryfewpastandpresentchessplayers.Itistypicalforgrandmasterstospendatleastadecadepracticingandstudyingtolearnthousandsofmemorychunkpatterns.7Thesereadilyavailablepatternsallowthemtorecognizethekeyelementsinanygamesetupmuchmorequicklythanamateurs;theydevelopaprofessionaleyesotheycanrapidlyintuitthebestcourseofactioninanysituation.8

Butwait.Aren’tchessmastersandpeoplewhocanmultiplysix-digitnumbersintheirheadssimplyexceptionallygifted?Notnecessarily.I’mgoingtotellittoyoustraight—sure,intelligencematters.Beingsmarteroftenequatestohavingalargerworkingmemory.Yourhotrodofamemorymaybeabletoholdninethingsinsteadoffour,andyoulatchontothosethingslikeabulldog,whichmakesiteasiertolearnmathandscience.

Butguesswhat?Italsomakesitmoredifficultforyoutobecreative.Howisthat?It’souroldfriendandenemy—Einstellung.Theideayoualreadyareholdinginmindblocksyou

fromfreshthoughts.Asuperbworkingmemorycanholditsthoughtssotightlythatnewthoughtscan’teasilypeekthrough.SuchtightlycontrolledattentioncoulduseanoccasionalwhiffofADHD-likefreshair—theability,inotherwords,tohaveyourattentionshiftevenifyoudon’twantittoshift.Yourabilitytosolvecomplexproblemsmaymakeyouoverthinksimpleproblems,goingfortheconvolutedanswerandoverlookingthesimple,moreobvioussolution.Researchhasshownthatsmartpeoplecanhavemoreofatendencytolosethemselvesintheweedsofcomplexity.Peoplewithlessapparentintellectualhorsepower,ontheotherhand,cancutmoreeasilytosimplersolutions.9

IT ’SNOTWHATYOUKNOW;IT ’SHOWYOUTHINK

“ExperiencehasshownmeanalmostinversecorrelationbetweenhighGREscoresandultimatecareersuccess.Indeed,manyofthestudentswiththelowestscoresbecamehighlysuccessful,whereasasurprisingnumberofthe‘geniuses’fellbythewaysideforsomereasonorother.”10

—BillZettler,Ph.D.,ProfessorofBiology,longtimeacademicadvisor,andwinneroftheTeacheroftheYearAward,UniversityofFlorida,Gainesville,Florida

Ifyouareoneofthosepeoplewhocan’tholdalotinmindatonce—youlosefocusandstartdaydreaminginlectures,andhavetogettosomeplacequiettofocussoyoucanuseyourworkingmemorytoitsmaximum—well,welcometotheclanofthecreative.Havingasomewhatsmallerworkingmemorymeansyoucanmoreeasilygeneralizeyourlearningintonew,morecreativecombinations.Becauseyourworkingmemory,whichgrowsfromthefocusingabilitiesoftheprefrontalcortex,doesn’tlockeverythingupsotightly,youcanmoreeasilygetinputfromotherpartsofyourbrain.Theseotherareas,whichincludethesensorycortex,notonlyaremoreintunewithwhat’sgoingonintheenvironment,butalsoarethesourceofdreams,nottomentioncreativeideas.11Youmayhavetoworkhardersometimes(orevenmuchofthetime)tounderstandwhat’sgoingon,butonceyou’vegotsomethingchunked,youcantakethatchunkandturnitoutsideinandinsideround—puttingitthroughcreativepacesevenyoudidn’tthinkyouwerecapableof!

Here’sanotherpointtoputintoyourmentalchunker:Chess,thatbastionofintellectuals,hassomeeliteplayerswithroughlyaverageIQs.Theseseeminglymiddlingintellectsareabletodobetterthansomemoreintelligentplayersbecausetheypracticemore.12That’sthekeyidea.Everychessplayer,whetheraverageorelite,growstalentbypracticing.Itisthepractice—particularlydeliberatepracticeonthetoughestaspectsofthematerial—thatcanhelpliftaveragebrainsintotherealmofthosewithmore“natural”gifts.Justasyoucanpracticeliftingweightsandgetbiggermusclesovertime,youcanalsopracticecertainmentalpatternsthatdeepenandenlargeinyourmind.Interestingly,itseemsthatpracticemayhelpyouexpandyourworkingmemory.Researchersonrecallhavefoundthatdoingexercisestorepeatlongerandlongerstringsofdigits

backwardseemstoimproveworkingmemory.13Giftedpeoplehavetheirownsetofdifficulties.Sometimeshighlygiftedkidsarebullied,sothey

learntohideorsuppresstheirgiftedness.Thiscanbedifficulttorecoverfrom.14Smarterpeoplealsosometimesstrugglebecausetheycansoeasilyimagineeverycomplexity,goodandbad.Extremelysmartpeoplearemorelikelythanpeopleofnormalintelligencetoprocrastinatebecauseitalwaysworkedwhentheyweregrowingup,whichmeanstheyarelesslikelytolearncertaincriticallifeskillsearlyon.

Whetheryouarenaturallygiftedoryouhavetostruggletogetasolidgraspthefundamentals,youshouldrealizethatyouarenotaloneifyouthinkyouareanimpostor—thatit’saflukewhenyouhappentodowellonatest,andthatonthenexttest,forsurethey(andyourfamilyandfriends)arefinallygoingtofigureouthowincompetentyoureallyare.Thisfeelingissoextraordinarilycommonthatitevenhasaname—the“impostorphenomenon.”15Ifyousufferfromthesekindsoffeelingsofinadequacy,justbeawarethatmanyotherssecretlysharethem.

Everyonehasdifferentgifts.Astheoldsayinggoes,“Whenonedoorcloses,anotheropens.”Keepyourchinupandyoureyeontheopendoor.

REACHINGTOWARDTHEINFINITE

Somefeelthatdiffuse,intuitivewaysofthinkingaremoreintunewithourspirituality.Thecreativitythatdiffusethinkingpromotessometimesseemsbeyondhumanunderstanding.AsAlbertEinsteinnoted,“Thereareonlytwowaystoliveyourlife.Oneisasthoughnothingisamiracle.Theother

isasifeverythingis.”

DON’TUNDERESTIMATEYOURSELF

“IcoachScienceOlympiadatourschool.Wehavewonthestatechampionshipeightoutofthelastnineyears.Wefellonepointshortofwinningthestatethisyear,andweoftenfinishinthetopteninthenation.Wehavefoundthatmanyseeminglytopstudents(whoaregettinganA+inalltheirclasses)donotperformaswellunderthepressureofaScienceOlympiadeventasthosewhocanmentallymanipulatetheknowledgetheyhave.Interestingly,thissecondtier(ifyouwill)ofstudentsattimesseemtothinkofthemselvesaslessintelligentthanthesetopstudents.Iwouldmuchrathertakeostensiblylower-performingstudentswhocanthinkcreativelyontheirfeet,astheOlympiadrequires,thantopstudentswhogetflusteredifthequestionsbeingposeddon’texactlyfitthememorizedchunksintheirbrains.”

—MarkPorter,biologyteacher,MiraLomaHighSchool,Sacramento,California

SUMMINGITUP

Atsomepoint,afteryou’vegotchunkedmaterialwellinhand(andinbrain),youstarttoletgoofconsciousawarenessofeverylittledetailanddothingsautomatically.Itmayseemintimidatingtoworkalongsideotherstudentswhograspmaterialmorequicklythanyoudo.But“average”studentscansometimeshaveadvantageswhenitcomestoinitiative,abilitytogetthingsdone,andcreativity.Partofthekeytocreativityistobeabletoswitchfromfullfocusedconcentrationtotherelaxed,daydreamydiffusemode.

Focusingtoointentlycaninhibitthesolutionyouareseeking—liketryingtohammerascrewbecauseyouthinkit’sanail.Whenyouarestuck,sometimesit’sbesttogetawayfromaproblemforawhileandmoveontosomethingelse,ortosimplysleeponit.

PAUSEANDRECALL

Closethebookandlookaway.What werethemainideasofthischapter?Pausealsotot rytorecalltheessent ialideasofthebookasawholesofar.

ENHANCEYOURLEARNING

1.Thinkofanareawherepersistencehaspaidoffforyouinyourlife.Isthereanewareawhereyouwouldliketostartdevelopingyourpersistence?Whatbackupplancanyoudevelopforlowtimeswhenyoumightfeellikefaltering?

2.Peopleoftentrytostoptheirdaydreaming,becauseitinterruptsactivitiestheytrulyintendtofocuson,likelisteningtoanimportantlecture.Whatworksbetterforyou—forcingyourselftomaintainfocus,orsimplybringingyourattentionbacktothematterathandwhenyounoticeyourattentionwandering?

FROMSLOWLEARNERTOSUPERSTAR:NICKAPPLEYARD’SSTORY

NickAppleyardleadstheAmericasbusinessunitasavicepresidentinahigh-techcompanythatdevelopsandsupportsadvancedphysicssimulationtoolsusedinaerospace,automotive,energy,biomedical,andmanyothersectorsoftheeconomy.HereceivedhisdegreeinmechanicalengineeringdegreefromtheUniversityofSheffieldinEngland.“Growingup,Iwasbrandedaslowlearnerandaproblemchildbecauseofit.Theselabelsimpactedmedeeply.Ifeltlikemyteacherstreatedmeasifthey’dgivenupanyhopethatIcouldsucceed.Tomakemattersworse,myparentsalsobecamefrustratedwithmeandmyeducationalprogress.Ifeltthedisappointmentmostseverelyfrommyfather,aseniorphysicianatamajorteachinghospital.(Ilearnedlaterinlifethathehadhadsimilardifficultiesearlyinhischildhood.)Itwasaviciouscirclethatimpactedmyconfidenceineveryaspectoflife.“Whatwastheproblem?Mathandeverythingassociatedwithit—fractions,times

tables,longdivision,algebra,younameit.Itwasallboringandcompletelypointless.“Oneday,somethingbegantochange,althoughIdidn’trealizeitatthetime.Myfather

broughthomeacomputer.Ihadheardaboutkidsintheirteenswritinghomecomputergamesthateveryonewantedtoplay,andbecomingmillionairesovernight.Iwantedtobeoneofthosekids.“Iread,practiced,andwroteharderandharderprograms,allofwhichinvolvedsomekindofmath.Eventually,apopularUK

computermagazineacceptedoneofmyprogramsforpublication—arealthrillforme.“NowIseeeverydayhowmathematicsisappliedfordesigningthenextgenerationofautomobiles,forhelpingtoputrockets

intospace,andforanalyzinghowthehumanbodyworks.“Mathematicsisnolongerpointless.Itisinsteadasourceofwonder—andofagreatcareer!”

T

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sculptingyourbrain

histime,eleven-year-oldSantiagoRamónyCajal’scrimehadbeentobuildasmallcannonandblowaneighbor ’snew,largewoodengateintosplinters.InruralSpainofthe1860s,there

weren’tmanyoptionsforoddballjuveniledelinquents.That’showtheyoungCajalfoundhimselflockedinaflea-riddenjail.

Cajalwasstubbornandrebellious.Hehadasingleoverwhelmingpassion:art.Butwhatcouldhedowithpaintinganddrawing?EspeciallysinceCajalignoredtherestofhisstudies—particularlymathandscience,whichhethoughtwereuseless.

Cajal’sfather,DonJusto,wasastrictmanwhohadbroughthimselfupfromvirtuallynothing.Thefamilywasdefinitelynotonaristocraticeasystreet.Totryandgivehissonmuch-neededdisciplineandstability,DonJustoapprenticedhimouttoabarber.Thiswasadisaster,asCajaljustneglectedhisstudiesevenfurther.Beatenandstarvedbyhisteachersinanattempttobringhimaround,Cajalwasamocking,shockingdisciplinarynightmare.

SantiagoRamónyCajalwontheNobelPrizeforhismanyimportantcontributionstoourunderstandingofthestructureandfunctionofthenervoussystem.1Inthispicture,Cajallooksmorelikeanartistthanascientist.Hiseyesshowahintofthesamemischiefthatbroughthimsomuchtroubleasachild.

Cajalmetandworkedwithmanybrilliantscientiststhroughhislifetime,peoplewhowereoftenfarsmarterthanhe.InCajal’srevealingautobiography,however,hepointedoutthatalthoughbrilliantpeoplecandoexceptionalwork,justlikeanyoneelse,theycanalsobecarelessandbiased.Cajalfeltthekeytohissuccesswashisperseverance(the“virtueofthelessbrilliant”2)coupledwithhisflexibleabilitytochangehismindandadmiterrors.Underlyingeverythingwasthesupportofhislovingwife,DoñaSilveríaFañanásGarcía(thecouplehadsevenchildren).Anyone,Cajalnoted,evenpeoplewithaverageintelligence,cansculpttheirownbrain,sothateventheleastgiftedcanproduceanabundantharvest.3

WhoknewthatSantiagoRamónyCajalwouldonedaynotonlyearntheNobelPrize,buteventuallybecomeknownasthefatherofmodernneuroscience?

ChangeYourThoughts,ChangeYourLife

SantiagoRamónyCajalwasalreadyinhisearlytwentieswhenhebeganclimbingfrombad-boydelinquencyintothetraditionalstudyofmedicine.Cajalhimselfwonderedifperhapshisheadhad

simply“grownwearyoffrivolityandirregularbehaviorandwasbeginningtosettledown.”4There’sevidencethatmyelinsheaths,thefattyinsulationthathelpssignalsmovemorequickly

alonganeuron,oftendon’tfinishdevelopinguntilpeopleareintheirtwenties.Thismayexplainwhyteenagersoftenhavetroublecontrollingtheirimpulsivebehavior—thewiringbetweenintentionandcontrolareasisn’tcompletelyformed.5

“Deficienciesofinnateabilitymaybecompensatedforthroughpersistenthardworkandconcentration.Onemightsaythatworksubstitutesfortalent,orbetteryetthatitcreatestalent.”6

—SantiagoRamónyCajal

Whenyouuseneuralcircuits,however,itseemsyouhelpbuildthemyelinsheathoverthem—nottomentionmakingmanyothermicroscopicchanges.7Practiceappearstostrengthenandreinforceconnectionsbetweendifferentbrainregions,creatinghighwaysbetweenthebrain’scontrolcentersandthecentersthatstoreknowledge.InCajal’scase,itseemshisnaturalmaturationprocesses,coupledwithhisowneffortstodevelophisthinking,helpedhimtotakecontrolofhisoverallbehavior.8

Itseemspeoplecanenhancethedevelopmentoftheirneuronalcircuitsbypracticingthoughtsthatusethoseneurons.9We’restillintheinfancyofunderstandingneuraldevelopment,butonethingisbecomingclear—wecanmakesignificantchangesinourbrainbychanginghowwethink.

What’sparticularlyinterestingaboutCajalisthatheachievedhisgreatnesseventhoughhewasn’tagenius—atleast,notintheconventionalsenseoftheterm.Cajaldeeplyregrettedthatheneverhada“quickness,certainty,andclearnessintheuseofwords.”10What’sworseisthatwhenCajalgotemotional,helosthiswaywithwordsalmostentirely.Hecouldn’trememberthingsbyrote,whichmadeschool,whereparrotingbackinformationwasprized,agonyforhim.ThebestCajalcoulddowastograspandrememberkeyideas;hefrequentlydespairedhismodestpowersofunderstanding.11YetsomeofthemostexcitingareasofneuroscientificresearchtodayarerootedinCajal’soriginalfindings.12

Cajal’steachers,asCajallaterrecollected,showedasadlymistakenvaluingofabilities.Quicknesswastakenascleverness,memoryforability,andsubmissivenessforrightness.13Cajal’ssuccessdespitehis“flaws”showsushoweventoday,teacherscaneasilyunderestimatetheirstudents—andstudentscanunderestimatethemselves.

DeepChunking

Cajalworkedhiswayfitfullythroughmedicalschool.AfteradventuresinCubaasanarmydoctorandseveralfailedattemptsatcompetitiveexaminationstoplaceasaprofessor,hefinallyobtainedapositionasaprofessorofhistology,studyingthemicroscopicanatomyofbiologicalcells.

Eachmorninginhisworkinstudyingthecellsofthebrainandthenervoussystem,Cajalcarefullypreparedhismicroscopeslides.Thenhespenthourscarefullyviewingthecellsthathisstainshadhighlighted.Intheafternoon,Cajallookedtotheabstractpictureofhismind’seye—whathecouldrememberfromhismorning’sviewings—andbegantodrawthecells.Oncefinished,Cajal

comparedhisdrawingwiththeimagehesawinthemicroscope.ThenCajalwentbacktothedrawingboardandstartedagain,redrawing,checking,andredrawing.Onlyafterhisdrawingcapturedthesynthesizedessence,notofjustasingleslide,butoftheentirecollectionofslidesdevotedtoaparticulartypeofcell,didCajalrest.14

Cajalwasamasterphotographer—hewaseventhefirsttowriteabookinSpanishonhowtodocolorphotography.Butheneverfeltthatphotographscouldcapturethetrueessenceofwhathewasseeing.Cajalcouldonlydothatthroughhisart,whichhelpedhimabstract—chunk—realityinawaythatwasmostusefulforhelpingothersseetheessenceofthechunks.

Asynthesis—anabstraction,chunk,orgistidea—isaneuralpattern.Goodchunksformneuralpatternsthatresonate,notonlywithinthesubjectwe’reworkingin,butwithothersubjectsandareasofourlives.Theabstractionhelpsyoutransferideasfromoneareatoanother.15That’swhygreatart,poetry,music,andliteraturecanbesocompelling.Whenwegraspthechunk,ittakesonanewlifeinourownminds—weformideasthatenhanceandenlightentheneuralpatternswealreadypossess,allowingustomorereadilyseeanddevelopotherrelatedpatterns.

Oncewehavecreatedachunkasaneuralpattern,wecanmoreeasilypassthatchunkedpatterntoothers,asCajalandothergreatartists,poets,scientists,andwritershavedoneformillennia.Onceotherpeoplegraspthatchunk,notonlycantheyuseit,butalsotheycanmoreeasilycreatesimilarchunksthatapplytootherareasintheirlives—animportantpartofthecreativeprocess.

Hereyoucanseethatthechunk—theripplingneuralribbon—ontheleftisverysimilartothechunkontheright.Thissymbolizestheideathatonceyougraspachunkinonesubject,itismucheasierforyoutograsporcreateasimilarchunkinanothersubject.Thesameunderlyingmathematics,forexample,echothroughoutphysics,chemistry,andengineering—andcansometimesalsobeseenineconomics,business,andmodelsofhumanbehavior.Thisiswhyitcanbeeasierforaphysicsorengineeringmajortoearnamaster’sinbusinessadministrationthansomeonewithabackgroundinEnglishorhistory.16

Metaphorsandphysicalanalogiesalsoformchunksthatcanallowideasevenfromverydifferentareastoinfluenceoneanother.17Thisiswhypeoplewholovemath,science,andtechnologyoftenalsofindsurprisinghelpfromtheiractivitiesorknowledgeofsports,music,language,art,orliterature.Myownknowledgeofhowtolearnalanguagehelpedmeinlearninghowtolearnmathandscience.

Oneimportantkeytolearningswiftlyinmathandscienceistorealizethatvirtuallyeveryconceptyoulearnhasananalogy—acomparison—withsomethingyoualreadyknow.18Sometimestheanalogyormetaphorisrough—suchastheideathatbloodvesselsarelikehighways,orthatanuclearreactionislikefallingdominoes.Butthesesimpleanalogiesandmetaphorscanbepowerfultoolstohelpyouuseanexistingneuralstructureasascaffoldtohelpyoumorerapidlybuildanew,morecomplexneuralstructure.Asyoubegintousethisnewstructure,youwilldiscoverthatithasfeaturesthatmakeitfarmoreusefulthanyourfirstsimplisticstructure.Thesenewstructurescaninturnbecomesourcesofmetaphorandanalogyforstillnewerideasinverydifferentareas.(This,indeed,iswhyphysicistsandengineershavebeensoughtafterintheworldoffinance.)PhysicistEmanualDerman,forexample,whodidbrilliantresearchintheoreticalparticlephysics,movedontothecompanyGoldmanSachs,eventuallyhelpingtodeveloptheBlack-Derman-Toyinterest-ratemodel.Dermaneventuallytookchargeofthefirm’sQuantitativeRiskStrategiesgroup.

SUMMINGITUP

Brainsmatureatdifferentspeeds.Manypeopledonotdevelopmaturityuntiltheirmidtwenties.Someofthemostformidableheavyweightsinsciencestartedoutasapparentlyhopelessjuveniledelinquents.Onetraitthatsuccessfulprofessionalsinscience,math,andtechnologygraduallylearnishowtochunk—toabstractkeyideas.Metaphorsandphysicalanalogiesformchunksthatcanallowideasfromverydifferentareastoinfluenceoneanother.Regardlessofyourcurrentorintendedcareerpath,keepyourmindopenandensurethatmathandscienceareinyourlearningrepertoire.Thisgivesyouarichreserveofchunkstohelpyoubesmarteraboutyourapproachtoallsortsoflifeandcareerchallenges.

PAUSEANDRECALL

Closethebookandlookaway.What werethemainideasofthischapter?Youwillfindthatyoucanrecalltheseideasmoreeasilyifyourelatethemtoyourownlifeandcareergoals.

ENHANCEYOURLEARNING

1.Inhiscareer,SantiagoRamónyCajalfoundawaytocombinehispassionforartwithapassionforscience.Doyouknowotherpeople,eitherfamouspublicfiguresorfamilyfriendsoracquaintances,whohavedonesomethingsimilar?Issuchaconfluencepossibleinyourownlife?

2.Howcanyouavoidfallingintothetrapofthinkingthatquickerpeopleareautomaticallymoreclever?

3.Doingwhatyouaretoldtodocanhavebenefitsanddrawbacks.CompareCajal’slifewithyourown.Whenhasdoingwhatyouweretoldbeenbeneficial?Whenhasitinadvertentlycreatedproblems?

4.ComparedtoCajal’shandicaps,howdoyourownlimitationsstackup?Canyoufindwaystoturnyourdisadvantagesintoadvantages?

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developingthemind’seyethroughequationpoems

LearntoWriteanEquationPoem—UnfoldingLinesThatProvideaSenseofWhatLiesBeneathaStandardEquation

PoetSylviaPlathoncewrote:“ThedayIwentintophysicsclassitwasdeath.”1Shecontinued:

Ashortdarkmanwithahigh,lispingvoice,namedMr.Manzi,stoodinfrontoftheclassinatightbluesuitholdingalittlewoodenball.Heputtheballonasteepgroovedslideandletitrundowntothebottom.Thenhestartedtalkingaboutletaequalaccelerationandlettequaltimeandsuddenlyhewasscribblinglettersandnumbersandequalssignsallovertheblackboardandmymindwentdead.

Mr.Manzihad,atleastinthissemiautobiographicalretellingofPlath’slife,writtenafour-hundred-pagebookwithnodrawingsorphotographs,onlydiagramsandformulas.AnequivalentwouldbetryingtoappreciatePlath’spoetrybybeingtoldaboutit,ratherthanbeingabletoreaditforyourself.Plathwas,inherversionofthestory,theonlystudenttogetanA,butshewasleftwithadreadforphysics.

“What,afterall,ismathematicsbutthepoetryofthemind,andwhatispoetrybutthemathematicsoftheheart?”

—DavidEugeneSmith,Americanmathematicianandeducator

PhysicistRichardFeynman’sintroductoryphysicsclasseswereentirelydifferent.Feynman,aNobelPrizewinner,wasanexuberantguywhoplayedthebongosforfunandtalkedmorelikeadown-to-earthtaxidriverthanapointy-headedintellectual.

WhenFeynmanwasaboutelevenyearsold,anoff-the-cuffremarkhadatransformativeimpactonhim.Heremarkedtoafriendthatthinkingisnothingmorethantalkingtoyourselfinside.

“Ohyeah?”saidFeynman’sfriend.“Doyouknowthecrazyshapeofthecrankshaftinacar?”“Yeah,whatofit?”“Good.Nowtellme:Howdidyoudescribeitwhenyouweretalkingtoyourself?”ItwasthenthatFeynmanrealizedthatthoughtscanbevisualaswellasverbal.2Helaterwroteabouthow,whenhewasastudent,hehadstruggledtoimagineandvisualize

conceptssuchaselectromagneticwaves,theinvisiblestreamsofenergythatcarryeverythingfromsunlighttocellphonesignals.Hehaddifficultydescribingwhathesawinhismind’seye.3Ifevenoneoftheworld’sgreatestphysicistshadtroubleimagininghowtoseesome(admittedlydifficult-to-imagine)physicalconcepts,wheredoesthatleaveusnormalfolks?

Wecanfindencouragementandinspirationintherealmofpoetry.4Let’stakeafewpoeticlinesfromasongbyAmericansinger-songwriterJonathanCoulton,called“MandelbrotSet,”5aboutafamousmathematician,BenoitMandelbrot.

Mandelbrot’sinheavenHegaveusorderoutofchaos,hegaveushopewheretherewasnoneHisgeometrysucceedswhereothersfailSoifyoueverloseyourway,abutterflywillflapitswingsFromamillionmilesaway,alittlemiraclewillcometotakeyouhome

TheessenceofMandelbrot’sextraordinarymathematicsiscapturedinCoulton’semotionallyresonantphrases,whichformimagesthatwecanseeinourownmind’seye—thegentleflapofabutterfly’swingsthatspreadsandhaseffectsevenamillionmilesaway.

Mandelbrot’sworkincreatinganewgeometryallowedustounderstandthatsometimes,thingsthatlookroughandmessy—likecloudsandshorelines—haveadegreeofordertothem.Visualcomplexitycanbecreatedfromsimplerules,asevidencedinmodernanimatedmovie-makingmagic.Coulton’spoetryalsoalludestotheidea,embeddedinMandelbrot’swork,thattiny,subtleshiftsinonepartoftheuniverseultimatelyaffecteverythingelse.

ThemoreyouexamineCoulton’swords,themorewaysyoucanseeitappliedtovariousaspectsoflife—thesemeaningsbecomeclearerthemoreyouknowandunderstandMandelbrot’swork.

Therearehiddenmeaningsinequations,justasthereareinpoetry.Ifyouareanovicelookingatanequationinphysics,andyou’renottaughthowtoseethelifeunderlyingthesymbols,thelineswilllookdeadtoyou.Itiswhenyoubegintolearnandsupplythehiddentextthatthemeaningslips,slides,thenfinallyleapstolife.

Inaclassicpaper,physicistJeffreyPrentiscompareshowabrand-newstudentofphysicsandamaturephysicistlookatequations.6Theequationisseenbythenoviceasjustonemorethingtomemorizeinavastcollectionofunrelatedequations.Moreadvancedstudentsandphysicists,however,seewiththeirmind’seyethemeaningbeneaththeequation,includinghowitfitsintothebigpicture,andevenasenseofhowthepartsoftheequationfeel.

“Amathematicianwhoisnotatthesametimesomethingofapoetwillneverbeafullmathematician.”

—GermanmathematicianKarlWeierstrass

Whenyouseethelettera,foracceleration,youmightfeelasenseofpressingontheacceleratorinacar.Zounds!Feelthecar ’saccelerationpressingyoubackagainsttheseat.

Doyouneedtobringthesefeelingstomindeverytimeyoulookatthelettera?Ofcoursenot;youdon’twanttodriveyourselfcrazyrememberingeverylittledetailunderlyingyourlearning.Butthatsenseofpressingaccelerationshouldhoverasachunkinthebackofyourmind,readytoslipintoworkingmemoryifyou’retryingtoanalyzethemeaningofawhenyouseeitroamingaroundinanequation.

Similarly,whenyouseem,formass,youmightfeeltheinertiallazinessofafifty-poundboulder—ittakesalottogetitmoving.Whenyouseetheletterf,forforce,youmightseewithyourmind’seyewhatliesunderneathforce—thatitdependsonbothmassandacceleration:m·a,asintheequationf=m·a.Perhapsyoucanfeelwhat’sbehindthefaswell.Forcehasbuiltintoitaheavingoomph(acceleration),againstthelazymassoftheboulder.

Let’sbuildonthatjustaweebitmore.Thetermworkinphysicsmeansenergy.Wedowork(thatis,wesupplyenergy)whenwepush(force)somethingthroughadistance.Wecanencryptthatwithpoeticsimplicity:w=f×d.Onceweseewforwork,thenwecanimaginewithourmind’seye,andevenourbody’sfeelings,what’sbehindit.Ultimately,wecandistillalineofequationpoetrythatlookslikethis:

ww=f·dw=(ma)·d

Symbolsandequations,inotherwords,haveahiddentextthatliesbeneaththem—ameaningthatbecomesclearonceyouaremorefamiliarwiththeideas.Althoughtheymaynotphraseitthisway,scientistsoftenseeequationsasaformofpoetry,ashorthandwaytosymbolizewhattheyaretryingtoseeandunderstand.Observantpeoplerecognizethedepthofapieceofpoetry—itcanhavemanypossiblemeanings.Injustthesameway,maturingstudentsgraduallylearntoseethehiddenmeaningofanequationwiththeirmind’seyeandeventointuitdifferentinterpretations.It’snosurprisetolearnthatgraphs,tables,andothervisualsalsocontainhiddenmeaning—meaningthatcanbeevenmorerichlyrepresentedinthemind’seyethanonthepage.

SimplifyandPersonalizeWhateverYouAreStudying

We’vealludedtothisbefore,butit’sworthrevisitingnowthatwe’vegotbetterinsightintohowtoimaginetheideasthatunderlieequations.Oneofthemostimportantthingswecandowhenwearetryingtolearnmathandscienceistobringtheabstractideastolifeinourminds.SantiagoRamónyCajal,forexample,treatedthemicroscopicscenesbeforehimasiftheywereinhabitedbylivingcreaturesthathopedanddreamedjustaspeoplethemselvesdo.7Cajal’scolleagueandfriend,SirCharlesSherrington,whocoinedthewordsynapse,toldfriendsthathehadnevermetanotherscientistwhohadthisintenseabilitytobreathelifeintohiswork.SherringtonwonderedwhetherthismighthavebeenakeycontributingfactortoCajal’slevelofsuccess.

Einsteinwasabletoimaginehimselfasaphoton.8WecangainasenseofwhatEinsteinsawbylookingatthisbeautifulvisionbyItalianphysicistMarcoBelliniofanintenselaserpulse(theoneinfront),beingusedtomeasuretheshapeofasinglephoton(theoneintheback).

Einstein’stheoriesofrelativityarosenotfromhismathematicalskills(heoftenneededtocollaboratewithmathematicianstomakeprogress)butfromhisabilitytopretend.Heimaginedhimselfasaphotonmovingatthespeedoflight,thenimaginedhowasecondphotonmightperceivehim.Whatwouldthatsecondphotonseeandfeel?

BarbaraMcClintock,whowontheNobelPrizeforherdiscoveryofgenetictransposition(“jumpinggenes”thatcanchangetheirplaceontheDNAstrand),wroteabouthowsheimaginedthecornplantsshestudied:“Ievenwasabletoseetheinternalpartsofthechromosomes—actuallyeverythingwasthere.ItsurprisedmebecauseIactuallyfeltasifIwererightdownthereandtheseweremyfriends.”9

PioneeringgeneticistBarbaraMcClintockimaginedgiganticversionsofthemolecularelementsshewasdealingwith.LikeotherNobelPrizewinners,shepersonalized—evenmadefriendswith—theelementsshewasstudying.

Itmayseemsillytostageaplayinyourmind’seyeandimaginetheelementsandmechanismsyouarestudyingaslivingcreatures,withtheirownfeelingsandthoughts.Butitisamethodthatworks—itbringsthemtolifeandhelpsyouseeandunderstandphenomenathatyoucouldn’tintuitwhenlookingatdrynumbersandformulas.

Simplifyingisalsoimportant.RichardFeynman,thebongo-playingphysicistwemetearlierinthischapter,wasfamousforaskingscientistsandmathematicianstoexplaintheirideasinasimplewaysothathecouldgraspthem.Surprisingly,simpleexplanationsarepossibleforalmostanyconcept,nomatterhowcomplex.Whenyoucultivatesimpleexplanationsbybreakingdowncomplicatedmaterialtoitskeyelements,theresultisthatyouhaveadeeperunderstandingofthematerial.10LearningexpertScottYounghasdevelopedthisideainwhathecallstheFeynmantechnique,whichaskspeopletofindasimplemetaphororanalogytohelpthemgrasptheessenceofanidea.11

ThelegendaryCharlesDarwinwoulddomuchthesamething.Whentryingtoexplainaconcept,heimaginedsomeonehadjustwalkedintohisstudy.Hewouldputhispendownandtrytoexplaintheideainthesimplestterms.Thathelpedhimfigureouthowhewoulddescribetheconceptinprint.

Alongthoselines,thewebsiteReddit.comhasasectioncalled“ExplainlikeI’m5”whereanyonecanmakeapostaskingforasimpleexplanationofacomplextopic.12

Youmaythinkyoureallyhavetounderstandsomethinginordertoexplainit.Butobservewhathappenswhenyouaretalkingtootherpeopleaboutwhatyouarestudying.You’llbesurprisedtoseehowoftenunderstandingarisesasaconsequenceofattemptstoexplaintoothersandyourself,ratherthantheexplanationarisingoutofyourpreviousunderstanding.Thisiswhyteachersoftensaythatthefirsttimetheyeverreallyunderstoodthematerialwaswhentheyhadtoteachit.

IT ’SNICETOGETTOKNOWYOU!

“Learningorganicchemistryisnotanymorechallengingthangettingtoknowsomenewcharacters.Theelementseachhavetheirownuniquepersonalities.Themoreyouunderstandthosepersonalities,themoreyouwillbeabletoreadtheirsituationsandpredicttheoutcomesofreactions.”

—KathleenNolta,Ph.D.,SeniorLecturerinChemistryandrecipientoftheGoldenAppleAward,recognizingexcellenceinteachingattheUniversityofMichigan

NOWYOUTRY!

StageaMentalPlay

Imagineyourselfwithintherealmofsomethingyouarestudying—lookingattheworldfromtheperspectiveofthecell,ortheelectron,orevenamathematicalconcept.Trystagingamentalplaywithyournewfriends,imagininghowtheyfeelandreact.

Transfer—ApplyingWhatYou’veLearnedinNewContexts

Transferistheabilitytotakewhatyoulearninonecontextandapplyittosomethingelse.Forexample,youmaylearnoneforeignlanguageandthenfindthatyoucanpickupasecondforeignlanguagemoreeasilythanthefirst.That’sbecausewhenyoulearnedthefirstforeignlanguage,youalsoacquiredgenerallanguage-learningskills,andpotentiallysimilarnewwordsandgrammaticalstructures,thattransferredtoyourlearningthesecondforeignlanguage.13

Learningmathbyapplyingitonlytoproblemswithinaspecificdiscipline,suchasaccounting,engineering,oreconomics,canbealittlelikedecidingthatyouarenotreallygoingtolearnaforeignlanguageafterall—you’rejustgoingtosticktoonelanguageandjustlearnafewextraEnglishvocabularywords.Manymathematiciansfeelthatlearningmaththroughentirelydiscipline-specificapproachesmakesitmoredifficultforyoutousemathematicsinaflexibleandcreativeway.

Mathematiciansfeelthatifyoulearnmaththewaytheyteachit,whichcentersontheabstract,chunkedessencewithoutaspecificapplicationinmind,you’vecapturedskillsthatareeasyforyoutotransfertoavarietyofapplications.Inotherwords,you’llhaveacquiredtheequivalentofgenerallanguage-learningskills.Youmaybeaphysicsstudent,forexample,butyoucoulduseyourknowledgeofabstractmathtoquicklygrasphowsomeofthatmathcouldapplytoverydifferent

biological,financial,orevenpsychologicalprocesses.Thisispartofwhymathematiciansliketoteachmathinanabstractway,withoutnecessarily

zoominginonapplications.Theywantyoutoseetheessenceoftheideas,whichtheyfeelmakesiteasiertotransfertheideastoavarietyoftopics.14It’sasiftheydon’twantyoutolearnhowtosayaspecificAlbanianorLithuanianorIcelandicphrasemeaningIrunbutrathertounderstandthemoregeneralideathatthereisacategoryofwordscalledverbs,whichyouconjugate.

Thechallengeisthatit’softeneasiertopickuponamathematicalideaifitisapplieddirectlytoaconcreteproblem—eventhoughthatcanmakeitmoredifficulttotransferthemathematicalideatonewareaslater.Unsurprisingly,thereendsupbeingaconstanttusslebetweenconcreteandabstractapproachestolearningmathematics.Mathematicianstrytoholdthehighgroundbysteppingbacktomakesurethatabstractapproachesarecentraltothelearningprocess.Incontrast,engineering,business,andmanyotherprofessionsallnaturallygravitatetowardmaththatfocusesontheirspecificareastohelpbuildstudentengagementandavoidthecomplaintof“WhenamIevergoingtousethis?”Concretelyappliedmathalsogetsaroundtheissuethatmany“real-world”wordproblemsinmathematicstextbooksaresimplythinlydisguisedexercises.Intheend,bothconcreteandabstractapproacheshavetheiradvantagesanddisadvantages.

Transferisbeneficialinthatitoftenmakeslearningeasierforstudentsastheyadvanceintheirstudiesofadiscipline.AsProfessorJasonDechantoftheUniversityofPittsburghsays,“Ialwaystellmystudentsthattheywillstudylessastheyprogressthroughtheirnursingprograms,andtheydon’tbelieveme.They’reactuallydoingmoreandmoreeachsemester;theyjustgetbetteratbringingitalltogether.”

Oneofthemostproblematicaspectsofprocrastination—constantlyinterruptingyourfocustocheckyourphonemessages,e-mails,orotherupdates—isthatitinterfereswithtransfer.Studentswhointerrupttheirworkconstantlynotonlydon’tlearnasdeeply,butalsoaren’tabletotransferwhatlittletheydolearnaseasilytoothertopics.15Youmaythinkyou’relearninginbetweencheckingyourphonemessages,butinreality,yourbrainisnotfocusinglongenoughtoformthesolidneuralchunksthatarecentraltotransferringideasfromoneareatoanother.

TRANSFERRINGIDEASWORKS!

“ItookfishingtechniquesfromtheGreatLakesandtriedusingthemdownintheFloridaKeysthispastyear.Completelydifferentfish,differentbait,andatechniquethathadneverbeenusedbutitworkedgreat.PeoplethoughtIwascrazyanditwasfunnytoshowthemthatitactuallycaughtfish.”

—PatrickScoggin,senior,history

SUMMINGITUP

Equationsarejustwaysofabstractingandsimplifyingconcepts.Thismeansthatequationscontaindeepermeaning,similartothedepthofmeaningfoundinpoetry.Your“mind’seye”isimportantbecauseitcanhelpyoustageplaysandpersonalizewhatyouarelearningabout.Transferistheabilitytotakewhatyoulearninonecontextandapplyittosomethingelse.

It’simportanttograspthechunkedessenceofamathematicalconcept,becausethen

it’seasiertotransferandapplythatideainnewanddifferentways.Multitaskingduringthelearningprocessmeansyoudon’tlearnasdeeply—thiscaninhibityourabilitytotransferwhatyouarelearning.

PAUSEANDRECALL

Closethebookandlookaway.What werethemainideasofthischapter?Canyoupicturesomeoftheseideaswithsymbolsinyourmind’seye?

ENHANCEYOURLEARNING

1.Writeanequationpoem—severalunfoldinglinesthatprovideasenseofwhatliesbeneathastandardequation.

2.Writeaparagraphthatdescribeshowsomeconceptsyouarestudyingcouldbevisualizedinaplay.Howdoyouthinktheactorsinyourplaymightrealisticallyfeelandreacttooneanother?

3.Takeamathematicalconceptyouhavelearnedandlookataconcreteexampleofhowthatconceptisapplied.Thenstepbackandseeifyoucansensetheabstractchunkofanideaunderlyingtheapplication.Canyouthinkofacompletelydifferentwaythatconceptmightbeused?

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renaissancelearning

TheValueofLearningonYourOwn

PeoplelikeCharlesDarwin,whosetheoryofevolutionhasmadehimoneofthemostinfluentialfiguresinhumanhistory,areoftenthoughtofasnaturalgeniuses.YoumaybesurprisedtolearnthatmuchlikeCajal,Darwinwasapoorstudent.Hewashedoutofmedicalschoolandendedup,tohisfather ’shorror,headingoutonaround-the-worldvoyageastheship’snaturalist.Outonhisown,Darwinwasabletolookwithfresheyesatthedatahewascollecting.

Persistenceisoftenmoreimportantthanintelligence.1Approachingmaterialwithagoaloflearningitonyourowngivesyouauniquepathtomastery.Often,nomatterhowgoodyourteacherandtextbookare,it’sonlywhenyousneakoffandlookatotherbooksorvideosthatyoubegintoseethatwhatyoulearnthroughasingleteacherorbookisapartialversionofthefull,three-dimensionalrealityofthesubject,whichhaslinkstostillotherfascinatingtopicsthatareofyourchoosing.

NeurosurgeonBenCarson,winnerofthePresidentialMedalofFreedomforhispioneeringsurgicalinnovations,wasinitiallyflunkingandgentlyurgedtoleavemedicalschool.Carsonknewhelearnedbestthroughbooks,notin-classlectures.Hetookacounterintuitivestepandstoppedattendinglecturestogivehimselftimetofocusonlearningthroughbooks.Hisgradessoaredandtherestishistory.(Notethatthistechniquewouldnotworkforeveryone—andifyouusethisstoryasanexcusetosimplystopattendingclasses,youarecourtingdisaster!)

Inthefieldsofscience,math,andtechnology,manyindividualshadtocarvetheirownpathinlearning,eitherbecausetheyhadnootherway,orbecauseforwhateverreason,they’dthrownawaypreviouslearningopportunities.Researchhasshownthatstudentslearnbestwhentheythemselvesareactivelyengagedinthesubjectinsteadofsimplylisteningtosomeoneelsespeak.2Astudent’sabilitytograpplepersonallywiththematerial,sometimesbouncingitofffellowlearners,iskey.

SantiagoRamónyCajalwashorrifiedwhenhehadtolearncollegecalculusasanadult,afterhehadbecomeseriousaboutbecomingadoctor.He’dneverpaidattentiontomathinhisyouthandlackedevenarudimentaryunderstandingofthematerial.Hehadtogorummagingbackthrougholdbooks,scratchinghisheadtofigureoutthebasics.Cajallearnedallthemoredeeply,however,becausehewasdrivenbyhispersonalgoals.

“Whatawonderfulstimulantitwouldbeforthebeginnerifhisinstructor,insteadofamazinganddismayinghimwiththesublimityofgreatpastachievements,wouldrevealinsteadtheoriginofeachscientificdiscovery,theseriesoferrorsandmisstepsthatprecededit—informationthat,fromahumanperspective,isessentialtoanaccurateexplanationof

thediscovery.”3

—SantiagoRamónyCajal

InventorandauthorWilliamKamkwamba,bornin1987inAfrica,couldnotaffordtoattendschool.Sohebeganteachinghimselfbygoingtohisvillage’slibrary,wherehestumbledacrossabooktitledUsingEnergy.ButKamkwambadidn’tjustreadthebook.Whenhewasonlyfifteenyearsold,heusedthebooktoguidehiminactivelearning:Hebuilthisownwindmill.Hisneighborscalledhimmisala—crazy—buthiscreationhelpedbegingeneratingelectricityandrunningwaterforhisvillageandsparkedthegrowthofgrassrootstechnologicalinnovationinAfrica.4

AmericanneuroscientistandpharmacologistCandacePerthadanexcellenteducation,earningadoctorateinpharmacologyfromJohnsHopkinsUniversity.Butpartofherinspirationandsubsequentsuccessarosefromanunusualsource.Justbeforeenteringmedicalgraduateschool,shehurtherbackinahorseback-ridingaccidentandspentasummerundertheinfluenceofdeeppainmedication.5Herpersonalexperienceswithpainandpainmedicationdroveherscientificresearch.Ignoringheradvisor ’sattemptstostopher,shemadesomeofthefirstkeydiscoveriesinvolvingopiatereceptors—amajorstepforwardinunderstandingaddiction.

Collegeisn’ttheonlywaytolearn.Someofthemostpowerfulandrenownedpeopleofourtime,includingpowerhousesBillGates,LarryEllison,MichaelDell,MarkZuckerberg,JamesCameron,SteveJobs,andSteveWozniak,droppedoutofcollege.Wewillcontinuetoseefascinatinginnovationsfrompeoplewhoareabletocombinethebestaspectsoftraditionalandnontraditionallearningwiththeirownself-taughtapproaches.

Takingresponsibilityforyourownlearningisoneofthemostimportantthingsyoucando.Teacher-centeredapproaches,wheretheteacherisconsideredtobetheonewiththeanswers,maysometimesinadvertentlyfosterasenseofhelplessnessaboutlearningamongstudents.6Surprisingly,teacherevaluationsystemsmayfosterthesamehelplessness—thesesystemsallowyoutoplacetheblameforfailureonyourteacher ’sinabilitytomotivateorinstruct.7Student-centeredlearning,wherestudentsarechallengedtolearnfromoneanotherandareexpectedtobetheirowndriverstowardmasteryofthematerial,isextraordinarilypowerful.

TheValueofGreatTeachers

Youwillalsosometimeshaveachancetointeractwithtrulyspecialmentorsorteachers.Whenthisluckyopportunityarises,seizeit.Trainyourselftogetpastthegulpstageandforceyourselftoreachoutandaskquestions—realandto-the-pointquestions,notquestionsmeanttoshowoffwhatyouknow.Themoreyoudothis,theeasieritwillbecome,andthemorehelpfulitwillbeinwaysyouneveranticipated—asimplesentencegrowingfromtheirvastexperiencecanchangethecourseofyourfuture.Andalsobesuretoshowappreciationforthepeopleguidingyou—itisessentialtoletthemknowthatthehelpismeaningful.

Bewary,however,offallinginto“stickystudent”syndrome.Kindteachers,inparticular,canbecomemagnetsforstudentswhosetrueneedsinvolvedesirefortheego-boostingattentionoftheinstructorfarmorethananswerstotheactualquestionsbeingposed.Well-meaningteacherscanburnouttryingtosatisfynever-to-be-satisfieddesires.

Alsoavoidthetrapoffeelingcertainyouransweriscorrect,andattemptingtoforceyourteachertofollowthetorturedstepsofyourlogicwhenyouranswerisobviouslywrong.Everyonceinawhile,youmightultimatelybeprovencorrect,butformanyteachers,particularlyatmoreadvancedlevelsinmathandscience,tryingtofollowtwisted,erroneousthinkingislikelisteningtoout-of-tunemusic—athankless,painfulexercise.It’sgenerallybesttostartyourthinkingafreshandlistentoyourteacher ’ssuggestions.Whenyoufinallyunderstandtheanswer,youcangobackifyouwanttodebugyourpreviouserror.(Oftenyou’llrealize,inonefellswoop,thatit’sdifficulttoevenputintowordshowwrongyourpreviousapproachwas.)Goodteachersandmentorsareoftenverybusypeople,andyouneedtousetheirtimewisely.

Trulygreatteachersmakethematerialseembothsimpleandprofound,setupmechanismsforstudentstolearnfromeachother,andinspirestudentstolearnontheirown.CelsoBatalha,forexample,arenownedprofessorofphysicsatEvergreenValleyCollege,hassetupapopularreadinggroupforhisstudentsaboutlearninghowtolearn.Andmanyprofessorsuse“active”and“collaborativeteaching”techniquesintheclassroomthatgivestudentsachancetoactivelyengagewiththematerialandwitheachother.8

Onethinghassurprisedovertheyears.SomeofthegreatestteachersI’veevermettoldmethatwhentheywereyoung,theyweretooshy,tootongue-tiedinfrontofaudiences,andtoointellectuallyincapabletoeverdreamofbecomingateacher.Theywereultimatelysurprisedtodiscoverthatthequalitiestheysawasdisadvantageshelpedpropelthemintobeingthethoughtful,attentive,creativeinstructorsandprofessorstheybecame.Itseemedtheirintroversionmadethemmorethoughtfulandsensitivetoothers,andtheirhumbleawarenessoftheirpastfailingsgavethempatienceandkeptthemfrombecomingaloofknow-it-alls.

TheOtherReasonforLearningonYourOwn—QuirkyTestQuestions

Let’sreturntotheworldoftraditionallearninginhighschoolandcollege,wherealittleinsiderknowledgewillhelpyousucceed.Onesecretofmathandscienceteachersisthattheyoftentakequizandtestquestionsfrombooksthataren’tintheassignedreadingforthecourse.Afterall,it’shardtocomeupwithnewtestquestionseachsemester.Thismeansthattestquestionsoftenhaveslightdifferencesinterminologyorapproachthatcanthrowyouoffyourgameevenifyouarecomfortablewithyourtextbookandyourteacher ’slectures.Youcanendupthinkingthatyoudon’thavetalentformathandscience,whenallyoureallyneededtodowaslookatthematerialthroughdifferentlensesasyouwerestudyingthroughoutthesemester.

BewareofIntellectualSnipers

SantiagoRamónyCajalhadadeepunderstandingnotonlyofhowtoconductscience,butalsoofhowpeopleinteractwithoneanother.Hewarnedfellowlearnersthattherewillalwaysbethosewhocriticizeorattempttoundermineanyeffortorachievementyoumake.Thishappenstoeveryone,notjustNobelPrizewinners.Ifyoudowellinyourstudies,thepeoplearoundyoucanfeelthreatened.Thegreateryourachievement,themoreotherpeoplewillsometimesattackanddemeanyourefforts.

Ontheotherhand,ifyouflunkatest,youmayalsoencountercriticswhothrowmorebarbs,sayingyoudon’thavewhatittakes.Failureisnotsoterrible.Analyzewhatyoudidwronganduseittocorrectyourselftodobetterinthefuture.Failuresarebetterteachersthansuccessesbecausetheycauseyoutorethinkyourapproach.

Some“slower”studentsstrugglewithmathandsciencebecausetheycan’tseemtounderstandideasthatothersfindobvious.Thesestudentsunfortunatelysometimesthinkofthemselvesasnotverybright,buttherealityisthattheirslowerwayofthinkingcanallowthemtoseeconfusingsubtletiesthatothersaren’tawareof.It’stheequivalentofahikerwhonoticesthescentofpineandsmall-animalpathsinthewoods,asopposedtotheobliviousmotoristwho’swhizzingbyatseventymilesanhour.Sadly,someinstructorsfeelthreatenedbythedeceptivelysimplequestionsthatseeminglypedestrianstudentscanpose.Ratherthanacknowledginghowperceptivethesequestionsare,instructorsattackthequestionerwithbrusque,brushoffanswersthatequateto“justdoasyou’retoldlikeeverybodyelsedoes.”Thisleavesthequestionerfeelingfoolishandonlydeepenstheconfusion.(Keepinmindthatinstructorssometimescan’ttellwhetheryouarethinkingdeeplyaboutthematerial,orwhetheryou’rehavingtroubletakingownershipofyourownroleinunderstandingsimplematters,aswasthecasewithmytruculentbehaviorinhighschool.)

Inanycase,ifyoufindyourselfstrugglingwiththe“obvious,”don’tdespair.LooktoyourclassmatesortheInternetforhelp.Oneusefultrickistotrytofindanotherinstructor—onewithniceevaluations—whooccasionallyteachesthesameclass.Theseinstructorsoftenunderstandwhatyouareexperiencingandaresometimeswillingtohelpifyoudon’toverusethemasaresource.Remindyourselfthatthissituationisonlytemporary,andnocircumstanceistrulyasoverwhelmingasitmightseematthetime.

Asyouwillfindwhenyoureachtheworkworld(ifyouhaven’talready),manyindividualsarefarmoreinterestedinaffirmingtheirownideasandmakingthemselveslookgoodthantheyareinhelpingyou.Inthiskindofsituation,therecanbeafinelinebetweenkeepingyourselfopentoconstructiveexplanationandcriticism,versusbeingclosedtocommentaryorcriticismthatiscouchedasconstructivebutisactuallysimplyspiteful.Whateverthecriticism,ifyoufeelastrongwashofemotionorcertainty(“ButI’mright!”),itmaybeacluethatyou’recorrect—oralternatively(andperhapsevenmorelikely,becauseofyourtelltaleemotions),itmaybethatyouneedtogobackandreexaminemattersusingamoreobjectiveperspective.

We’reoftentoldthatempathyisuniversallybeneficial,butit’snot.9It’simportanttolearntoswitchonanoccasionalcooldispassionthathelpsyoutonotonlyfocusonwhatyouaretryingtolearn,butalsototunepeopleoutifyoudiscovertheirinterestslieinundercuttingyou.Suchundercuttingisall-too-common,aspeopleareoftenjustascompetitiveastheyarecooperative.Whenyou’reayoungperson,masteringsuchdispassioncanbedifficult.Wearenaturallyexcitedaboutwhatweareworkingon,andweliketobelievethateveryonecanbereasonedwithandthatalmosteveryoneisnaturallygood-heartedtowardus.

LikeCajal,youcantakeprideinaimingforsuccessbecauseoftheverythingsthatmakeotherpeoplesayyoucan’tdoit.Takeprideinwhoyouare,especiallyinthequalitiesthatmakeyou“different,”andusethemasasecrettalismanforsuccess.Useyournaturalcontrarinesstodefythealways-presentprejudicesfromothersaboutwhatyoucando.

NOWYOUTRY!

UnderstandingtheValueof“Bad”

Pickaseeminglybadtraitanddescribehowitcouldbebeneficialinhelpingyoulearnorthinkcreativelyorindependently.Couldyouthinkofawaytodiminishthenegativeaspectsofthattrait,evenasyouenhancethepositiveaspects?

SUMMINGITUP

Learningonyourownisoneofthedeepest,mosteffectivewaystoapproachlearning:Itimprovesyourabilitytothinkindependently.Itcanhelpyouanswerthestrangequestionsthatteacherssometimesthrowatyouontests.

Inlearning,persistenceisoftenfarmoreimportantthanintelligence.Trainyourselftooccasionallyreachouttopeopleyouadmire.Youcangainwisenewmentorswho,withasimplesentence,canchangethecourseofyourfuture.Butuseyourteachers’andmentors’timesparingly.Ifyouaren’tveryfastatgraspingtheessentialsofwhateveryouarestudying,don’tdespair.Surprisinglyoften,“slower”studentsaregrapplingwithfundamentallyimportantissuesthatquickerstudentsmiss.Whenyoufinallygetwhat’sgoingon,youcangetitatadeeperlevel.Peoplearecompetitiveaswellascooperative.Therewillalwaysbethosewhocriticizeorattempttoundermineanyeffortorachievementyoumake.Learntodealdispassionatelywiththeseissues.

PAUSEANDRECALL

Closethebookandlookaway.What werethemainideasofthischapter?Whichideaismostimportant—orarethereseveralcompet ingequallyimportant ideas?

ENHANCEYOURLEARNING

1.Whataretheadvantagesanddisadvantagesoflearningonyourown,withoutbeingguidedbyaformalprogramofstudy?

2.LookupthephraseListofautodidactsonWikipedia.Whichofthemanyautodidactstherewouldyoumostliketoemulate?Why?

3.Chooseapersonamongyourownacquaintances(thatis,notacelebrity)whomyouadmirebuttowhomyouhaveneverreallyspoken.Formulateaplantosayhelloandintroduce

yourself—thencarryitout.

NEWYORKTIMESSCIENCEWRITERNICHOLASWADEONANINDEPENDENTMIND

NicholasWadewritesfortheScienceTimessectionoftheNewYorkTimes.Alwaysanindependentthinker,Wadeoweshisveryexistencetothesimilarindependentthinkingofhisgrandfather—oneofthefewmalesurvivorsoftheTitanic.Whenmostmenfollowedarumorandmovedtotheportside,Wade’sgrandfatherfollowedhisintuitionanddeliberatelymovedtheotherway,tostarboard.Here,Nicholasgiveshisinsightonwhathethinksarethemostinterestingbooks

aboutscientistsandmathematicians.“TheManWhoKnewInfinity:ALifeoftheGeniusRamanujan,byRobertKanigel.Thisbooktellstheunbelievable,ragstointellectualrichesstoryoftheIndianmathematicalgeniusSrinivasaRamanujanandhisfriendBritishmathematicianG.H.Hardy.Myfavoriteepisodeisthis:‘Once,inthetaxifromLondon,Hardynoticeditsnumber,1729.Hemusthave

thoughtaboutitalittlebecauseheenteredtheroomwhereRamanujanlayinbedand,withscarcelyahello,blurtedouthisdisappointmentwithit.Itwas,hedeclared,“ratheradullnumber,”addingthathehopedthatwasn’tabadomen.‘“No,Hardy,”saidRamanujan.“Itisaveryinterestingnumber.Itisthesmallest

numberexpressibleasthesumoftwocubesindifferentways.”‘“NobleSavages,byNapoleonChagnon.Thisbeautifullywrittenadventurestorygives

asenseofwhatit’sliketolearntosurviveandthriveinanutterlyalienculture.Chagnonwasoriginallytrainedasanengineer.Hisscientificresearchhasshiftedour

understandingofhowculturesdevelop.“MenofMathematics,byE.T.Bell.Thisisanoldclassicthat’sashow-stoppingreadforanyonewho’sinterestedinhow

fascinatingpeoplethink.Whocouldforgetbrilliant,doomedÉvaristeGaloiswhospentthenightbeforeheknewhewastodie‘feverishlydashingoffhislastwillandtestament,writingagainsttimetogleanafewofthegreatthingsinhisteemingmindbeforethedeathwhichheforesawcouldovertakehim.Timeaftertimehebrokeofftoscribbleinthemargin“Ihavenottime;Ihavenottime,”andpassedontothenextfranticallyscrawledoutline.’Truthbetold,thisisoneofthefewexcitingstoriesthatProfessorBellperhapsexaggerated,althoughGaloisunquestionablyspentthatlasteveningputtingthefinalpolishonhislife’swork.Butthisbrilliantbookhasinspiredgenerationsofbothmenandwomen.”

F

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avoidingoverconfidence

ThePowerofTeamwork

redhadaproblem.Hecouldn’tmovehislefthand.Thiswasn’tsurprising.Whilesingingintheshower,Fredhadsufferedanearlylethalright-hemisphereischemicstrokeamonthbefore.The

brain’srighthemispherecontrolstheleftsideofthebody,whichwaswhyFred’slefthandwasnowlifeless.

Fred’srealproblem,though,wasworse.Eventhoughhecouldn’tmovehislefthand,Fredinsisted—andtrulybelieved—thathecould.Sometimeshewouldexcusethelackofmotionbysayinghewasjusttootiredtoliftafinger.Orhe’dinsistthathislefthandhadmoved.Itwasjustthatpeoplehadn’tbeenwatching.Fredwouldevencovertlymovehislefthandwithhisright,andthenloudlyproclaimthathishandhadmovedonitsown.

Fortunately,asthemonthswentby,Fred’slefthandgraduallyregaineditsfunction.Fredlaughedwithhisdoctorabouthowhe’dtrickedhimselfintobelievingthathecouldmovehishandintheweeksimmediatelyfollowingthestroke;hespokecheerfullyaboutreturningtohisworkasanaccountant.

ButthereweresignsthatFredwasn’treturningtobusinessasusual.Heusedtobeacaring,considerateguy,butthenewFredwasdogmaticandself-righteous.

Therewereotherchanges.Fredusedtobeakeenpracticaljoker,butnowhejustnoddedalongwithoutunderstandingthepunchlinestoothers’jokes.Fred’sskillatinvestingalsoevaporated,andhiscautiousnesswasreplacedbynaiveoptimismandoverconfidence.

Evenworse,Fredseemedtohavebecomeemotionallytone-deaf.Hetriedtosellhiswife’scarwithoutaskingherpermissionandwassurprisedwhenshebecameupset.Whentheirbelovedoldfamilydogdied,Fredsatplacidlyeatingpopcorn,watchinghiswifeandchildrencryasifitwereasceneoutofamovie.

WhatmadethesechangesmoredifficulttounderstandwasthatFredseemedtohaveretainedhisintelligence—evenhisformidablewaywithnumbers.Hecouldstillquicklyworkupabusinessprofit-and-lossstatementandsolvecomplexalgebraproblems.Oneinterestinganomaly,however,wasthatifFredmadeamistakeinhiscalculations,concludingsomethingnonsensical,suchasthatahotdogstandhadalossofnearlyabilliondollars,itdidn’tbotherhim.Therewasnobig-picture“click”thatsaid,“Waitaminute,thatanswerdoesn’tmakesense.”

ItturnsoutthatFredisatypicalvictimof“broad-perspectiveperceptualdisorderoftherighthemisphere.”1Fred’sstrokehadincapacitatedbroadareasoftherighthemisphereofhisbrain.He

couldstillfunction,butonlypartially.Althoughweneedtobecarefulaboutfaultyandsuperficial“leftbrain/rightbrain”assumptions,

wealsodon’twanttothrowthebabyoutwiththebathwaterandignoreworthwhileresearchthatgivesintriguinghintsabouthemisphericdifferences.2Fredremindsusofthedangersofnotusingourfullcognitiveabilities,whichinvolvemanyareasofourbrain.Notusingsomeofourabilitiesisn’tasdevastatingforusasitisforFred.Butevensubtleavoidanceofsomeofourcapabilitiescanhaveasurprisinglynegativeimpactonourwork.

ThearrowonthisCTscanofthebrainpointstowardtheshadoweddamagecausedbyaright-hemisphereischemicstroke.

AvoidingOverconfidence

There’sagreatdealofevidencefromresearchthattherighthemispherehelpsusstepbackandputourworkintobig-pictureperspective.3Peoplewithdamagetotherighthemisphereareoftenunabletogain“aha!”insights.That’swhyFredwasn’tabletocatchthepunchlinesofjokes.Therighthemisphere,itturnsout,isvitallyimportantingettingontotherighttrackanddoing“realitychecks.”4

Insomesense,whenyouwhizthroughahomeworkortestproblemanddon’tgobacktocheckyourwork,youareactingalittlelikeapersonwhoisrefusingtousepartsofyourbrain.You’renotstoppingtotakeamentalbreathandthenrevisitwhatyou’vedonewiththebiggerpictureinmind,toseewhetheritmakessense.5AsleadingneuroscientistV.S.Ramachandranhasnoted,therighthemisphereservesasasortof“‘Devil’sAdvocate,’toquestionthestatusquoandlookfor

globalinconsistencies,”while“thelefthemispherealwaystriestoclingtenaciouslytothewaythingswere.”6ThisechoesthepioneeringworkofpsychologistMichaelGazzaniga,whopositedthatthelefthemisphereinterpretstheworldforus—andwillgotogreatlengthstokeepthoseinterpretationsunchanging.7

Whenyouworkinfocusedmode,itiseasytomakeminormistakesinyourassumptionsorcalculations.Ifyougoofftrackearlyon,itdoesn’tmatteriftherestofyourworkiscorrect—youranswerisstillwrong.Sometimesit’sevenlaughablywrong—theequivalentofcalculatingacircumferenceoftheearththatisonly21/2feetaround.Yetthesenonsensicalresultsjustdon’tmattertoyou,becausethemoreleft-centeredfocusedmodehasassociatedwithitadesiretoclingtowhatyou’vedone.

That’stheproblemwiththefocused,left-hemisphere-leaningmodeofanalysis.Itprovidesforananalyticalandupbeatapproach.Butabundantresearchevidencesuggeststhatthereisapotentialforrigidity,dogmatism,andegocentricity.

Whenyouareabsolutelycertainthatwhatyou’vedoneonahomeworkortestisfine—thankyouverymuch—beawarethatthisfeelingmaybebasedonoverlyconfidentperspectivesarisinginpartfromthelefthemisphere.Whenyoustepbackandrecheck,youareallowingformoreinteractionbetweenhemispheres—takingadvantageofthespecialperspectivesandabilitiesofeach.

Peoplewhohaven’tfeltcomfortablewithmathoftenfallintothetrapof“equationsheetbingo.”Theydesperatelytrytofindapatterninwhattheteacherorbookdidandfittheirequationstothatpattern.Goodlearnersvettheirworktoensurethatitmakessense.Theyaskthemselveswhattheequationsmeanandwheretheycomefrom.

“Thefirstprincipleisthatyoumustnotfoolyourself—andyouaretheeasiestpersontofool.”8

—PhysicistRichardFeynman,advisinghowtoavoidpseudo-sciencethatmasqueradesasscience

TheValueofBrainstormingwithOthers

NielsBohrwasheavilyinvolvedintheManhattanProject—theU.S.raceduringWorldWarIItobuildthenuclearbombbeforetheNazis.Hewasalsooneofthegreatestphysicistswhoeverlived—whichultimatelymadeitdifficultforhimtothinkintelligentlyaboutphysics.

Bohrwassorespectedasthegeniuswhohadintuitedquantumtheorythathisthinkingwasconsideredunassailable.Thismeantthathecouldnolongerbrainstormwithothers.NomatterwhatcockamamieideaBohrmightpropose,theotherphysicistsworkingonthebombwouldoohandahhoveritasifitweresomethingsacred.

Bohrhandledthischallengeinanintriguingway.RichardFeynman,asitturnedout,wasgoodatnotbeingintimidatedbyotherpeople—atsimply

doingphysics,nomatterwhohewaswith.HewassogoodthathebecameBohr ’saceinthehole.FeynmanwasatthattimejustayoungsterinthecrowdofhundredsofprominentphysicistsatLosAlamos.ButhewassingledoutbyBohrtodoprivatebrainstormingtogetherbeforeBohrwouldmeetwiththeotherphysicists.Why?Feynmanwastheonlyonewhowasn’tintimidatedbyBohrandwhowouldtellBohrthatsomeofhisideaswerefoolish.9

NielsBohrloungingwithAlbertEinsteinin1925.

AsBohrknew,brainstormingandworkingwithothers—aslongastheyknowthearea—canbehelpful.It’ssometimesjustnotenoughtousemoreofyourownneuralhorsepower—bothmodesandhemispheres—toanalyzeyourwork.Afterall,everyonehasblindspots.Yournaivelyupbeatfocusedmodecanstillskiprightovererrors,especiallyifyou’retheonewhocommittedtheoriginalerrors.10Worseyet,sometimesyoucanblindlybelieveyou’vegoteverythingnaileddownintellectually,butyouhaven’t.(Thisisthekindofthingthatcanleaveyouinshockwhenyoudiscoveryou’veflunkedatestyou’dthoughtyouaced.)

Bymakingitapointtodosomeofyourstudyingwithfriends,youcanmoreeasilycatchwhereyourthinkinghasgoneastray.Friendsandteammatescanserveasasortofever-questioning,larger-scalediffusemode,outsideyourownbrain,thatcancatchwhatyoumissed,orwhatyoujustcan’tsee.Andofcourse,asmentionedearlier,explainingtofriendshelpsbuildyourownunderstanding.

Theimportanceofworkingwithothersdoesn’tjustrelatetoproblemsolving—it’salsoimportantincareerbuilding.AsinglesmalltipfromateammatetotakeacoursefromtheoutstandingProfessorPassionate,ortocheckoutanewjobopening,canmakeanextraordinarydifferenceinhowyourlifeunfolds.Oneofthemost-citedpapersinsociology,“TheStrengthofWeakTies,”bysociologistMarkGranovetter,describeshowthenumberofacquaintancesyouhave—notthenumberofgoodfriends—predictsyouraccesstothelatestideasaswellasyoursuccessonthejobmarket.11Yourgoodfriends,afterall,tendtoruninthesamesocialcirclesthatyoudo.But

acquaintancessuchasclassteammatestendtorunindifferentcircles—meaningthatyouraccesstothe“outsideyourbrain”interpersonaldiffusemodeisexponentiallylarger.

Thoseyoustudywithshouldhave,atleastonoccasion,anaggressivelycriticaledgetothem.Researchoncreativityinteamshasshownthatnonjudgmental,agreeableinteractionsarelessproductivethansessionswherecriticismisacceptedandevensolicitedaspartofthegame.12Ifyouoroneofyourstudybuddiesthinkssomethingiswronginyourunderstanding,it’simportanttobeabletoplainlysayso,andtohashoutwhyit’swrongwithoutworryingabouthurtfeelings.Ofcourse,youdon’twanttogoaboutgratuitouslybashingotherpeople,buttoomuchconcernforcreatinga“safeenvironment”forcriticismactuallykillstheabilitytothinkconstructivelyandcreatively,becauseyou’refocusingontheotherpeopleratherthanthematerialathand.LikeFeynman,youwanttorememberthatcriticism,whetheryouaregivingorreceivingit,isn’treallyaboutyou.It’saboutwhatyouaretryingtounderstand.Inarelatedvein,peopleoftendon’trealizethatcompetitioncanbeagoodthing—competitionisanintenseformofcollaborationthatcanhelpbringoutpeople’sbest.

Brainstormingbuddies,friends,andteammatescanhelpinanotherway.Youoftendon’tmindlookingstupidinfrontoffriends.Butyoudon’twanttolooktoostupid—atleast,nottoooften.Studyingwithothers,then,canbealittlebitlikepracticinginfrontofanaudience.Researchhasshownthatsuchpublicpracticemakesiteasierforyoutothinkonyourfeetandreactwellinstressfulsituationssuchasthoseyouencounterwhenyoutaketestsorgiveapresentation.13Thereisyetanothervaluetostudybuddies—thisrelatestowhencrediblesourcesareinerror.Inevitably,nomatterhowgoodtheyare,yourinstructor—orthebook—willmakeamistake.Friendscanhelpvalidateanduntangletheresultingconfusionandpreventhoursoffollowingfalseleadsasyoutrytofindawaytoexplainsomethingthat’sflat-outwrong.

Butafinalwordofwarning:studygroupscanbepowerfullyeffectiveforlearninginmath,science,engineering,andtechnology.Ifstudysessionsturnintosocializingoccasions,however,allbetsareoff.Keepsmalltalktoaminimum,getyourgroupontrack,andfinishyourwork.14Ifyoufindthatyourgroupmeetingsstartfivetofifteenminuteslate,membershaven’treadthematerial,andtheconversationconsistentlyveersofftopic,findyourselfanothergroup.

TEAMWORKFORINTROVERTS

“I’manintrovertandIdon’tlikeworkingwithpeople.ButwhenIwasn’tdoingsowellinmycollegeengineeringclasses(backinthe1980s),IdecidedthatIneededasecondpairofeyes,althoughIstilldidn’twanttoworkwithanyone.Sincewedidn’thaveonlinechattingbackthen,wewrotenotesoneachother’sdoorsinthedorms.MyclassmateJeffandIhadasystem:Iwouldwrite‘1)1.7m/s’—meaningthattheanswertohomeworkproblemonewas1.7meterspersecond.ThenI’dgetbackfromashowerandseethatJeffhadwritten,‘No,1)11m/s.’I’ddesperatelygothroughmyownworkandfindamistake,butnowIhad8.45m/s.I’dgodowntoJeff’sroomandwe’dargueintensivelywithbothoursolutionsoutwhilehehadaguitarslungaroundhisshoulder.Thenwe’dbothgobacktoourownworkonourowntimeandI’dsuddenlyseethattheanswerwas9.37m/s,andsowouldhe,andwe’dbothget100percentonthehomeworkassignment.Asyoucansee,therearewaystoworkwithothersthatrequireonlyminimalinteractionifyoudon’tlikeworkingingroups.”

—PaulBlowers,UniversityDistinguishedProfessor(forextraordinaryteaching),UniversityofArizona

SUMMINGITUP

Thefocusedmodecanallowyoutomakecriticalerrorseventhoughyoufeelconfident

you’vedoneeverythingcorrectly.Recheckingyourworkcanallowyoutogetabroaderperspectiveonit,usingslightlydifferentneuralprocessesthatcanallowyoutocatchblunders.Workingwithotherswhoaren’tafraidtodisagreecan:

Helpyoucatcherrorsinyourthinking.Makeiteasierforyoutothinkonyourfeetandreactwellinstressfulsituations.Improveyourlearningbyensuringthatyoureallyunderstandwhatyouareexplainingtoothersandreinforcingwhatyouknow.Buildimportantcareerconnectionsandhelpsteeryoutowardbetterchoices.

Criticisminyourstudies,whetheryouaregivingorreceivingit,shouldn’tbetakenasbeingaboutyou.It’saboutwhatyouaretryingtounderstand.Itiseasiestofalltofoolyourself.

PAUSEANDRECALL

Closethebookandlookaway.What werethemainideasofthischapter?Tryrecallingsomeoftheseideaswhenyouarearoundfriends—it willalsohelpyourfriendstoknowhowvaluabletheirinteract ionswithyouactuallyare!

ENHANCEYOURLEARNING

1.Describeanexampleofhowyouwereabsolutely100percentcertainofsomethingandwerelaterprovenwrong.Asaresultofthisandsimilarincidents,doyouthinkyouaremorecapablenowofacceptingcriticismofyourideasfromothers?

2.Howcouldyoumakeyourstudysessionswithclassmatesmoreeffective?

3.Howwouldyouhandleitifyoufoundyourselfinagroupthatseemedtofocusonotherissuesbesidesyourstudies?

BradRothandhisdogSuki,enjoyingtheMichiganfallcolor.

INSIGHTSONLEARNINGFROMPHYSICSPROFESSORBRADROTH,AFELLOWOFTHEAMERICANPHYSICALSOCIETYANDCO-AUTHOROFINTERMEDIATEPHYSICSFORMEDICINEANDBIOLOGY

“OnethingIstressinmyclassesistothinkbeforeyoucalculate.Ireallyhatethe‘plugandchug’approachthatmanystudentsuse.Also,IfindmyselfconstantlyremindingstudentsthatequationsareNOTmerelyexpressionsyouplugnumbersintotogetothernumbers.Equationstellastoryabouthowthephysicalworldworks.Forme,thekeytounderstandinganequationinphysicsistoseetheunderlyingstory.Aqualitativeunderstandingofanequationismoreimportantthangettingquantitativelycorrectnumbersoutofit.“Hereareafewmoretips:

1.“Often,ittakeswaylesstimetocheckyourworkthantosolveaproblem.Itisapitytospendtwentyminutessolvingaproblemandthengetitwrongbecauseyoudidnotspendtwominutescheckingit.

2.“Unitsofmeasurementareyourfriend.Iftheunitsdon’tmatchoneachsideofanequation,yourequationisnotcorrect.Youcan’taddsomethingwithunitsofsecondstosomethingwithunitsofmeters.It’slikeaddingapplesandrocks—nothingediblecomesofit.Youcanlookbackatyourwork,andifyoufindtheplacewheretheunits

stopmatching,youprobablywillfindyourmistake.Ihavebeenaskedtoreviewresearchpapersthataresubmittedtoprofessionaljournalsthatcontainsimilaruniterrors.

3.“Youneedtothinkaboutwhattheequationmeans,sothatyourmathresultandyourintuitionmatch.Iftheydon’tmatch,thenyouhaveeitheramistakeinyourmathoramistakeinyourintuition.Eitherway,youwinbyfiguringoutwhythetwodon’tmatch.

4.“(Somewhatmoreadvanced)Foracomplicatedexpression,takelimitingcaseswhereonevariableoranothergoestozeroorinfinity,andseeifthathelpsyouunderstandwhattheequationissaying.”

W

{17}

testtaking

e’vementioneditearlier,butit’sworthrepeating,inboldletters:Testingisitselfanextraordinarilypowerfullearningexperience.Thismeansthattheeffortyouputintotest

taking,includingthepreliminarymini-testsofyourrecallandyourabilitytoproblem-solveduringyourpreparation,isoffundamentalimportance.Ifyoucomparehowmuchyoulearnbyspendingonehourstudyingversusonehourtakingatestonthatsamematerial,youwillretainandlearnfarmoreasaresultofthehouryouspenttakingatest.Testing,itseems,hasawonderfulwayofconcentratingthemind.

Virtuallyeverythingwe’vetalkedaboutinthisbookhasbeendesignedtohelpmakethetestingprocessseemstraightforwardandnatural—simplyanextensionofthenormalproceduresyouusetolearnthematerial.Soit’stimenowtocutdirectlytooneofthecentralfeaturesofthischapterandtheentirebook—achecklistyoucanusetoseewhetheryourpreparationfortesttakingisontarget.

TESTPREPARATIONCHECKLIST

ProfessorRichardFelderisalegendamongengineeringeducators—hehasarguablydoneasmuchasormorethananyeducatorinthiscenturytohelpstudentsworldwidetoexcelinmathandscience.1OneofthesimplestandperhapsmosteffectivetechniquesDr.Felderhasusedtohelpstudentsislaidoutinamemohewrotetostudentswhohavebeendisappointedwiththeirtestgrades.2“Manyofyouhavetoldyourinstructorthatyouunderstoodthecoursematerialmuchbetterthanyourlasttestgradeshowed,andsomeofyouaskedwhatyoushoulddotokeepthesamethingfromhappeningonthenexttest.“Letmeaskyousomequestionsabouthowyoupreparedforthetest.Answerthemas

honestlyasyoucan.Ifyouanswer‘No’tomanyofthem,yourdisappointingtestgradeshouldnotbetoosurprising.Iftherearestillalotof‘Nos’afterthenexttest,yourdisappointinggradeonthattestshouldbeevenlesssurprising.Ifyouranswertomostofthesequestionsis‘Yes’andyoustillgotapoorgrade,somethingelsemustbegoingon.Itmightbeagoodideaforyoutomeetwithyourinstructororacounselortoseeifyoucanfigureoutwhatitis.

“You’llnoticethatseveralofthequestionspresumethatyou’reworkingwithclassmatesonthehomework—eithercomparingsolutionsyoufirstobtainedindividuallyoractuallygettingtogethertoworkoutthesolutions.Eitherapproachisfine.Infact,ifyou’vebeenworkingentirelybyyourselfandyourtestgradesareunsatisfactory,Iwouldstronglyencourageyoutofindoneortwohomeworkandstudypartnerstoworkwithbeforethenexttest.(Becarefulaboutthesecondapproach,however;ifwhatyou’redoingismainlywatchingothersworkoutsolutions,you’reprobablydoingyourselfmoreharmthangood.)“Theanswertothequestion‘HowshouldIprepareforthetest?’becomesclearonceyou’vefilledoutthechecklist.You

should:

DoWhateverItTakestoBeAbletoAnswer“Yes”toMostoftheQuestions.

Test Preparat ionChecklist

Answer“Yes”onlyifyouusuallydidthethingsdescribed(asopposedtooccasionallyornever).

Homework

_Yes_No1.Didyoumakeaseriousefforttounderstandthetext?(Justhuntingforrelevantworked-outexamplesdoesn’tcount.)

_Yes_No2.Didyouworkwithclassmatesonhomeworkproblems,oratleastcheckyoursolutionswithothers?

_Yes_No3.Didyouattempttooutlineeveryhomeworkproblemsolutionbeforeworkingwithclassmates?

Test Preparat ion

Themore“Yes”responsesyourecorded,thebetteryourpreparationforthetest.Ifyourecordedtwoormore“No”responses,thinkseriouslyaboutmakingsomechangesinhowyouprepareforthenexttest.

_Yes_No4.Didyouparticipateactivelyinhomeworkgroupdiscussions(contributingideas,askingquestions)?

_Yes_No5.Didyouconsultwiththeinstructororteachingassistantswhenyouwerehavingtroublewithsomething?

_Yes_No6.DidyouunderstandALLofyourhomeworkproblemsolutionswhentheywerehandedin?

_Yes_No7.Didyouaskinclassforexplanationsofhomeworkproblemsolutionsthatweren’tcleartoyou?

_Yes_No8.Ifyouhadastudyguide,didyoucarefullygothroughitbeforethetestandconvinceyourselfthatyoucoulddoeverythingonit?

_Yes_No9.Didyouattempttooutlinelotsofproblemsolutionsquickly,withoutspendingtimeonthealgebraandcalculations?

_Yes_No10.Didyougooverthestudyguideandproblemswithclassmatesandquizoneanother?

_Yes_No11.Iftherewasareviewsessionbeforethetest,didyouattenditandaskquestionsaboutanythingyouweren’tsureabout?

_Yes_No12.Didyougetareasonablenight’ssleepbeforethetest?(Ifyouranswerisno,youranswersto1–11maynotmatter.)

_Yes_NoTOTAL

TheHard-Start–Jump-to-EasyTechnique

Theclassicwaystudentsaretaughttoapproachtestsinmathandscienceistotackletheeasiestproblemsfirst.Thisisbasedonthenotionthatthatbythetimeyou’vefinishedtherelativelysimpleproblems,you’llbeconfidentinhandlingthemoredifficult.

Thisapproachworksforsomepeople,mostlybecauseanythingworksforsomepeople.Unfortunately,however,formostpeopleit’scounterproductive.Toughproblemsoftenneedlotsoftime,meaningyou’dwanttostartonthemfirstthingonatest.Difficultproblemsalsoscreamforthecreativepowersofthediffusemode.Buttoaccessthediffusemode,youneedtonotbefocusingonwhatyouwantsobadlytosolve!

Whattodo?Easyproblemsfirst?Orhard?Theansweristostartwiththehardproblems—butquicklyjumptotheeasyones.Here’swhatI

mean.Whenthetestishandedouttoyou,firsttakeaquicklooktogetasenseofwhatitinvolves.(You

shoulddothisinanycase.)Keepyoureyeoutforwhatappearstobethehardestproblem.Thenwhenyoustartworkingproblems,startfirstwithwhatappearstobethehardestone.

Butsteelyourselftopullawaywithinthefirstminuteortwoifyougetstuckorgetasensethatyoumightnotbeontherighttrack.

Thisdoessomethingexceptionallyhelpful.“Startinghard”loadsthefirst,mostdifficultprobleminmind,andthenswitchesattentionawayfromit.Boththeseactivitiescanhelpallowthediffusemodetobeginitswork.

Ifyourinitialworkonthefirsthardproblemhasunsettledyou,turnnexttoaneasyproblem,andcompleteordoasmuchasyoucan.Thenmovenexttoanotherdifficult-lookingproblemandtrytomakeabitofprogress.Again,changetosomethingeasierassoonasyoufeelyourselfgettingboggeddownorstuck.

“Withmystudents,Italkaboutgoodworryandbadworry.Goodworryhelpsprovidemotivationandfocuswhilebadworrysimplywastesenergy.”

—BobBradshaw,ProfessorofMath,OhloneCollege

Whenyoureturntothemoredifficultproblems,you’lloftenbepleasedthatthenextsteporstepsintheproblemwillseemmoreobvioustoyou.Youmaynotbeabletogetallthewaytotheendimmediately,butatleastyoucangetfurtherbeforeyouswitchtosomethingelseonwhichyoucanmakeprogress.

Insomesense,withthisapproachtotesttaking,you’rebeinglikeanefficientchef.Whileyou’rewaitingforasteaktofry,youcanswiftlyslicethetomatogarnish,thenturntoseasonthesoup,andthenstirthesizzlingonions.Thehard-start–jump-to-easytechniquemaymakemoreefficientuseofyourbrainbyallowingdifferentpartsofthebraintoworksimultaneouslyondifferentthoughts.3

Usingthehard-start–jump-to-easytechniqueontestsguaranteesyouwillhaveatleastalittleworkdoneoneveryproblem.ItisalsoavaluabletechniqueforhelpingyouavoidEinstellung—gettingstuckinthewrongapproach—becauseyouhaveachancetolookattheproblemsfromdifferingperspectivesatdifferenttimes.Allthisisparticularlyimportantifyourinstructorgivesyoupartialcredit.

Theonlychallengewiththisapproachisthatyoumusthavetheself-disciplinetopullyourselfoffaproblemonceyoufindyourselfstuckforaminuteortwo.Formoststudents,it’seasy.Forothers,ittakesdisciplineandwillpower.Inanycase,bynowyouareveryawarethatmisplacedpersistencecancreateunnecessarychallengeswithmathandscience.

Thismaybewhytesttakerssometimesfindthatthesolutionpopstomindrightastheywalkoutthedoor.Whentheygaveup,theirattentionswitched,allowingthediffusemodethetinybitoftractionitneededtogotoworkandreturnthesolution.Toolate,ofcourse.

Sometimespeopleareconcernedthatstartingaproblemandthenpullingawayfromitmightcauseconfusioninanexamination.Thisdoesn’tseemtobeaproblemformostpeople;afterall,chefslearntobringvariousfacetsofadinnertogether.Butifyoustillhaveworriesaboutwhetherthisstrategymightworkforyou,tryitfirstonhomeworkproblems.

Beawareofsomeoccasionswhenhard-start–jump-to-easymightnotbeappropriate.Ifthe

instructorgivesonlyafewpointsforareallydifficultproblem(someinstructorsliketodothis),youmaywishtoconcentrateyoureffortselsewhere.Somecomputerizedlicensureexaminationsdon’tallowforbacktracking,soyourbestbetwhenfacingatoughquestionissimplytotakeadeepbreathortwofromthebelly(makesuretobreatheoutalltheway,also)anddoyourbest.Andifyouhaven’tpreparedwellforthetest,thenallbetsareoff.Takewhatsimplepointsyoucan.

DEALINGWITHPANICBEFOREATEST

“Itellmystudentstofaceyourfears.Often,yourworstfearisnotgettingthegradesyouneedforyourchosencareer.Howcanyouhandlethis?Simple.HaveaplanBforanalternativecareer.Onceyouhaveaplanfortheworstcontingency,you’llbesurprisedtoseethatthefearwillbegintosubside.“Studyhardupuntilthedayofthetest,andthenletitgo.Tellyourself,‘Oh,well,letmejustseehowmanyquestionsI

cangetright.Icanalwayspursuemyothercareerchoice.’Thathelpsreleasestresssoyouactuallydobetterandgetclosertoyourfirstcareerchoice.”

—TraceyMagrann,ProfessorofBiologicalSciences,SaddlebackCollege

WhyAnxietyCanAriseonTestsandHowtoDealwithIt

Ifyou’reastressed-outtesttaker,keepinmindthatthebodyputsoutchemicals,suchascortisol,whenitisunderstress.Thiscancausesweatypalms,aracingheart,andaknotinthepitofyourstomach.Butinterestingly,researchfindsthatit’showyouinterpretthosesymptoms—thestoryyoutellyourselfaboutwhyyouarestressed—thatmakesallthedifference.Ifyoushiftyourthinkingfrom“thistesthasmademeafraid”to“thistesthasgotmeexcitedtodomybest!”itcanmakeasignificantimprovementinyourperformance.4

Anothergoodtipforpanickytesttakersistomomentarilyturnyourattentiontoyourbreathing.Relaxyourstomach,placeyourhandonit,andslowlydrawadeepbreath.Yourhandshouldmoveout,evenasyourwholechestismovingoutwardlikeanexpandingbarrel.

Bydoingthistypeofdeepbreathing,youaresendingoxygentocriticalareasofyourbrain.Thissignalsthatalliswellandhelpscalmyoudown.Butdon’tjuststartthisbreathingonthedayofthetest.Ifyouhavepracticedthisbreathingtechniqueintheweeksbefore—justaminuteortwohereandthereisallittakes—youwillslidemoreeasilyintothebreathingpatternduringthetest.(Remember,practicemakespermanent!)It’sparticularlyhelpfultomoveintothedeeperbreathingpatterninthosefinalanxiousmomentsbeforeatestishandedout.(Andyes,ifyou’reinterested,therearedozensofappstohelpyou.)

Anothertechniqueinvolvesmindfulness.5Inthistechnique,youlearntodistinguishbetweenanaturallyarisingthought(Ihaveabigtestnextweek)andanemotionalprojectionthatcantagalongafterthatinitialthought(IfIflunkthetest,Iwillwashoutoftheprogram,andI’mnotsurewhatI’lldothen!).Thesetagalongthoughts,itseems,areprojectionsthatariseasglimmersfromthediffusemode.Evenafewweeksofsimplepracticeinlearningtoreframethesethoughtsandfeelingsassimplementaltagalongprojectionsseemstohelpeaseandquietthemind.Reframingyourreactiontosuchintrusivethoughtsworksmuchbetterthansimplytryingtosuppressthem.Studentswhospentafewweekspracticingwiththemindfulnessapproachperformedbetterontheirtests,experiencing

fewerdistractingthoughts.Nowyoucanseewhywaitinguntiltheendofthetesttoworkonthehardestquestionscanleadto

problems.Justwhenyouareincreasinglystressedoutbecauseyouarerunningoutoftime,youarealsosuddenlyfacingthetoughestproblems!Asyourstresslevelssoar,youconcentrateintently,thinkingthatfocusedattentionwillsolveyourproblems,butofcourse,yourfocusinsteadpreventsthediffusemodefrombeingabletogotowork.

Theresult?“Paralysisbyanalysis.”6The“hard-start–jump-to-easytechniquehelpspreventthis.

MULTIPLE“GUESS”ANDPRACTICETESTS...AFEWTIPS

“WhenIgivemultiple-choicetests,Isometimesfindthatstudentsfailtofullygraspwhatthequestionisaskingbeforetheybargeahead,readingtheansweroptions.Iadvisethemtocoveruptheanswersandtotrytorecalltheinformationsotheycananswerthequestionontheirownfirst.“Whenmystudentscomplainthatthepracticetestwaswaaaaayeasierthantherealone,Iask:Whatarethe

confoundingvariablesthatmakethetwosituationsdifferent?Whenyoutookthepracticetest,wereyouathomerelaxingwithtuneson?Takingitwithafellowstudent?Notimelimit?Answerkeyandclassmaterialsathand?Thesecircumstancesarenotexactlylikeacrowdedclassroomwithaclocktickingaway.Iactuallyencouragethosewithtestanxietytobringtheirpracticetesttoanotherclass(bigclasseswhereonecansliprightinandsitatthebackunnoticed)andtrytakingitthere.”

—SusanSajnaHebert,ProfessorofPsychology,LakeheadUniversity

FinalThoughtsonTesting

Thedaybeforeatest(ortests),haveaquicklookoverthematerialstobrushuponthem.You’llneedbothyourfocused-modeanddiffusemode“muscles”thenextday,soyoudon’twanttopushyourbraintoohard.(Youwouldn’trunaten-mileracethedaybeforerunningamarathon.)Don’tfeelguiltyifyoucan’tseemtogetyourselftoworktoohardthedaybeforeabigexamination.Ifyou’vepreparedproperly,thisisanaturalreaction:Youaresubconsciouslypullingbacktoconservementalenergy.

Whiletakingatest,youshouldalsorememberhowyourmindcantrickyouintothinkingwhatyou’vedoneiscorrect,evenifitisn’t.Thismeansthat,wheneverpossible,youshouldblink,shiftyourattention,andthendouble-checkyouranswersusingabig-pictureperspective,askingyourself,“Doesthisreallymakesense?”Thereisoftenmorethanonewaytosolveaproblem,andcheckingyouranswersfromadifferentperspectiveprovidesagoldenopportunityforverifyingwhatyou’vedone.

Ifthere’snootherwaytocheckexcepttostepbackthroughyourlogic,keepinmindthatsimpleissueslikemissedminussigns,incorrectlyaddednumbers,and“droppedatoms”havetrippedupeventhemostadvancedmathematics,science,andengineeringstudents.Justdoyourbesttocatchthem.Inscienceclasses,havingyourunitsofmeasurementmatchoneachsideoftheequationcanprovideanimportantclueaboutwhetheryou’vedonetheproblemcorrectly.

Theorderinwhichyouworktestsisalsoimportant.Studentsgenerallyworktestsfromfronttoback.Whenyouarecheckingyourwork,ifyoustartmoretowardthebackandworktowardthefront,itsometimesseemstogiveyourbrainafresherperspectivethatcanallowyoutomoreeasily

catcherrors.Nothingisevercertain.Occasionallyyoucanstudyhardandthetestgodssimplydon’t

cooperate.Butifyoupreparewellbypracticingandbybuildingastrongmentallibraryofproblem-solvingtechniques,andapproachtesttakingwisely,youwillfindthatluckwillincreasinglybeonyourside.

SUMMINGITUP

Notgettingenoughsleepthenightbeforeatestcannegateanyotherpreparationyou’vedone.Takingatestisseriousbusiness.Justasfighterpilotsanddoctorsgothroughchecklists,goingthroughyourowntestpreparationchecklistcanvastlyimproveyourchancesofsuccess.Counterintuitivestrategiessuchasthehard-start–jump-to-easytechniquecangiveyourbrainachancetoreflectonharderchallengesevenasyou’refocusingonother,morestraightforwardproblems.Thebodyputsoutchemicalswhenitisunderstress.Howyouinterpretyourbody’sreactiontothesechemicalsmakesallthedifference.Ifyoushiftyourthinkingfrom“Thistesthasmademeafraid”to“Thistesthasgotmeexcitedtodomybest!”ithelpsimproveyourperformance.Ifyouarepanickedonatest,momentarilyturnyourattentiontoyourbreathing.Relaxyourstomach,placeyourhandonit,andslowlydrawadeepbreath.Yourhandshouldmoveoutward,andyourwholechestshouldexpandlikeabarrel.Yourmindcantrickyouintothinkingthatwhatyou’vedoneiscorrect,evenifitisn’t.Thismeansthat,wheneverpossible,youshouldblink,shiftyourattention,andthendouble-checkyouranswersusingabig-pictureperspective,askingyourself,“Doesthisreallymakesense?”

PAUSEANDRECALL

Closethebookandlookaway.What werethemainideasofthischapter?What newideaswillbepart icularlyimportant foryoutot ryrelatedtotest ing?

ENHANCEYOURLEARNING

1.Whatistheoneextraordinarilyimportantpreparationstepfortakingatest?(Hint:Ifyoudon’ttakethisstep,nothingelseyoudotoprepareforthetestmatters.)

2.Explainhowyouwoulddeterminewhetheritistimetopullyourselfoffadifficultproblemonatestwhenyouareusingthehard-start–jump-to-easytechnique.

3.Adeep-breathingtechniquewassuggestedtohelpwithfeelingsofpanic.Whydoyouthink

thediscussionemphasizedbreathingsothatthebellyrises,ratherthanjusttheupperchest?

4.Whywouldyouwanttotrytoshiftyourattentionmomentarilybeforerecheckingyouranswersonatest?

PSYCHOLOGISTSIANBEILOCKONHOWTOPREVENTTHEDREADED“CHOKE”

SianBeilockisapsychologyprofessorattheUniversityofChicago.Sheisoneoftheworld’sleadingexpertsonhowtoreducefeelingsofpanicunderhigh-stakesconditions,andistheauthorofthebookChoke:WhattheSecretsoftheBrainRevealaboutGettingItRightWhenYouHaveTo.7“High-stakeslearningandperformancesituationscanputyouunderalotofstress.However,thereisagrowingbodyofresearchshowingthatfairlysimplepsychologicalinterventionscanloweryouranxietyabouttestsandboostwhatyoulearnintheclassroom.Theseinterventionsdon’tteachacademiccontent;theytargetyourattitudes.“Myresearchteamhasfoundthatifyouwriteaboutyourthoughtsandfeelingsabout

anupcomingtestimmediatelybeforeyoutakethetest,itcanlessenthenegativeimpactofpressureonperformance.Wethinkthatwritinghelpstoreleasenegativethoughtsfrommind,makingthemlesslikelytopopupanddistractyouintheheatofthemoment.“Theminorstressofmanyself-testsasyoumasterthematerialcanalsoprepareyou

forthemoreintensestressofrealtests.Asyou’velearnedinthisbook,testingyourselfwhileyouarelearningisagreatwaytocommitinformationtomind,makingiteasiertofishoutintheheatofahigh-stakesexam.“It’salsotruethatnegativeself-talk—thatis,negativethoughtsarisingfromyourown

mind—canreallyhurtyourperformance,somakesurethatwhatyousayandthinkaboutyourselfasyouarepreparingfortestsisalwaysupbeat.Cutyourselfoffinmidthoughtif

needbetopreventnegativity,evenifyoufeelthedragonsofdoomawaityou.Ifyouflubaproblem,orevenmanyproblems,keepyourspiritsupandturnyourfocustothenextproblem.“Finally,onereasonstudentssometimeschokeonatestisthattheyfranticallydiverightintosolvingaproblembeforethey’ve

reallythoughtaboutwhattheyarefacing.Learningtopauseforafewsecondsbeforeyoustartsolvingaproblemorwhenyouhitaroadblockcanhelpyouseethebestsolutionpath—thiscanhelppreventtheultimatechokingfeelingwhenyousuddenlyrealizeyou’vespentalotoftimepursuingadeadend.“Youcandefinitelylearntokeepyourstresswithinbounds.Surprisingly,youwouldn’twanttoeliminatestressaltogether,

becausealittlestresscanhelpyouperformatyourbestwhenitmattersmost.“Goodluck!”

R

{18}

unlockyourpotential

ichardFeynman,thebongo-playing,NobelPrize–winningphysicist,wasahappy-go-luckyguy.Buttherewereafewyears—thebestandworstofhislife—whenhisexuberancewas

challenged.Intheearly1940s,Feynman’sbelovedwife,Arlene,layinadistanthospital,deathlyillwith

tuberculosis.HeonlyrarelycouldgetawaytoseeherbecausehewasintheisolatedNewMexicotownofLosAlamos,workingononeofthemostimportantprojectsofWorldWarII—thetop-secretManhattanProject.Backthen,Feynmanwasnobodyfamous.Nospecialprivilegeswereaffordedhim.

Tohelpkeephismindoccupiedwhenhisworkdayendedandanxietyorboredomreareditshead,Feynmanbeganafocusedefforttopeerintopeople’sdeepest,darkestsecrets:Hebeganfiguringouthowtoopensafes.

Becominganaccomplishedsafecrackerisn’teasy.Feynmandevelopedhisintuition,masteringtheinternalstructuresofthelocks,practicinglikeaconcertpianistsohisfingerscouldswiftlyrunthroughremainingpermutationsifhecoulddiscoverthefirstnumbersofacombination.

Eventually,FeynmanhappenedtolearnofaprofessionallocksmithwhohadrecentlybeenhiredatLosAlamos—arealexpertwhocouldopenasafeinseconds.

Anexpert,rightathand!Feynmanrealizedifonlyhecouldbefriendthisman,thedeepestsecretsofsafecrackingwouldbehis.

INTHISBOOKwe’veexplorednewwaysoflookingathowyoulearn.Sometimes,aswe’vediscovered,yourdesiretofigurethingsoutrightnowiswhatpreventsyoufrombeingabletofigurethingsout.It’salmostasif,whenyoureachtooquicklywithyourrighthand,yourlefthandautomaticallylatchesonandholdsyouback.

Greatartists,scientists,engineers,andchessmasterslikeMagnusCarlsentapintothenaturalrhythmoftheirbrainsbyfirstintentlyfocusingtheirattention,workinghardtogettheproblemwellinmind.Thentheyswitchtheirattentionelsewhere.Thisalternationbetweenfocusedanddiffusemethodsofthinkingallowsthoughtcloudstodriftmoreeasilyintonewareasofthebrain.Eventually,snippetsoftheseclouds—refined,refluffed—canreturnwithusefulpartsofasolution.

Reshapingyourbrainisunderyourcontrol.Thekeyispatientpersistence—workingknowledgeablywithyourbrain’sstrengthsandweaknesses.

Youcanimproveyourfocusingabilitybygentlyredirectingyourresponsestointerruptingcues

likeyourphone’sringorthebeepofatextmessage.ThePomodoro—abrief,timedperiodoffocusedattention—isapowerfultoolindivertingthewell-meaningzombiesofyourhabitualresponses.Onceyou’vedoneaboutofhard,focusedwork,youcanthenreallysavorthementalrelaxationthatfollows.

Theresultofweeksandmonthsofgradualeffort?Sturdyneuralstructureswithwell-curedmortarlaidbetweeneachnewlearningperiod.Learninginthisway,withregularperiodsofrelaxationbetweentimesoffocusedattention,notonlyallowsustohavemorefun,butalsoallowsustolearnmoredeeply.Therelaxationperiodsprovidetimetogainperspective—tosynthesizeboththecontextandthebigpictureofwhatwearedoing.

Bemindfulthatpartsofourbrainarewiredtobelievethatwhateverwe’vedone,nomatterhowglaringlywrongitmightbe,isjustfine,thankyouverymuch.Indeed,ourabilitytofoolourselvesispartofwhywecheckback—Doesthisreallymakesense?—beforeturninginanexamination.Byensuringthatwestepbackandtakefreshperspectivesonourwork,bytestingourselvesthroughrecall,andbyallowingourfriendstoquestionus,wecanbettercatchourillusionsofcompetenceinlearning.Itistheseillusions,asmuchasanyreallackofunderstanding,thatcantripusupenroutetosuccessinstudyingmathandscience.

Rotememorization,oftenatthelastminute,hasgivenmanylower-levellearnerstheillusorysensethattheyunderstandmathandscience.Astheyclimbtohigherlevels,theirweakunderstandingeventuallycrumbles.Butourgrowingunderstandingofhowthemindtrulylearnsishelpingusmovepastthesimplisticideathatmemorizationisalwaysbad.Wenowknowthatdeep,practicedinternalizationofwell-understoodchunksisessentialtomasteringmathandscience.Wealsoknowthat,justasathletescan’tproperlydeveloptheirmusclesiftheytraininlast-minutecrammingsessions,studentsinmathandsciencecan’tdevelopsolidneuralchunksiftheyprocrastinateintheirstudies.

Nomatterwhatourageanddegreeofsophistication,partsofourbrainremainchildlike.Thismeansthatwesometimescanbecomefrustrated,asignaltoustotakeabreather.Butourever-presentinnerchildalsogivesusthepotentialtoletgoanduseourcreativitytohelpusvisualize,remember,makefriendswith,andtrulyunderstandconceptsinmathandsciencethatatfirstcanseemterriblydifficult.

Inasimilarway,we’vefoundthatpersistencecansometimesbemisplaced—thatrelentlessfocusonaproblemblocksourabilitytosolvethatproblem.Atthesametime,big-picture,long-termpersistenceiskeytosuccessinvirtuallyanydomain.Thiskindoflong-termstick-to-it-ivenessiswhatcanhelpgetuspasttheinevitablenaysayersorunfortunatevicissitudesoflifethatcantemporarilymakeourgoalsanddreamsseemtoofartograsp.

Acentralthemeofthisbookistheparadoxicalnatureoflearning.Focusedattentionisindispensableforproblemsolving—yetitcanalsoblockourabilitytosolveproblems.Persistenceiskey—butitcanalsoleaveusunnecessarilypoundingourheads.Memorizationisacriticalaspectofacquiringexpertise—butitcanalsokeepusfocusedonthetreesinsteadoftheforest.Metaphorallowsustoacquirenewconcepts—butitcanalsokeepusweddedtofaultyconceptions.

Studyingroupsoralone,starthardorstarteasy,learnconcretelyorinabstract,successorfailure...Intheend,integratingthemanyparadoxesoflearningaddsvalueandmeaningtoeverythingwedo.

Partofthemagiclongusedbytheworld’sbestthinkershasbeentosimplify—toputthingsintotermsthatevenakidbrotherorsistercanunderstand.This,indeed,wasRichardFeynman’sapproach;hechallengedsomeofthemostesoterictheoreticalmathematiciansheknewtoputtheircomplicated

theoriesinsimpleterms.Itturnedouttheycould.Youcan,too.AndlikebothFeynmanandSantiagoRamónyCajal,you

canusethestrengthsoflearningtohelpreachyourdreams.

ASFEYNMANCONTINUEDtorefinehissafecrackingskills,hebefriendedtheprofessionallocksmith.Throughtimeandtalk,Feynmangraduallysweptawaysuperficialpleasantries,diggingdeeperanddeepersothathecouldunderstandthenuancebehindwhathesawtobethelocksmith’suttermastery.

Lateonenight,atlonglast,thatmostvaluableofarcaneknowledgebecameclear.Thelocksmith’ssecretwasthathewasprivytothemanufacturers’defaultsettings.Byknowingthedefaultsettings,thelocksmithwasoftenabletoslipintosafesthathadbeenleft

unchangedsincethey’darrivedfromthemanufacturer.Whereaseveryonethoughtthatsafecrackingwizardrywasinvolved,itwasasimpleunderstandingofhowthedevicearrivedfromthemanufacturerthatwasfundamental.

LikeFeynman,youcanachievestartlinginsightsintohowtounderstandmoresimply,easily,andwithlessfrustration.Byunderstandingyourbrain’sdefaultsettings—thenaturalwayitlearnsandthinks—andtakingadvantageofthisknowledge,you,too,canbecomeanexpert.

Inthebeginningofthebook,Imentionedthattherearesimplementaltricksthatcanbringmathandscienceintofocus,tricksthatarehelpfulnotonlyforpeoplewhoarebadatmathandsciencebutalsoforthosewhoalreadygoodatit.You’vewalkedthroughallthesetricksinthecourseofreadingthisbook.But,asyounowknow,nothingbeatsgraspingthechunkedandsimplifiedessence.Sowhatfollowssumsupmyfinalthoughts—thechunkedessenceofsomeofthecentralideasinthisbook,distilledintothetenbestandworstrulesofstudying.

Remember—LadyLuckfavorstheonewhotries.Alittleinsightintolearninghowtolearnbestdoesn’thurt,either.

TENRULESOFGOODSTUDYING

1.Userecall.Afteryoureadapage,lookawayandrecallthemainideas.Highlightverylittle,andneverhighlightanythingyouhaven’tputinyourmindfirstbyrecalling.Tryrecallingmainideaswhenyouarewalkingtoclassorinadifferentroomfromwhereyouoriginallylearnedit.Anabilitytorecall—togeneratetheideasfrominsideyourself—isoneofthekeyindicatorsofgoodlearning.

2.Test yourself.Oneverything.Allthetime.Flashcardsareyourfriend.

3.Chunkyourproblems.Chunkingisunderstandingandpracticingwithaproblemsolutionsothatitcanallcometomindinaflash.Afteryousolveaproblem,rehearseit.Makesureyoucansolveitcold—everystep.Pretendit’sasongandlearntoplayitoverandoveragaininyourmind,sotheinformationcombinesintoonesmoothchunkyoucanpullupwheneveryouwant.

4.Spaceyourrepet it ion.Spreadoutyourlearninginanysubjectalittleeveryday,justlikeanathlete.Yourbrainislikeamuscle—itcanhandleonlyalimitedamountofexerciseononesubjectatatime.

5.Alternatedifferent problem-solvingtechniquesduringyourpract ice.Neverpracticetoolongatanyonesessionusingonlyoneproblem-solvingtechnique—afterawhile,youarejustmimickingwhatyoudidonthepreviousproblem.Mixitupandworkondifferenttypesofproblems.Thisteachesyoubothhowandwhentouseatechnique.(Booksgenerallyarenotsetupthisway,soyou’llneedtodothisonyourown.)Aftereveryassignmentandtest,gooveryourerrors,makesureyouunderstandwhyyoumadethem,andthenreworkyoursolutions.Tostudymosteffectively,handwrite(don’ttype)aproblemononesideofaflashcardandthesolutionontheother.(Handwritingbuildsstrongerneuralstructuresinmemorythantyping.)Youmightalsophotographthecardifyouwanttoloaditintoastudyapponyoursmartphone.Quizyourselfrandomlyondifferenttypesofproblems.

Anotherwaytodothisistorandomlyflipthroughyourbook,pickoutaproblem,andseewhetheryoucansolveitcold.

6.Takebreaks.Itiscommontobeunabletosolveproblemsorfigureoutconceptsinmathorsciencethefirsttimeyouencounterthem.Thisiswhyalittlestudyeverydayismuchbetterthanalotofstudyingallatonce.Whenyougetfrustratedwithamathorscienceproblem,takeabreaksothatanotherpartofyourmindcantakeoverandworkinthebackground.

7.Useexplanatoryquest ioningandsimpleanalogies.Wheneveryouarestrugglingwithaconcept,thinktoyourself,HowcanIexplainthissothataten-year-oldcouldunderstandit?Usingananalogyreallyhelps,likesayingthattheflowofelectricityisliketheflowofwater.Don’tjustthinkyourexplanation—sayitoutloudorputitinwriting.Theadditionaleffortofspeakingandwritingallowsyoutomoredeeplyencode(thatis,convertintoneuralmemorystructures)whatyouarelearning.

8.Focus.Turnoffallinterruptingbeepsandalarmsonyourphoneandcomputer,andthenturnonatimerfortwenty-fiveminutes.Focusintentlyforthosetwenty-fiveminutesandtrytoworkasdiligentlyasyoucan.Afterthetimergoesoff,giveyourselfasmall,funreward.Afewofthesesessionsinadaycanreallymoveyourstudiesforward.Trytosetuptimesandplaceswherestudying—notglancingatyourcomputerorphone—isjustsomethingyounaturallydo.

9.Eat yourfrogsfirst .Dothehardestthingearliestintheday,whenyouarefresh.

10.Makeamentalcont rast .Imaginewhereyou’vecomefromandcontrastthatwiththedreamofwhereyourstudieswilltakeyou.Postapictureorwordsinyourworkspacetoremindyouofyourdream.Lookatthatwhenyoufindyourmotivationlagging.Thisworkwillpayoffbothforyouandthoseyoulove!

TENRULESOFBADSTUDYING

Avoidthesetechniques—theycanwasteyourtimeevenwhiletheyfoolyouintothinkingyou’relearning!

1.Passiverereading—sittingpassivelyandrunningyoureyesbackoverapage.Unlessyoucanprovethatthematerialismovingintoyourbrainbyrecallingthemainideaswithoutlookingatthepage,rereadingisawasteoftime.

2.Let t inghighlightsoverwhelmyou.Highlightingyourtextcanfoolyourmindintothinkingyouareputtingsomethinginyourbrain,whenallyou’rereallydoingismovingyourhand.Alittlehighlightinghereandthereisokay—sometimesitcanbehelpfulinflaggingimportantpoints.Butifyouareusinghighlightingasamemorytool,makesurethatwhatyoumarkisalsogoingintoyourbrain.

3.Merelyglancingat aproblem’ssolut ionandthinkingyouknowhowtodoit .Thisisoneoftheworsterrorsstudentsmakewhilestudying.Youneedtobeabletosolveaproblemstep-by-step,withoutlookingatthesolution.

4.Wait ingunt ilthelast minutetostudy.Wouldyoucramatthelastminuteifyouwerepracticingforatrackmeet?Yourbrainislikeamuscle—itcanhandleonlyalimitedamountofexerciseononesubjectatatime.

5.Repeatedlysolvingproblemsofthesametypethat youalreadyknowhowtosolve.Ifyoujustsitaroundsolvingsimilarproblemsduringyourpractice,you’renotactuallypreparingforatest—it’slikepreparingforabigbasketballgamebyjustpracticingyourdribbling.

6.Let t ingstudysessionswithfriendsturnintochat sessions.Checkingyourproblemsolvingwithfriends,andquizzingoneanotheronwhatyouknow,canmakelearningmoreenjoyable,exposeflawsinyourthinking,anddeepenyourlearning.Butifyourjointstudysessionsturntofunbeforetheworkisdone,you’rewastingyourtimeandshouldfindanotherstudygroup.

7.Neglect ingtoreadthetextbookbeforeyoustart workingproblems.Wouldyoudiveintoapoolbeforeyouknewhowtoswim?Thetextbookisyourswimminginstructor—itguidesyoutowardtheanswers.Youwillflounderandwasteyourtimeifyoudon’tbothertoreadit.Beforeyoubegintoread,however,takeaquickglanceoverthechapterorsectiontogetasenseofwhatit’sabout.

8.Not checkingwithyourinst ructorsorclassmatestoclearuppointsofconfusion.Professorsareusedtoloststudentscominginforguidance—it’sourjobtohelpyou.Thestudentsweworryaboutaretheoneswhodon’tcomein.Don’tbeoneofthosestudents.

9.Thinkingyoucanlearndeeplywhenyouarebeingconstant lydist racted.Everytinypulltowardaninstantmessageorconversationmeansyouhavelessbrainpowertodevotetolearning.Everytugofinterruptedattentionpullsouttinyneuralrootsbeforetheycangrow.

10.Not get t ingenoughsleep.Yourbrainpiecestogetherproblem-solvingtechniqueswhenyousleep,anditalsopracticesandrepeatswhateveryouputinmindbeforeyougotosleep.Prolongedfatigueallowstoxinstobuildupinthebrainthatdisrupttheneuralconnectionsyouneedtothinkquicklyandwell.Ifyoudon’tgetagoodsleepbeforeatest,NOTHINGELSEYOUHAVEDONEWILLMATTER.

PAUSEANDRECALL

Closethebookandlookaway.What werethemost important ideasinthisbook?Asyoureflect ,consideralsohowyouwillusetheseideastohelpreshapeyourlearning.

M

afterword

yeighth-grademathandscienceteacherhadapowerfulimpactonmylife.Hepluckedmefromthebackoftheclassandmotivatedmetostriveforexcellence.Irepaidhiminhigh

schoolbygettingaDingeometry—twice.Ijustcouldn’tgetthematerialonmyown,andIdidn’thavetheluxuryofagreatteachertoprodmeinthewaysIneeded.Eventually,incollege,Ifigureditout.Butitwasafrustratingjourney.IwishI’dhadabooklikethisbackthen.

Flashforwardadecadeandahalf.MydaughterturnedmathhomeworkintoaformoftortureDantewouldbetooshytowriteabout.Shewouldhitawallandthenhititagainandagain.Whenshefinallyfinishedcrying,shewouldcirclearoundandeventuallyfigureitout.ButIcouldnevergethertojustbackoffandregroupwithoutthedrama.Iletherreadthisbook.Thefirstthingshesaidwas,“IwishI’dhadthisbookwhenIwasinschool!”

Therehaslongbeenastreamofpotentiallyproductivestudyadvicecomingfromscientists.Unfortunately,ithasseldombeentranslatedsotheaveragestudentcaneasilygraspanduseit.Noteveryscientisthasaknackfortranslation,andnoteverywriterhasafirmgraspofthescience.Inthisbook,BarbaraOakleythreadedthisneedlebeautifully.Heruseofvividexamplesandexplanationsofthestrategiesrevealsnotonlyhowusefulbuthowcredibletheseideasare.WhenIaskedmydaughterwhyshelikedtheadviceinthebook,eventhoughIhadmentionedseveralofthetechniquestoherwhenshewasinmiddleschool,shesaid,“Shetellsyouwhyanditmakessense.”Anotherhittomyparentalego!

Nowthatyouhavereadthisbook,youhavebeenexposedtosomesimpleyetpotentiallypowerfulstrategies—strategies,bytheway,thatcouldbenefityouinmorethanjustmathandscience.Asyou’vediscovered,thesestrategiesgrewfromconsiderableevidenceabouthowthehumanmindworks.Theinterplaybetweenemotionandcognition,thoughseldomputintowords,isanessentialcomponenttoalllearning.Inherownway,mydaughterpointedoutthatstudyingisn’tjustaboutthestrategies.Youhavetobeconvincedthatthosestrategiescanactuallywork.Theclearandcompellingevidenceyoureadinthisbookshouldgiveyoutheconfidencetotrytechniqueswithoutthedoubtandresistancethatoftensabotagesourbestefforts.Learningis,ofcourse,personallyempirical.Theultimateevidencewillcomewhenyouevaluateyourperformanceandattitudeonceyouearnestlydeploythesestrategies.

IamnowacollegeprofessorandIhaveadvisedthousandsofstudentsovertheyears.Manystudentstrytoavoidmathandsciencebecausethey“arenotgoodatit”or“don’tlikeit.”MyadvicetothesestudentshasalwaysbeenthesameadviceIgavemydaughter:“Getgoodatit,andthenseeifyoustillwanttoquit.”Afterall,isn’teducationsupposedtobeaboutgettinggoodatchallengingthings?

Rememberhowdifficultlearningtodrivewas?Now,itisalmostautomaticandgivesyouasenseofindependenceyouwillvaluethroughouttheiradultlife.Bybeingopentonewstrategiesliketheonesinthisbook,learnersnowhavetheopportunitytomovepastanxietyandavoidancetoward

masteryandconfidence.Itisnowuptoyou:Getgood!

—DavidB.Daniel,Ph.D.Professor,PsychologyDepartment

JamesMadisonUniversity

acknowledgments

Inacknowledgingthesupportoftheseindividuals,Iwouldliketomakeclearthatanyerrorsoffactorinterpretationinthisbookaremyown.ToanyonewhosenameImighthaveinadvertentlyomitted,myapologies.

Underlyingthisentireefforthavebeentheunwaveringsupport,encouragement,enthusiasm,andsuperbinsightofmyhusband,PhilipOakley.WemetthirtyyearsagoattheSouthPoleStationinAntarctica—trulyIhadtogototheendsoftheearthtomeetthatextraordinaryman.Heismysoulmateandmyhero.(And,incaseyoumighthavewondered,heisalsothemaninthepuzzle.)

AmastermentorthroughoutmyteachingcareerisDr.RichardFelder—hehasmadeanenormousdifferenceinhowthatcareerunfolded.KevinMendez,thisbook’sartist,hasdoneanincrediblejobinrenderingtheillustrations—Iaminaweofhisartisticabilityandvision.Ourelderdaughter,RosieOakley,hasprovidedkeeninsightandunbelievableencouragementthroughoutthedevelopmentofthisbook.Ouryoungerdaughter,RachelOakley,hasalwaysbeenapillarofsupportinourlives.

MygoodfriendAmyAlkonhaswhatamountstoeditorialX-rayvision—shehasanuncannyabilitytoferretoutareasforimprovement,andwithherhelpthisbookhasreachedafarhigherlevelofclarity,accuracy,andwit.MyoldfriendGuruprasadMadhavanoftheNationalAcademyofScienceshashelpedmeseethebig-pictureimplications,ashasourmutualfriendJoshBrandoff.WritingcoachDaphneGray-Granthasalsobeenagreatsupporterinthedevelopmentofthiswork.

IwouldespeciallyliketoacknowledgethefoundationaleffortsofRitaRosenkranz,aliteraryagentofunparalleledexcellence.AtPenguin,mydeepestthanksandappreciationgotoSaraCarderandJoannaNg,whosevision,editorialacumen,andvastexpertisewithpublishinghavehelpedimmeasurablyinstrengtheningthisbook.Inparticular,IcanonlywishthateveryauthorwouldbesoluckyastoworkwithsomeonewhopossessesJoannaNg’sextraordinaryeditorialtalent.IwouldalsoliketoextendmythankstoAmyJ.Schneider,whosecopyeditingabilitieshavebeenawonderfulboonforthiswork.

SpecialthanksgotoPaulKruchko,whosesimplequestionabouthowIchangedgotmestartedonthisbook.DanteRanceattheInterlibraryLoanDepartmenthascontinuallygonewellaboveandbeyondthecallofduty;mythanksaswelltothesupremelycapablePatClark.Manycolleagueshavebeenverysupportiveinthiswork,particularlyProfessorsAnnaSpagnuolo,LászlóLipták,andLauraWicklundinmath;BarbPenpraseandKellyBerishajinnursing;ChrisKobus,MikePolis,Mohammad-RezaSiadat,andLorenzoSmithinengineering;andBradRothinphysics.AaronBird,U.S.trainingmanagerforCD-adapco,andhiscolleagueNickAppleyard,vicepresidentatCD-adapco,havebothbeenofexceptionalhelp.IwouldalsoliketothankTonyProhaskaforhiskeeneditorialeye.

Thefollowingpeoplehavealsobeenremarkablyhelpfulinsharingtheirexpertise:SianBeilock,MarcoBellini,RobertM.Bilder,MariaAngelesRamónyCajal,NormanD.Cook,TerrenceDeacon,

JavierDeFelipe,LeonardDeGraaf,JohnEmsley,NormanFortenberry,DavidC.Geary,KaryMullis,NancyCosgroveMullis,RobertJ.Richards,DougRohrer,SherylSorby,NeelSundaresan,andNicholasWade.

Someoftheworld’stop-rankeduniversityandcollegeprofessors,asnotedonRateMyProfessors.com,havelentinvaluablesupporttothiseffort.Theirexpertiseincludesmathematics,physics,chemistry,biology,science,engineering,business,economics,finance,education,psychology,sociology,nursing,andEnglish.Highschoolteachersfromtopmagnetschoolshavecontributedaswell.Iwouldliketoparticularlyacknowledgetheassistanceofthefollowingindividuals,whohavereadallorportionsofthebookandprovidedhelpfulfeedbackandinsights:LolaJeanAagaard-Boram,ShaheemAbrahams,JohnQ.Adams,JudiAddelston,AprilLacsinaAkeo,RavelF.Ammerman,RhondaAmsel,J.ScottArmstrong,CharlesBamforth,DavidE.Barrett,JohnBartelt,CelsoBatalha,JoyceMillerBean,JohnBell,PaulBerger,SydneyBergman,RobertaL.Biby,PaulBlowers,AbyA.Boumarate,DanielBoylan,BobBradshaw,DavidS.Bright,KenBrounJr.,MarkE.Byrne,LisaK.Davids,ThomasDay,AndrewDeBenedictis,JasonDechant,RoxannDeLaet,DebraGassnerDragone,KellyDuffy,AlisonDunwoody,RalphM.FeatherJr.,A.VennieFilippas,JohnFrye,CostaGerousis,RichardA.Giaquinto,MichaelGolde,FranklinF.GorospeIV,BruceGurnick,CatherineHandschuh,MikeHarrington,BarrettHazeltine,SusanSajnaHebert,LindaHenderson,MaryM.Jensen,JohnJones,ArnoldKondo,PatrycjaKrakowiak,AnuskaLarkin,KennethR.Leopold,Fok-ShuenLeung,MarkLevy,KarstenLook,KennethMacKenzie,TraceyMagrann,BarryMargulies,RobertMayes,NelsonMaylone,MelissaMcNulty,ElizabethMcPartlan,Heta-MariaMiller,AngeloB.Mingarelli,NormaMinter,ShereseMitchell,DinaMiyoshi,GeraldineMoore,CharlesMullins,RichardMusgrave,RichardNadel,ForrestNewman,KathleenNolta,Pierre-PhilippeOuimet,DelgelPabalan,SusanMaryPaige,JeffParent,VeraPavri,LarryPerez,WilliamPietro,DebraPoole,MarkPorter,JeffreyPrentis,AdelaidaQuesada,RobertRiordan,LindaRogers,JannaRosales,MikeRosenthal,JosephF.Santacroce,Oraldo“Buddy”Saucedo,DonaldSharpe,Dr.D.A.Smith,RobertSnyder,RogerSolano,FrancesR.Spielhagen,HilarySproule,WilliamSproule,ScottPaulStevens,AkelloStone,JamesStroud,FabianHadiprionoTan,CyrilThong,B.LeeTuttle,VinUrbanowski,LynnVazquez,CharlesWeidman,FrankWerner,DaveWhittlesey,NaderZamani,BillZettler,andMingZhang.

Thefollowingstudentshavecontributedinsightfulquotes,sidebars,orsuggestionsforwhichIamverygrateful:NataleeBaetens,RhiannonBailey,LindsayBarber,CharleneBrisson,RandallBroadwell,MaryCha,KyleChambers,ZacharyCharter,JoelCole,BradleyCooper,ChristopherCooper,AukuryCowart,JosephCoyne,MichaelCulver,AndrewDavenport,KatelindDavidson,BrandonDavis,AlexanderDebusschere,HannahDeVilbiss,BrennaDonovan,ShelbyDrapinski,TrevorDrozd,DanielEvola,KatherineFolk,AaronGarofalo,MichaelGashaj,EmanuelGjoni,CassandraGordon,YusraHasan,ErikHeirman,ThomasHerzog,JessicaHill,DylanIdzkowski,WestonJeshurun,EmilyJohns,ChristopherKarras,AllisonKitchen,BryanKlopp,WilliamKoehle,ChelseyKubacki,NikolasLangley-Rogers,XuejingLi,ChristoperLoewe,JonathonMcCormick,JakeMcNamara,PaulaMeerschaert,MateuszMiegoc,KevinMoessner,HarryMooradian,NadiaNoui-Mehidi,MichaelOrrell,MichaelPariseau,LeviParkinson,RachaelPolaczek,MichelleRadcliffe,SunnyRishi,JenniferRose,BrianSchroll,PaulSchwalbe,AnthonySciuto,ZacShaw,DavidSmith,KimberleeSomerville,DavySproule,P.J.Sproule,DarioStrazimiri,JonathanStrong,JonathanSulek,RaviTadi,AaronTeachout,GregoryTerry,AmberTrombetta,RajivVarma,BingxuWang,FangfeiWang,JessicaWarholak,ShaunWassell,MalcolmWhitehouse,MichaelWhitney,DavidWilson,AmandaWolf,AnyaYoung,HuiZhang,andCoryZink.

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endnotes

Chapter1:OpentheDoor

1I’dliketopointeducatorstowardthebookRedirect,bypsychologyprofessorTimothyWilson,whichdescribestheseminalimportanceoffailure-to-successstories(Wilson2011).Helpingstudentschangetheirinnernarrativesformsoneoftheimportantgoalsofthisbook.AleaderindescribingtheimportanceofchangeandgrowthinmindsetisCarolDweck(Dweck2006).

2Sklaretal.2012;Root-BernsteinandRoot-Bernstein1999,chap.1.

Chapter2:EasyDoesIt:WhyTryingTooHardCanSometimesBePartoftheProblem

1Default-modenetworkdiscussions:Andrews-Hanna2012;RaichleandSnyder2007;Takeuchietal.2011.Moregeneraldiscussionofrestingstates:Moussaetal.2012.Inaverydifferentlineofinvestigation,BruceManganhasnotedthatWilliamJames’sdescriptionofthefringeincludesthefollowingfeature:“Thereisan‘alternation’ofconsciousness,suchthatthefringebrieflybutfrequentlycomestotheforeandisdominantoverthenucleusofawareness”(Cook2002,p.237;Mangan1993).

2Immordino-Yangetal.2012.3EdwarddeBonoisthegrandmasterofcreativitystudies,andhisverticalandlateralterminologyisroughlyanalogoustomyuseof

thetermsfocusedanddiffuse(deBono1970).Astutereaderswillnoticemymentionthatthediffusemodeseemstosometimesworkinthebackgroundwhilethefocusedmode

isactive.However,researchfindingsshowthatthedefault-modenetworkforexample(whichisjustoneofthemanyrestingstatenetworks),seemstogoquietwhenthefocusedmodeisactive.Sowhichisit?Mysenseasaneducatorandalearnermyselfisthatsomenonfocusedactivitiescancontinueinthebackgroundwhenfocusedworkistakingplace,aslongasthefocusedattentionisshiftedawayfromtheareaofinterest.Insomesense,then,myuseofthetermdiffusemodemightbethoughtofas“nonfocusedmodeactivitiesdirectedtowardlearning”ratherthansimply“default-modenetwork.”

4Therearealsoafewtightlinkstomoredistantnodesofthebrain,aswe’llexplorelaterwiththeattentionaloctopusanalogy.5Thediffusemodemayalsoinvolveprefrontalareas,butitprobablyhasmoreconnectionsoverallandlessfilteringoutofseemingly

irrelevantconnections.6PsychologistNormanCookhasproposedthat“thefirstelementsinacentraldogmaforhumanpsychologycanbeexpressedas(1)the

flowofinformationbetweentherightandlefthemispheresand(2)betweenthe“dominant”[lefthemisphere]andtheperipheraleffectormechanismsusedforverbalcommunication”(Cook1989,p.15).Butitshouldalsobenotedthathemisphericdifferenceshavebeenusedtolaunchcountlessspuriousoverextrapolationsandinaneconclusions(Efron1990).

7AccordingtotheNationalSurveyofStudentEngagement(2012),engineeringstudentsspendthemosttimestudying—seniorengineeringstudentsspendeighteenhoursonaverageperweekpreparingforclass,whilesenioreducationstudentsspendfifteenhoursandseniorsocialscienceandbusinessstudentsspendaboutfourteenhours.InaNewYorkTimesarticletitled“WhyScienceMajorsChangeTheirMinds(It’sJustSoDarnHard),”emeritusengineeringprofessorDavidE.Goldberghasnotedthattheheavydemandsofcalculus,physics,andchemistrycaninitiatethe“math-sciencedeathmarch”asstudentswashout(Drew2011).

8Foradiscussionofevolutionaryconsiderationsinmathematicalthinking,seeGeary2005,chap.6.Ofcourse,manyabstracttermsaren’trelatedtomathematics.Asurprisingnumberofthesetypesofabstractideas,however,relate

toemotions.Wemaynotbeabletoseethoseterms,butwecanfeelthem,oratleastimportantaspectsofthem.TerrenceDeacon,authorofTheSymbolicSpecies,notestheinherentcomplexityoftheencryption/decryptionproblemof

mathematics:“Imaginebackwhenyouwerefirstencounteringanovelkindofmathematicalconcept,likerecursivesubtraction(i.e.,division).Most

oftenthisabstractconceptistaughtbysimplyhavingchildrenlearnasetofrulesformanipulatingcharactersfornumbersandoperations,thenusingtheserulesagainandagainwithdifferentnumbersinhopesthatthiswillhelpthem‘see’howthisparallelscertainphysicalrelationships.Weoftendescribethisasinitiallylearningtodothemanipulations‘byrote’(whichisinmytermsindexicallearning)andthenwhenthiscanbedonealmostmindlessly,wehopethattheywillseehowthiscorrespondstoaphysicalworldprocess.Atsomepoint,ifallgoeswell,kids‘get’thegeneralabstractcommonalitythatlies‘behind’thesemanyindividualsymbol-to-symbolandformula-to-formulaoperations.Theythusreorganizewhattheyalreadyknowbyroteaccordingtoahigher-ordermnemonicthatisaboutthesecombinatorialpossibilitiesandtheirabstractcorrespondencetothingmanipulation.Thisabstractionstepisoftenquitedifficultformanykids.Butnowconsiderthatthissametransformationatayethigherlevelofabstractionisrequiredtounderstandcalculus.Differentiationiseffectivelyrecursivedivision,andintegrationiseffectivelyrecursivemultiplication,each

carriedoutindefinitely,i.e.,toinfinitesimalvalues(whichispossiblebecausetheydependonconvergentseries,whichthemselvesareonlyknownbyinference,notdirectinspection).ThisabilitytoprojectwhatanoperationentailswhencarriedoutinfinitelyiswhatsolvesZeno’sparadox,whichseemsimpossiblewhenstatedinwords.Butinadditiontothisdifficulty,theLeibnizianformalismwenowusecollapsesthisinfiniterecursionintoasinglecharacter ortheintegralsign)becauseonecan’tactuallykeepwritingoperationsforever.Thismakesthecharactermanipulationofcalculusevenlessiconicofthecorrespondingphysicalreferent.

“Sothereferenceofanoperationexpressedincalculusisineffectdoubly-encrypted.Yes,we’veevolvedmentalcapacitieswell-suitedtothemanipulationofphysicalobjects,soofcoursethisisdifficult.Butmathisaformof‘encryption,’notmerelyrepresentation,anddecryptionisanintrinsicallydifficultprocessbecauseofthecombinatorialchallengesitpresents.Thisiswhyencryptionworkstomakethereferentialcontentofcommunicationsdifficulttorecover.Mypointisthatthisisintrinsictowhatmathis,irrespectiveofourevolvedcapacities.Itisdifficultforpreciselythesamereasonthatdecipheringacodedmessageisdifficult.

“Whatsurprisesmeisthatweallknowthatmathematicalequationsareencryptedmessages,forwhichyouneedtoknowthekeyifyouwanttocrackthecodeandknowwhatisrepresented.Nevertheless,wewonderwhyhighermathisdifficulttoteach,andoftenblametheeducationalsystemorbadteachers.Ithinkthatitissimilarlyabitmisplacedtoblameevolution.”(Personalcommunicationwiththeauthor,July11,2013.)

9Bilalićetal.2008.10Geary2011.SeealsothelandmarkdocumentaryAPrivateUniverse,availableathttp://www.learner.org/resources/series28.html?

pop=yes&pid=9,whichledtomuchresearchintomisconceptionsinunderstandingscience.11AlanSchoenfeld(1992)notesthatinhiscollectionofmorethanahundred“videotapesofcollegeandhighschoolstudentsworking

unfamiliarproblems,roughlysixtypercentofthesolutionattemptsareofthe‘read,makeadecisionquickly,andpursuethatdirectioncomehellorhighwater’variety.”Youcouldcharacterizethisasfocusedthinkingatitsworst.

12Goldacre2010.13Gerardietal.2013.14Hemisphericdifferencesmaysometimesbeimportant,butagain,claimsinthisareashouldbetakenwithcaution.NormanCooksaysit

bestwhenhenotes:“Manydiscussionsinthe1970swentwellbeyondthefacts—ashemispheredifferenceswereinvokedtoexplain,inonefellswoop,allofthepuzzlesofhumanpsychology,includingthesubconsciousmind,creativity,andparapsychologicalphenomena—buttheinevitablebacklashwasalsoexaggerated”(Cook2002,p.9).

15Demareeetal.2005;Gainotti2012.16McGilchrist2010;Mihovetal.2010.17Nielsenetal.2013.19Immordino-Yangetal.2012.18AdifferinglayoutofthisproblemwasprovidedindeBono1970—thatwastheinspirationfortheproblemoutlinedhere.DeBono’s

classicbookcontainsawealthofsuchinsightfulproblemsandiswellworthreading.20AlthoughI’mspeakingoflobbingbetweenthefocusedanddiffusemodes,thereappearstobeananalogouslobbingprocessof

informationbackandforthbetweenthehemispheres.Wecangetsomesenseofhowinformationmightflowbackandforthbetweenthehemispheresinhumansbylookingatstudiesofchicks.Learningnottopeckabitterbeadinvolvesacomplexbackandforthprocessingofthememorytracesbetweenthehemispheresoveranumberofhours(Güntürkün2003).

AnkeBoumaobserves,“Anobservedpatternoflateralitydoesnotmeanthatthesamehemisphereissuperiorforalloftheprocessingstagesrequiredbyaparticulartask.Thereareindicationsthatthe[righthemisphere]maybedominantforonestageofprocessing,whilethe[lefthemisphere]maybedominantforanotherprocessingstage.Therelativedifficultyofaparticularprocessingstageseemstodeterminewhichhemisphereissuperiorforaparticulartask”(Bouma1990,p.86).

21Justmovethecoinsasshown—doyouseehowthenewtrianglewillpointdown?

Chapter3:LearningIsCreating:LessonsfromThomasEdison’sFryingPan

1ThecerebraldistancemodeldevelopedbyMarcelKinsbourneandMerrillHiscock(1983)hypothesizesthatconcurrenttaskswillinterferemorewithoneanothertheclosertogetherthetwotasksareprocessedinthebrain.Twosimultaneoustasksusingthesamehemisphereandparticularlythesameareaofthebraincanreallymessthingsup(Bouma1990,p.122).Perhapsthediffusemodemaybemorecapableofhandlingseveraltasksatoncebecauseoftheunfocusednatureofdiffuseprocesses.

2Rocke2010,p.316,citingGruber1981.3Ibid.,pp.3–4.4Kaufmanetal.2010,inparticularthedisinhibitionhypothesisonpp.222–224;Takeuchietal.2012.5Inattemptingtotrackdowntheprovenanceofthislegend,IcorrespondedwithLeonardDeGraaf,anarchivistwiththeThomasEdison

NationalHistoricalPark.Henoted,“IhaveheardthestoryofEdisonandtheballbearingsbuthaveneverseenanydocumentationthatwouldconfirmit.I’malsonotsureaboutthestory’sorigin.ThismaybeoneofthoseanecdotesthathadsomebasisinrealitybutbecamepartoftheEdisonmythology.”

6Dalí1948,p.36.7GaboraandRanjan2013,p.19.8ChristopherLeeNiebauerandGarvey2004.Niebauerreferstothedistinctionbetweenobjectandmeta-levelthinking.Thethird,

paradoxicalerrorinthesentence,incidentally,isthatthereisnothirderror.9KapurandBielczyc2012,containsanexcellentreviewontheimportanceoffailureinproblemsolving.10ForanicediscussionofthemanyvariationsofwhatEdisonactuallymighthavesaidorwritten,see

http://quoteinvestigator.com/2012/07/31/edison-lot-results/11Andrews-Hanna2012;RaichleandSnyder2007.12DougRohrerandHaroldPashler(2010,p.406)note:”...recentanalysisofthetemporaldynamicsoflearningshowthatlearningis

mostdurablewhenstudytimeisdistributedovermuchgreaterperiodsoftimethaniscustomaryineducationalsettings.”Howthisrelatestoalternationbetweenfocusedandrestingstatenetworksisanimportanttopicforfutureresearch.SeeImmordino-Yangetal.2012.Inotherwords,whatI’vedescribedisareasonablesuppositionforwhatoccurswhilewelearn,butneedstobeborneoutbyfurtherresearch.

13BaumeisterandTierney2011.14Iwanttomakeitclearthattheseareonlymy“bestguess”ideasaboutwhatmightpromotediffuse-modethinking,basedonwhere

peopleseemtogetmanyoftheirmostcreative,“aha!”insights.15Bilalićetal.2008.16Nakanoetal.2012.17KouniosandBeeman2009,p.212.18Dijksterhuisetal.2006.

19Short-termmemoryistheactivatedinformationthatisnotactivelyrehearsed.Workingmemoryisthesubsetofshort-termmemoryinformationthatisthefocusofattentionandactiveprocessing(Baddeleyetal.2009).

20Cowan2001.21Ifyou’reinterestedintheneuralgeographyunderlyingallofthis,itlookslikebothlong-termmemoryandworkingmemoryuse

overlappingregionsinthefrontalandparietallobes.Butthemedialtemporallobeisusedonlyforlong-termmemory—notworkingmemory.SeeGuidaetal.2012,pp.225–226,andDudai2004.

22Baddeleyetal.2009,pp.71–73;Carpenteretal.2012.Spacedrepetitionisalsoknownasdistributedpractice.Dunloskyetal.2013,sec.9,providesanexcellentreviewofdistributedpractice.Unfortunately,asnotedinRohrerandPashler2007,manyeducators,particularlyinmathematics,believeoverlearningisagoodwaytoboostlong-termretention—hencemanysimilarproblemsareassignedthatultimatelydevolvetomake-workwithlittlelong-termbenefit.

23Xieetal.2013.24StickgoldandEllenbogen2008.25JiandWilson2006;Oudietteetal.2011.26Ellenbogenetal.2007.Thediffusemodemayalsoberelatedtolowlatentinhibition—thatis,beingratherabsentmindedandeasily

distractable(Carsonetal.2003).There’screativehopeforthoseofuswhotendtoswitchthoughtsinthemiddleofasentence!27ErlacherandSchredl2010.28Wamsleyetal.2010.

Chapter4:ChunkingandAvoidingIllusionsofCompetence:TheKeystoBecomingan“EquationWhisperer”

1Luria1968.2Beilock2010,pp.151–154.3Childrenlearnthroughfocusedattention,buttheyalsousethediffusemode,withlittleexecutivecontrol,tolearnevenwhentheyare

notpayingfocusedattention(Thompson-Schilletal.2009).Inotherwords,itseemsthatchildrendon’tneedtousethefocusedmodeasmuchasadultsdowhenlearninganewlanguage,whichmaybewhyit’seasierforyoungchildrentopickupanewlanguage.Butatleastsomefocusedlearningappearsnecessarytoacquireanewlanguagebeyondearlychildhood.

4Guidaetal.2012,sec.8.Recently,XinJin,FatuelTecuapetla,andRuiCostarevealedhowneuronsinthebasalgangliaplayanimportantroleinsignalingtheconcatenationofindividualelementsintoabehavioralsequence—theessenceofchunking(Jinetal.2014).RuiCostahasreceiveda2millioneurogranttostudythemechanismofchunking—hisunfoldingresearchwillbearwatching.

5BrentandFelder2012;Swelleretal.2011,chap.8.6AlessandroGuidaandcolleagues(2012,p.235)notedthatchunkcreationapparentlyreliesinitiallyonworkingmemory,whichisin

theprefrontalareas,andresultsfromfocusedattention,whichhelpsbindschunks.Thesechunksalsobegintoreside,withdevelopingexpertise,inlong-termmemoryrelatedtotheparietalregions.Averydifferentaspectofmemoryinvolvesneuraloscillatoryrhythms,whichhelpbindperceptualandcontextualinformationfrommanyareasofthebrain(NyhusandCurran2010).SeeChoetal.2012foranimagingstudyofthedevelopmentofretrievalfluencyinarithmeticproblemsolvinginchildren.

7Baddeleyetal.2009,chap.6;CreeandMcRae2003.8Baddeleyetal.2009,pp.101–104.9The“bigpicture”I’mreferringtocanbethoughtofasacognitivetemplate.SeeGuidaetal.2012,inparticularsec.3.1.Templates

arisingfromthestudyofmathandsciencewouldnaturallytendtobemoreamorphousthanthosearisingfromthecrispoutlinesofchess.Chunks,Guidanotes,canbebuiltveryquickly,buttemplates,whichinvolvefunctionalreorganization,taketime—atleastfiveweeksormore(Guidaetal.2012).SeealsothediscussionofschematainCooperandSweller1987;Mastascusaetal.2011,pp.23–43.AlsousefulinunderstandingtheseideasrelatedtodevelopingexpertiseisthediscussioninBransfordetal.2000,chap.2.Priorknowledgecanbehelpfulinlearningsomethingnewandrelated—butpriorknowledgecanalsoactasahindrance,asitcanmakeitmoredifficulttomakechangesinschemata.Thisisparticularlynoticeablewithstudents’erroneousembeddedbeliefsaboutbasicconceptsinphysics,whicharenotoriouslyresistanttochange(Hake1998;HallounandHestenes1985).AsPaulPintrichandcolleagues(1993,p.170)note:“aparadoxexistsforthelearner;ontheonehand,currentconceptionspotentiallyconstitutemomentumthatresistsconceptualchange,buttheyalsoprovideframeworksthatthelearnercanusetointerpretandunderstandnew,potentiallyconflictinginformation.”

10Gearyetal.2008,pages4-6through4-7;Karpicke2012;Karpickeetal.2009;KarpickeandGrimaldi2012;Kornelletal.2009;RoedigerandKarpicke2006.Forreviews,seeMcDanielandCallender2008;RoedigerandButler2011.

11Karpickeetal.2009,p.471.SeealsotheDunning-Krugereffect,whereincompetentpeoplemistakenlynotetheirabilityhigherthantheyshould.Dunningetal.2003;KrugerandDunning1999;Ehrlingeretal.2008;Bursonetetal.2006.

12Baddeleyetal.2009,p.111.13Dunloskyetal.2013,sec.4.14Longcampetal.2008.15Dunloskyetal.2013,sec.7.16SeeinparticularGuidaetal.2012,whichnoteshowexpertslearntouselong-termmemorytoexpandtheirworkingmemory.See

alsoGearyetal.2008,4-5,whichobserves,“Working-memorycapacitylimitsmathematicalperformance,butpracticecanovercomethislimitationbyachievingautomaticity.”

17Thesolutiontotheanagramis“MadameCurie.”AttributedtoMeyranKraus,http://www.fun-with-words.com/anag_names.html.

18JeffreyKarpickeandcolleagues(2009)suggestedtherelationshipbetweenillusionsofcompetenceinlearningandthedifficultyofanagramswhenyouseethesolutionasopposedtowhenyoudon’tseethesolution.

19HenryRoedigerandMaryPyc(2012,p.243)note:“Professorsinschoolsofeducationandteachersoftenworryaboutcreativityinstudents,alaudablegoal.Thetechniquesweadvocateshowimprovementsinbasiclearningandretentionofconceptsandfacts,andsomepeoplehavecriticizedthisapproachasemphasizing“rotelearning”or“purememorization”ratherthancreativesynthesis.Shouldn’teducationbeaboutfosteringasenseofwonder,discovery,andcreativityinchildren?Theanswertothequestionisyes,ofcourse,butwewouldarguethatastrongknowledgebaseisaprerequisitetobeingcreativeinaparticulardomain.Astudentisunlikelytomakecreativediscoveriesinanysubjectwithoutacomprehensivesetoffactsandconceptsathisorhercommand.Thereisnonecessaryconflictinlearningconceptsandfactsandinthinkingcreatively;thetwoaresymbiotic.”

20Geary2005,chap.6;Johnson2010.21Johnson2010,p.123.22Simonton2004,p.112.23Thisismyownrephrasingofacommonsentimentinscience.SantiagoRamónyCajalcitedDuclauxinnoting,“Chancesmilesnoton

thosewhowantit,butratheronthosewhodeserveit.”Cajalwentontonote,“Inscienceasinthelottery,luckfavorshewhowagersthemost—thatis,byanotheranalogy,theonewhoistillingconstantlythegroundinhisgarden”(RamónyCajal1999,pp.67-68).LouisPasteurnoted,“Inthefieldsofobservationchancefavorsonlythepreparedmind.”RelatedexpressionsincludetheLatin-basedproverb“Fortunefavorsthebold”andtheBritishSpecialAirServicemotto:“Whodareswins.”

24KouniosandBeeman2009[1897];RamónyCajal1999,p.5.25Rocke2010.26Thurston,1990,p.846–847.27SeethefoundationalworkofKarlAndersEricssonondevelopmentofexpertise(e.g.,Ericsson2009).Forinsightfulpopular

approachesrelatedtothedevelopmentoftalent,seeCoyle2009;Greene2012;Leonard1991.28KarpickeandBlunt2011a;KarpickeandBlunt2011b.Forfurtherinformation,seealsoGuidaetal.2012,p.239.29Ofinterestisthatlefthemisphereprefrontalregionsappearactiveduringtheencodingphaseofmemorization,whilerighthemisphere

regionsareactivatedduringretrieval.Thishasbeenreportedbymanygroupsusingagreatvarietyofimagingtechniques(Cook2002,p.37).Isitpossiblethatretrievingmemorizedmaterialscreatesthebeginningsofdiffuse-modeconceptmapping-likeconnections?SeealsoGearyetal.2008,4-6to4-7.

30Thereare,ofcourse,caveatshere.Forexample,whatifastudentisaskedtorecallmaterialtodeterminewhatbelongsonaconceptmap?Therearealsoundoubtedlydisciplinarydifferences.Somesubjects,suchasthoseinvolvingcommunicationprocessesinbiologicalcells,inherentlylendthemselvesmorereadilyto“conceptmap”approachesinunderstandingkeyideas.

31Brownetal.1989.32Johnson2010,p.110.33Baddeleyetal.2009,chap.8.34KenKoedinger,aprofessorofhuman-computerinteractionandpsychologyatCarnegieMellonUniversity,notes,“Tomaximize

retentionofmaterial,it’sbesttostartoutbyexposingthestudenttotheinformationatshortintervals,graduallylengtheningtheamountoftimebetweenencounters.Differenttypesofinformation—abstractconceptsversusconcretefacts,forexample—requiredifferentschedulesofexposure”(quotedinPaul2012).

35Dunloskyetal.2013,sec.10;RoedigerandPyc2012;TaylorandRohrer2010.36RohrerandPashler2007.37Itappearsthat“masspractice”techniquesofpresentingthematerialprovideanillusionofcompetenceinteaching.Studentsappearto

learnquickly,butasstudieshaveshown,theyforgetquicklyaswell.RoedigerandPyc(2012,p.244)note:“Theseoutcomesshowwhyteachersandstudentscanbefooledintousingstrategiesthatareinefficientinthelongrun.Whenwelearnwearesofocusedonhowwearelearning,weliketoadoptstrategiesthatmakelearningeasyandquick.Blockedormassedpracticedoesthis.Forbetterretentioninthelongrun,however,weshouldusespacedandinterleavedpractice,butwhilewearelearningthisprocedureseemsmorearduous.Interleavingmakesinitiallearningmoredifficult,butismoredesirablebecauselongtermretentionisbetter.”

38Rohreretal.2013.39DougRohrerandHaroldPashler(2010,p.406)observe:“...theinterleavingofdifferenttypesofpracticeproblems(whichisquite

rareinmathandsciencetexts)markedlyimproveslearning.”40Personalcommunicationwiththeauthor,August20,2013.SeealsoCarey2012.41Longcampetal.2008.42Forexamples,seehttp://usefulshortcuts.com/alt-codes.

Chapter5:PreventingProcrastination:EnlistingYourHabits(“Zombies”)asHelpers

1Emsley2005,p.103.2ChuandChoi2005;Graham2005;Partnoy2012.3Steel(2007,p.65)notes:“Estimatesindicatethat80%–95%ofcollegestudentsengageinprocrastination...approximately75%

considerthemselvesprocrastinators...andalmost50%procrastinateconsistentlyandproblematically.Theabsoluteamountofprocrastinationisconsiderable,withstudentsreportingthatittypicallyoccupiesoveronethirdoftheirdailyactivities,oftenenactedthroughsleeping,playing,orTVwatching...Furthermore,thesepercentagesappeartobeontherise...Inadditiontobeingendemic

duringcollege,procrastinationisalsowidespreadinthegeneralpopulation,chronicallyaffectingsome15%–20%ofadults.”4AinslieandHaslam1992;Steel2007.5LyonsandBeilock2012.6Emmett2000.7SeeextensivediscussioninDuhigg2012,whichinturncitesWeick1984.8RobertBoice(1996,p.155)notedthatprocrastinationappearstoinvolveanarrowingofthefieldofconsciousness.Seealsopp.118–

119.9Boice1996,p.176.10TiceandBaumeister1997.11Boice1996,p.131.

Chapter6:ZombiesEverywhere:DiggingDeepertoUnderstandtheHabitofProcrastination

1McClain2011;Wanetal.2011.2Duhigg2012,p.274.3Steel2010,p.190,citingOatenandCheng2006andOatenandCheng2007.4BaumeisterandTierney2011,pp.43–51.5Steel2010,citingtheoriginalworkofRobertEisenberger,1992,andothers.6Ibid.,p.128-130,referringinturntotheworkofGabrieleOettingen.7Beilock2010,pp.34-35.8Ericssonetal.2007.9Boice1996,pp.18–22.10Paul2013.

Chapter7:ChunkingversusChoking:HowtoIncreaseYourExpertiseandReduceAnxiety

1Oneimportantpointisthatmuchoftheliteratureonexpertsinvolvesindividualswhohavetrainedforyearstoattaintheirlevelofexpertise.Buttherearedifferinglevelsofexpertsandexpertise.Forexample,ifyouknowtheacronymsFBIandIBM,it’seasytorememberthesequenceasachunkoftworatherthanadisparategroupingofsixletters.Butthiseasychunkingpresumesthatyouarealreadyanexpert,notonlywiththemeaningofFBIandIBM,butwiththeRomanalphabetitself.ImaginehowmuchmoredifficultitwouldbetomemorizeaTibetansequencelikethis:

Whenwearelearningmathandscienceintheclassroom,wearestartingwithsomedegreeofexpertise,andwhatweareexpectedtolearnthroughthecourseofasemesterisnothinglikethevastjumpinexpertiseexperiencedasanovicebecomesagrandmasteratchess.Whenyouaretakingaclassinsomesubject,you’renotgoingtoseeadramaticneuraldifferenceoccurringinonesemester,similartothedramaticdifferencebetweenanoviceandagrandmaster.Butthereissomeindicationthatneuraldifferencesinhowyouprocessthematerialcanshowupeveninaperiodofafewweeks(Guidaetal.2012).Morespecifically,Guidaandcolleaguesnotethatexpertspreferentiallymakeuseofthetemporalregions,whicharecrucialforlong-termmemory(2012,p.239).Inotherwords,whenwesteerstudentsawayfrombuildingstructuresinlong-termmemory,wearemakingitmoredifficultforthemtoacquireexpertise.Ofcourse,concentrationonmemorizationalonewithoutcreativeapplicationisalsoaproblem.Again—anyteachingmethodalonecanbemisused;variety(nottomentioncompetence)isthespiceoflife!

2We’vetalkedaboutinterleavingthestudyofdifferenttechniqueswhileyouarestudyingatopic.Butwhataboutinterleavingthestudyofcompletelydifferentsubjects?Unfortunately,there’snoresearchliteratureavailableonthatasyet(RoedigerandPyc2012,p.244),sowhatI’msuggestingaboutvaryingwhatyouarestudyingissimplycommonsenseandcommonpractice.Thiswillbeaninterestingareatowatchforfutureresearch.

3Kalbfleisch2004.4Guidaandcolleagues(2012,pp.236–237)notethatchunksinworkingmemoryandthereforeinlong-termmemory(LTM)“getlarger

withpracticeandexpertise...thechunksgetalsoricherbecausemoreLTMknowledgeisassociatedwitheachoneofthem.Moreover,severalLTMchunkscanbecomelinkedtoknowledge.Andeventually,ifanindividualbecomesanexpert,thepresenceoftheselinksbetweenseveralchunkscanresultinthecreationofhigh-levelhierarchicalchunks....Forexample,inthegameofchess,templatescanlinkto‘...plans,moves,strategicalandtacticalconcepts,aswellasothertemplates’....WesuggestthatthefunctionalreorganizationofthebraincanbedetectedinexpertiseacquisitionwhenLTMchunksandknowledgestructuresexistandareeffectiveinthedomainofexpertise.”

5Dukeetal.2009.6Foragoodreviewofthecircumstanceswhendeliberatepracticeismosteffective,seePachmanetal.2013.7RoedigerandKarpicke2006,p.199.8Wanetal.2011.Thisstudysoughttodefinetheneuralcircuitsresponsibleforrapid(withintwoseconds)intuitivegenerationofthebest

nextmoveinspotgamesofshogi,anextraordinarilycomplexgameofstrategy.Thepartofthebrainassociatedwithquick,implicit,unconscioushabit(theprecuneus-caudatecircuit)appearedcentraltotherapidgenerationofthebestnextmoveinprofessionalplayers.SeealsoMcClain2011.

9Charnessetal.2005.

10Karpickeetal.2009;McDanielandCallender2008.11FischerandBidell2006,pp.363–370.12RoedigerandKarpicke2006,citingWilliamJames’sPrinciplesofPsychology.13Beilock2010,pp.54–57.14KarpickeandBlunt,2011b;Mastascusaetal.2011,chap.6;PycandRawson2010;RoedigerandKarpicke2006;Rohrerand

Pashler2010.JohnDunloskyandcolleagues,intheirin-depthreviewofvariouslearningtechniques(2013),ratepracticetestingashavinghighutilitybecauseofitseffectiveness,broadapplicability,andeaseofuse.SeealsoPennebakeretal2013.

15Keresztesetal.2013providesevidencethattestingpromoteslong-termlearningviastabilizingactivationpatternsinalargenetworkofbrainareas.

16Pashleretal.2005.17Dunloskyetal.2013,sec.8;KarpickeandRoediger2008;RoedigerandKarpicke2006.

Chapter8:Tools,Tips,andTricks

1Allen2001,pp.85,86.2Steel2010,p.182.3Beilock2010,pp.162–165;ChiesaandSerretti2009;Lutzetal.2008.4Forthosewithaninterest,pleaseseetheresourceslistedattheAssociationforContemplativeMindinHigherEducation,

http://www.acmhe.org/.5Boice1996,p.59.6Ferriss2010,p.485.7Ibid.,p.487.8Fiore2007,p.44.9ScullinandMcDaniel2010.10Newport2012;Newport2006.11Fiore2007,p.82.12Baddeleyetal.2009,pp.378–379.

Chapter9:ProcrastinationZombieWrap-Up

1Johansson2012,chap.7.2Boice1996,p.120;Fiore2007chap.6.3Ibid.,p.125.4Amabileetal.2002;BaerandOldham2006;Boice1996,p.66.5Rohrer,etal.(inpress).6Chietal.1981.7Noesner2010.8Newport2012,particularlychap.1(“Rule#1”).9Nakanoetal.2012.10Duhigg2012,p.137.11Newport2012.12SeeEdelman2012formanysuchideas.

Chapter10:EnhancingYourMemory

1EleanorMaguireandcolleagues(2003)studiedindividualsrenownedforoutstandingmemoryfeatsinforumssuchastheWorldMemoryChampionships.“Usingneuropsychologicalmeasures,aswellasstructuralandfunctionalbrainimaging,”theyfound“superiormemorywasnotdrivenbyexceptionalintellectualabilityorstructuralbraindifferences.Rather,[they]foundthatsuperiormemorizersusedaspatiallearningstrategy,engagingbrainregionssuchasthehippocampusthatarecriticalformemoryandforspatialmemoryinparticular.”

TonyBuzanhasdonemuchtobringtheimportanceofmemorytechniquestothepopulareye.HisbookUseYourPerfectMemory(Buzan,1991)providesfurtherinformationaboutsomepopulartechniques.

2EleanorMaguireandcolleagues(2003)notethatmemorytechniquesareoftenregardedasbeingtoocomplicatedtouse,butsometechniques,suchasthememorypalace,canindeedbeverynaturalandhelpfulinallowingustorememberinformationthatisimportanttous.

3Caietal.2013;Foer2011.DeniseCaiandcolleagues’workindicatesthatspecializationinonehemisphere(oftentheleft)forlanguageisaccompaniedbysimilarspecializationintheotherhemisphereforvisuospatialcapabilities.Specializationofafunctioninonehemisphere,inotherwords,appearstocausespecializationoftheotherfunctionintheotherhemisphere.

4RossandLawrence1968.5Baddeleyetal.2009,pp.363–365.

6http://www.ted.com/talks/joshua_foer_feats_of_memory_anyone_can_do.html.7http://www.skillstoolbox.com/career-and-education-skills/learning-skills/memory-skills/mnemonics/applications-of-mnemonic-

systems/how-to-memorize-formulas/.8AsenseoftheimportanceofspatialreasoningisprovidedinKelletal.2013.

Chapter11:MoreMemoryTips

1Twosourcesofinformationrelatedtometaphorinlate-nineteenth-centuryphysicsareCat2001andLützen2005.Formetaphorinchemistryandmorebroadlythroughoutscience,seeRocke2010,inparticularchap.11.SeealsoGentnerandJeziorski1993.Imageryandvisualizationarebeyondthescopeofanysinglebook—see,forexample,theJournalofMentalImagery.

2AsleadingmathematicalmodelerEmanuelDermannotes:“Theoriesdescribeanddealwiththeworldonitsowntermsandmuststandontheirowntwofeet.Modelsstandonsomeoneelse’sfeet.Theyaremetaphorsthatcomparetheobjectoftheirattentiontosomethingelsethatitresembles.Resemblanceisalwayspartial,andsomodelsnecessarilysimplifythingsandreducethedimensionsoftheworld....Inanutshell,theoriestellyouwhatsomethingis;modelstellyoumerelywhatsomethingislike”(Derman2011,p.6).

3Solomon1994.4Rocke2010,p.xvi.5Ibid.,p.287,citingBerichtederDurstigenChemischenGesellschaft(1886),p.3536.Thiswasamockissueofthenonexistent

“durstigen”(thirsty)ChemicalSociety.TheparodywassenttothesubscribersoftheBerichtederdeutschenchemischenGesellschaftandisvirtuallyimpossibletofindtoday,sinceitwasactuallyaspuriousissue.

6RawsonandDunlosky2011.7Dunloskyetal.2013;RoedigerandPyc2012.Inareviewofstudentflashcarduse,KathrynWissmanandcolleagues(2012,p.568)

observed:“studentsunderstandthebenefitsofpractisingtohighercriterionlevels(amountofpractice)butdonottypicallyimplementorunderstandthebenefitsofpractisingwithlongerlags(timingofpractice).”

8Morrisetal.2005.9Baddeleyetal.2009,pp.207–209.10Inthisbook,youmightthinkI’vediscussedallofthecomponentsoftheSQ3Rforstudy(sometimesSQ4R—forSurvey,Question,

Read,Recite,ReviewandwRite).SoyoumightaskwhyIhaven’texploredthismethodfurtherinthetext.TheSQ3RwasdevelopedbypsychologistFrancisPleasantRobinsonasageneralstudytool.Centraltothestudyofmathandscienceisproblemsolving—theSQ3Rapproachsimplydoesn’tlenditselftothis.I’mnottheonlyonetonotice.AsphysicsprofessorRonaldAaronandhissonRobinAaronnoteinImproveYourPhysicsGrade,”...onePsychologytextsuggestsstudyingbytheSQ3Rmethod....ForeffectivenotetakinginclassitsuggeststheLISANapproach....Doyoubelievethatsuchapproachescanhelpyou?DoyoubelieveinSantaClaus?TheEasterBunny?”(AaronandAaron1984,p.2).

11Curiously,itappearsverylittleworkhasbeendoneinthisarea—whatlittleisavailableseemstosimplyaffirmthatwritingthingsoutbyhandhelpsusassimilateinformationbetterthantyping.SeeRivardandStraw2000;Smokeretal.2009;VelayandLongcamp2012.

12Cassilhasetal.2012;Nagamatsuetal.2013;vanPraagetal.1999.13Guidaetal.2012,p.230;Leutneretal.2009.14Levinetal.1992describeshowstudentswhousemnemonicsoutperformstudentswhoapplycontextualandfreelearningstyles.15Guidaetal.2012pointsoutthattraininginmemorytechniquescanspeeduptheprocessofacquiringchunksandknowledge

structures,thushelpingpeoplebecomeexpertsmorerapidlybyallowingthemtousepartoftheirlong-termmemoryasworkingmemory.

16Baddeleyetal.2009,pp.376–377,citingresearchbyHelgaandTonyNoice(2007).

Chapter12:LearningtoAppreciateYourTalent

1Jinetal.2014.2Partnoy2012,p.73.Partnoygoesontonote:“Sometimeshavinganunderstandingofpreciselywhatwearedoingunconsciouslycan

killthenaturalspontaneity.Ifwearetooself-conscious,wewillimpedeourinstinctswhenweneedthem.Yetifwearen’tself-consciousatall,wewillneverimproveonourinstincts.Thechallengeduringaperiodofsecondsistobeawareofthefactorsthatgointoourdecisions...butnottobesoawareofthemthattheyarestiltedandineffectual”(Partnoy2012,p.111).

3Partnoy2012,p.72,citingKlein1999.4Klein1999,p.150,citingKleinandKlein1981.ButnotethesmallsamplesizeinKleinandKlein1981.5MauroPesentiandcolleagues(2001,p.103)note,“Wedemonstratedthatcalculationexpertisewasnotduetoincreasedactivityof

processesthatexistinnon-experts;rather,theexpertandthenon-expertsuseddifferentbrainareasforcalculation.Wefoundthattheexpertcouldswitchbetweenshort-termeffort-requiringstoragestrategiesandhighlyefficientepisodicmemoryencodingandretrieval,aprocessthatwassustainedbyrightprefrontalandmedialtemporalareas.”

Alreadyin1899brilliantpsychologistWilliamJameswrote,inhisclassicTalkstoTeachersonPsychology:“Younowseewhy‘cramming’mustbesopooramodeofstudy.Crammingseekstostampthingsinbyintenseapplicationimmediatelybeforetheordeal.Butathingthuslearnedcanformbutfewassociations.Ontheotherhand,thesamethingrecurringondifferentdays,indifferent

contexts,read,recitedon,referredtoagainandagain,relatedtootherthingsandreviewed,getswellwroughtintothementalstructure.Thisisthereasonwhyyoushouldenforceonyourpupilshabitsofcontinuousapplication”(William2008,[1899],p.73).

6Inaclassicstudy,WilliamChaseandHerbertSimon(1973)foundthattheintuitivegenerationofnextmovesbychessexpertsisbasedonthesuperior,quickperceptionofpatternsthathasbeenachievedthroughpractice.FernandGobetandcolleagues(2001,p.236)defineachunkas“acollectionofelementshavingstrongassociationswithoneanother,butweakassociationswithelementswithinotherchunks.”

7Amidzicetal.2001;Elo1978;Simon1974.Afigureof300,000chunkswascitedbyGobetandSimon2000.8Gobet2005.Gobetgoesontonotethatexpertiseinonedomaindoesn’ttransfertoanother.That’strue—certainlyifyoulearned

Spanish,it’snotgoingtohelpyouwhenyougotoordersauerkrautinGermany.Butthemetaskillsareimportant.Ifyoulearnhowtolearnalanguage,youcanpickupasecondlanguagemoreeasily.

That,again,iswheredevelopinganexpertiseinsomethinglikechesscanbequitevaluable—itprovidesasetofneuralstructuresthataresimilartothoseyouneedwhenlearningmathandscience.Eveniftheneuralstructuresareassimpleasyouneedtointernalizetherulesofthegame—that’savaluableinsight.

9Beilock2010,pp.77–78;WhiteandShah2006.10Indeed,thereismodestsupportforthistypeoffindingintheresearchliterature.SeeSimonton2009.11Carsonetal.2003;Ellenbogenetal.2007;WhiteandShah2011.12MerimBilalićandcolleagues(2007)pointoutthatsomeplayerswithanIQofbetween108and116fellintotheeliteplayergroup

byvirtueoftheirextrapractice.TheelitegrouphadanaverageIQof130.SeealsoDuckworthandSeligman2005.NobelPrizewinnerRichardFeynmanlikedtotouthisrelativelylowIQscoreof125asevidencethatyoucouldgoprettyfar

whatevertestsmightindicateaboutyourintelligence.Feynmanclearlyhadnaturalsmarts,butevenasayoungsterhewaspracticingobsessivelyindevelopinghismathematicalandphysicalknowledgeandintuition(Gleick1992).

13Klingberg2008.14Silverman2012.15Felder1988.SeealsoJustinKrugerandDavidDunning(1999),whonote“themiscalibrationoftheincompetentstemsfromanerror

abouttheself,wherethemiscalibrationofthehighlycompetentstemsfromanerroraboutothers.”

Chapter13:SculptingYourBrain

1DeFelipe2002.2RamónyCajal1937,309.3RamónyCajal1999[1897],pp.xv–xvi;RamónyCajal1937,p.278.4RamónyCajal1937,154.5Fields2008;Giedd2004;Spear2013.6RamónyCajal1999[1897].7Bengtssonetal.2005;Spear2013.8Cajalcouldclearlyplanwell—witnesshisconstructionofthecannon.Buthecouldn’tseemtomaketheconnectionwiththebigger

pictureconsequencesofhisactions.Takenupwiththeexcitingtaskofblowingupaneighbor’sgate,forexample,hecouldn’tmaketheobviouspredictionthathewouldbeindeeptroubleasaconsequence.SeeShannonetal.2011,withtheirintriguingfindingthatfunctionalconnectivityintroubledteensconnectsthedorsolateralpremotorcortextothedefault-modenetwork(“aconstellationofbrainareasassociatedwithspontaneous,unconstrained,self-referentialcognition”p.11241).Astroubledteensmatureandtheirbehaviorimproves,thedorsolateralpremotorcortexinsteadappearstobeginconnectingwiththeattentionandcontrolnetworks.

9Bengtssonetal.2005;Spear2013;ThomasandBaker2013.AsCibuThomasandcolleaguesnote(p.226),“theevidencefromanimalstudiessuggeststhatthelarge-scaleorganizationofaxonsanddendritesisverystableandexperience-dependentstructuralplasticityintheadultbrainoccurslocallyandistransient.”Inotherwords,wecanmakemodestchangesinourbrain,butwecan’tindulgeinwholesalerewiring.Thisisallcommonsensestuff.Foraterrificpopularbookonbrainplasticity,seeDoidge2007.ThebesttechnicalapproachtothistopicisShawandMcEachern2001.ItisfittingthatCajal’sownworkisnowgainingrecognitionasfoundationalinourunderstandingofbrainplasticity(DeFelipe2006).

10RamónyCajal1937,p.58.11Ibid.,pp.58,131.Theabilitytograspthekeyideas—thegistoftheproblems—appearstobemoreimportantthanverbatimabilityto

memorize.Verbatimasopposedto“gist”memoriesseemtobeencodeddifferently.SeeGearyetal.2008,4–9.12DeFelipe2002.13RamónyCajal1937,p.59.14Root-BernsteinandRoot-Bernstein1999,pp.88–89.15Bransfordetal.2000,chap.3;Mastascusaetal.2011,chaps.9–10.16FauconnierandTurner2002.17Mastascusaetal.2011,p.165.18GentnerandJeziorski1993.

Chapter14:DevelopingtheMind’sEyethroughEquationPoems

1Plath1971,p.34.2Feynman2001,p.54.3Feynman1965,2010.4ThissectionisbasedonthewonderfulpaperbyPrentis(1996).5Excerptsfromthesong“MandelbrotSet,”©JonathanCoulton,bykindpermissionofJonathanCoulton.Lyricsexcerptedfromsong

fullygivenathttp://www.jonathancoulton.com/wiki/Mandelbrot_Set/Lyrics.6Prentis1996.7Cannon1949,p.xiii;RamónyCajal1937,p.363.Inarelatedvein,seeJavierDeFelipe’sextraordinaryButterfliesoftheSoul,which

containssomeofthebeautifulillustrationsproducedintheearlydaysofresearchinneuroscience(DeFelipe2010).8Mastascusaetal.2011,p.165.9Keller1984,p.117.10Seediscussionsofelaborativeinterrogationandself-explanationinDunloskyetal.2013.11http://www.youtube.com/watch?v=FrNqSLPaZLc.12http://www.reddit.com/r/explainlikeimfive.13Seealsoendnote8fromchapter12.14Mastascusaetal.2011,chaps.9–10.15Foerdeetal.2006;Paul2013.

Chapter15:RenaissanceLearning

1Colvin2008;Coyle2009;Gladwell2008.2Deslauriersetal.2011;Felderetal.1998;Hake1998;Mitraetal.2005;President’sCouncilofAdvisorsonScienceandTechnology,

2012.3RamónyCajal1999[1897].4KamkwambaandMealer2009.5Pert1997,p.33.6McCord1978.SeeArmstrong2012foranextensivediscussionofthisandrelatedstudies.ManuKapurandKaterineBielaczyc(2012)

indicatethatlessheavy-handedguidancebyinstructorsmayresultincounterintuitiveimprovementinstudentperformance.7Oakleyetal.2003.8SeeArmstrong2012andreferencestherein.9Oakley2013.

Chapter16:AvoidingOverconfidence:ThePowerofTeamwork

1Schutz2005.“Fred”isahypotheticalamalgamoftypicaltraitsof“broad-perspectiveperceptualdisorderoftherighthemisphere.”2McGilchrist2010providesacomprehensivedescriptionsupportingthedifferencesinhemisphericfunction,whileEfron1990,although

dated,providesanexcellentcautionarynoteaboutproblemsinhemisphericresearch.SeealsoNielsenetal.2013;JeffAnderson,M.D.,Ph.D.,whowasinvolvedinthestudy,notes,“It’sabsolutelytruethatsomebrainfunctionsoccurinoneortheothersideofthebrain.Languagetendstobeontheleft,attentionmoreontheright.Butpeopledon’ttendtohaveastrongerleft-orright-sidedbrainnetwork.Itseemstobedeterminedmoreconnectionbyconnection”(UniversityofUtahHealthCareOfficeofPublicAffairs2013).

3McGilchrist2010,pp.192–194,203.4HoudéandTzourio-Mazoyer2003.Houdé2002,p.341notes,“ourneuroimagingresultsdemonstratethedirectinvolvement,in

neurologicallyintactsubjects,ofarightventromedialprefrontalareainthemakingoflogicalconsciousness,thatis,inwhatputsthemindon‘thelogicaltrack,’whereitcanimplementtheinstrumentsofdeduction....Hence,therightventromedialprefrontalcortexmaybetheemotionalcomponentofthebrain’serrorcorrectiondevice.Moreexactly,thisareamaycorrespondtotheself-feelingdevicethatdetectstheconditionsunderwhichlogicalreasoningerrorsarelikelytooccur.”

5SeeStephenChristmanandcolleagues2008,p.403,whonotethat“thelefthemispheremaintainsourcurrentbeliefswhiletherighthemisphereevaluatesandupdatesthosebeliefswhenappropriate.Beliefevaluationisthusdependentoninterhemisphericinteraction.”

6Ramachandran1999,p.136.7Gazzaniga2000;Gazzanigaetal.1996.8Feynman1985,p.341.Originallygiveninhis1974Caltechcommencementaddress.9Feynman1985,pp.132–133.10AsAlanBaddeleyandcolleagues(2009,pp.148–149)note:“Wearenotlackinginwaysofdefendingourselvesagainstchallenges

toourself-esteem.Wereadilyacceptpraisebuttendtobeskepticalofcriticism,oftenattributingcriticismtoprejudiceonthepartofthecritic.Weareinclinedtotakecreditforsuccesswhenitoccursbutdenyresponsibilityforfailure.Ifthisstratagemfails,wearerathergoodatselectivelyforgettingfailureandrememberingsuccessandpraise.”(Referencesomitted.)

11Granovetter1983;Granovetter1973.12Ellisetal.2003.13Beilock2010,p.34.14ArumandRoksa2010,p.120.

Chapter17:TestTaking

1VisitDr.Felder’swebsiteathttp://www4.ncsu.edu/unity/lockers/users/f/felder/public/foranenormousassortmentofusefulinformationonlearningintheSTEMdisciplines.

2Felder1999.UsedbypermissionofDr.RichardFelderandChemicalEngineeringEducation.3Forfoodforthoughtalongtheselines,seeMcClain2011andtheworkoftheresearchersMcClaincites.4Beilock2010,pp.140–141.5Mrazeketal.2013.6Beilock(2010,p.60)notesthat“athletesunderpressuresometimestrytocontroltheirperformanceinawaythatdisruptsit.This

control,whichisoftenreferredtoas‘paralysisbyanalysis,’stemsfromanoveractiveprefrontalcortex.”7Beilock2010;http://www.sianbeilock.com/.

credits

1.“Meatage10(September1966)withEarlthelamb,”imagecourtesytheauthor2.MagnusCarlsenandGarryKasparov,imagecourtesyCBSNews3.Prefrontalcortex,image©2013KevinMendez4.Pinballmachine,image©2013KevinMendez5.Focusedanddiffusethinking,image©2013KevinMendez6.Triangles,imagecourtesytheauthor,basedonanoriginalimageideabydeBono1970,p.537.Ping-Pong,image©2013KevinMendez8.Pyramidofdimes,courtesytheauthor9.NadiaNoui-Mehidi,photocourtesyKevinMendez10.ThomasEdison,courtesyU.S.DeptartmentoftheInterior,NationalParkService,ThomasEdisonNationalHistoricalPark11.SalvadorDalíwithocelotandcane,1965;http://en.wikipedia.org/wiki/File:Salvador_Dali_NYWTS.jpgFromtheLibraryof

Congress.NewYorkWorld-Telegram&Suncollection.http://hdl.loc.gov/loc.pnp/cph.3c14985;Author:RogerHiggins,WorldTelegramstaffphotographer;nocopyrightrestrictionknown.StaffphotographerreproductionrightstransferredtoLibraryofCongressthroughInstrumentofGift.

12.Brickwalls,image©2013KevinMendez13.Fouritemsinworkingmemory,imagecourtesyauthor14.RobertBilder,image©ChadEbesutani,photocourtesyRobertBilder15.Octopusfocusedandcrazy-hodgepodgediffusemodes,image©2013KevinMendez16.Aneuralpattern,image©2013KevinMendez17.Puzzleofman’sface,image©2013KevinMendezandPhilipOakley18.Top-downandbottom-uplearning,imagecourtesyauthor19.PuzzleofmaninMustang,partlyassembled,image©2013KevinMendezandPhilipOakley20.PuzzleofmaninMustang,mostlyassembled,image©2013KevinMendezandPhilipOakley21.Chunkingaconceptintoaribbon,imagecourtesytheauthor22.Skippingtotherightsolution,image©2013KevinMendez23.Practicemakespermanent,image©2013KevinMendez24.PuzzleofMustang,faintandpartlyassembled,image©2013KevinMendez25.Neuralhook,image©2013KevinMendez26.PaulKruchkoandfamily,photocourtesyPaulKruchko27.Procrastinationfunneling,image©2013KevinMendez28.NormanFortenberry,image©2011,AmericanSocietyforEngineeringEducation;photobyLung-ILo29.Manytinyaccomplishments,imagecourtesytheauthor30.Pomodorotimer,Autore:FrancescoCirillorilasciataaEratonellesottostantilicenzeseguiráOTRS,

http://en.wikipedia.org/wiki/File:Il_pomodoro.jpg31.PhysicistAntonyGarrettLisisurfing,authorCjean42,http://en.wikipedia.org/wiki/File:Garrett_Lisi_surfing.jpg32.Oraldo“Buddy”Saucedo,photocourtesyofOraldo“Buddy”Saucedo33.NeelSundaresan,photocourtesyTobyBurditt34.Zombietasklist,image©2013KevinMendez35.MaryCha,photocourtesyMaryCha36.Smilingzombie,image©2013KevinMendez37.PhotoofJoshuaFoer,©ChristopherLane38.Flyingmule,image©2013KevinMendez39.Zombiehandmnemonic,image©2013KevinMendez40.Memorypalace,image©2013KevinMendez41.SherylSorby,photobyBrockit,Inc.,suppliedcourtesySherylSorby42.Monkeysinaring,fromBerichtederDurstigenChemischenGesellschaft(1886),p.3536;benzenering,modifiedfrom

http://en.wikipedia.org/wiki/File:Benzene-2D-full.svg43.Metabolicvampires,image©2013KevinMendez

44.JonathonStrong,photocourtesyJonathonStrong45.Zombiebaseballplayer,image©2013KevinMendez46.NickAppleyard,photocourtesyNickAppleyard47.SantiagoRamónyCajal,bykindpermissionofSantiagoRamónyCajal´sheirs,withthegraciousassistanceofMariaAngelesRamón

yCajal48.Ripplingneuralribbons,imagecourtesyauthor49.Photons,illustrationcourtesyMarcoBellini,InstitutoNazionalediOttica—CNR,Florence,Italy50.BarbaraMcClintock,photocourtesySmithsonianInstitutionArchives,image#SIA2008–560951.BenCarson,photocourtesyJohnsHopkinsMedicine52.NicholasWade,photocourtesyNicholasWade53.Ischemicstroke,CTscanofthebrainwithanMCAinfarct,byLucienMonfils,

http://en.wikipedia.org/wiki/File:MCA_Territory_Infarct.svg54.NielsBohrloungingwithEinsteinin1925,picturebyPaulEhrenfest,

http://en.wikipedia.org/wiki/File:Niels_Bohr_Albert_Einstein_by_Ehrenfest.jpg55.BradRoth,photobyYangXia,courtesyBradRoth56.RichardM.Felder,courtesyRichardM.Felder57.SianBeilock,courtesyUniversityofChicago58.Dimesolution,imagecourtesytheauthor

index

Thepagenumbersinthisindexrefertotheprintedversionofthisbook.Thelinkprovidedwilltakeyoutothebeginningofthatprintpage.Youmayneedtoscrollforwardfromthatlocationtofindthecorrespondingreferenceonyoure-reader.

Pagenumbersinitalicsindicatephotographsorillustrations.

abstractions,197,210,212Seealsochunking

abstractnessandcomplexity,16–17AccountingEquation,60acnetreatments,128–29acquaintancesandsuccessinjobmarket,231activatorsfordiffusemodeofthinking,35“active”repetition,chunking,114,119activereview,142–43“active”teachingtechnique,218addictionandprocrastination,87,88–89addinganewproblem,chunking,114Afghanistan,142Africa,215“aha!”insights,30,227Seealsodiffusemodeofthinking

Alkon,Amy,44Allen,David,126alternatingdifferentproblem-solvingtechniques,257–58Alzheimer’s,45anagramsexercise,65Ankiflashcards,64,138,174anxiety,dealingwithchokingvs.chunking,112–25,250–51testtaking,103–4,244–46,248,250–51

Appleyard,Nick,192,192appreciatingyourtalent,183–92,221apps(best)forstudying,137–39arsenicpoison,83,89,90,145–46attentionaloctopus,14–15,16,52,53,53,57attentiondifficulties,149,150Austen,Jane,30“autodidacts,”222Avogadro’snumber,163avoidanceandprocrastination,85–86avoidingoverconfidence,20,225–37,247,248,254

background,workingonaproblem,44backward,working,68Baddeley,Alan,62“bad”trait,understandingvalueof,221ballbearingandThomasEdison,32Bannister,Roger,127

Batalha,Celso,217–18bed,bath,bus(threeB’s),30befuddlementandlearning,22Beilock,Sian,103,250,250–51beliefpartofzombies(habits),88,95,99–100,107Bell,E.T.,223–24Bellini,Marco,206,206benzoylperoxideandacne,129“big-picture”perspective,12,18,19,20,30,226,227,228,247,248Seealsodiffusemodeofthinking

big-picturetop-downchunkingprocess,59,60,61,61,70,79Bilder,Robert,49,49–50birds,survivalinstincts,20bite-sizedpieces,breakingworkinto,24–25,97,99,103,103–7,104,108,132,138,149,151,151,253,258Black-Derman-Toymodel,199blinkingandfocusing,37,247,248,249Blowers,Paul,233Bohr,Niels,229–30,230bottom-upchunkingprocess,59,60,61,61,70,79Bradley,JamesV.,xvii–xviiiBradshaw,Bob,242braindefaultsettingsofbrain,256designedforextraordinarymentalcalculations,6–7maturityofbrain,195,199prefrontalcortex,12,12,14–15,187procrastinationand,86–89,87retrainingthebrain,5–6sculptingyourbrain,193–200Seealsomathandscience,learning;neuralstructures,building

brainstorming,229–33,230breaks,taking,28,30,33,34,38,47,113,114,133,134,135,258breathingandtesttaking,245,248,249brickwallmetaphor,38,38,39,43,85,254Brisson,Charlene,98broad-perspectiveperceptualdisorderoftherighthemisphere,226Broadwell,Randall,133BuddhainBlueJeans(Sheridan),127buildingachunk,56–61,57,60,61,78,113–17burnout,145

Cajal,SantiagoRamóny,193–94,194,195,196–97,200,205,206,213,215,219,221,255calculuslimits,169CalculusMadeEasy(Thompson),169Cameron,James,216cancer,170Carlsen,Magnus,9–10,10,37,185–86,253Carson,Ben,214,214Cha,Mary,142,142–43Chagnon,Napoleon,223change,possibilityof,88changinghabits,timefor,149changingyourthoughtsandlife,195–96checkingyourwork,228,233,236,247,248,249chemistry,170,171,171,176chess,9–10,10,36–37,70,71,116–17,146,184,185–86,188,253Choke:WhattheSecretsoftheBrainRevealaboutGettingItRightWhenYouHaveTo(Beilock),103,250chokingvs.chunking,112–25,250–51chunking,51–82,112–25addinganewproblemfor,114

avoidingillusionsofcompetence,51–82,256,257bottom-upchunkingprocess,59,60,61,61,70,79breaks,taking,114buildingachunk,56–61,57,60,61,78,113–17chokingvs.,112–25,250–51contextfor,58–59,71creativityand,66–67,67deepchunking,196–99,198defined,54–55,57,57focusedattention,52–54,53,54,57,78,254,255illusionsofcompetence,61–68,64,67,77,79,117,125interleavingvs.overlearning,74,74–78,113,173knowledgecollapse(hittingthewall),118,123libraryofchunks,66–68,67,113,115,117,120,121,122,147,186limitedstudytimetechniques,81–82memorytraces,53–54,54,58,68,69,79,185mimickingsolutions,avoiding,77–78neuralstructures,building,52–53,53,54,54–55,67,67,68,69,71,78,93,113,121organizingmaterialsfor,73,118–19practicemakespermanent,68–72,69,74,74,78,82,120,188,257–58,259puzzlepiecesmetaphor,61,61,74,74recall,61–68,64,67,72–73,78,78,90,116,117,123,125repetitionofproblemfor,114summary,78,78,121testingeffect,119–20,122,238top-downbig-picturechunkingprocess,59,60,61,61,70,79transferand,59,209–11,212understandingbasicidea,58,78,79walkingandrecall,30,72–73,90workingaproblemthrough,56–57,58,82,114,259workingmemoryand,15,41,42,42–43,47,64,64,65,121,122,187Seealsomathandscience,learning;memory

“chunk-puters,”117Cirillo,Francesco,103ClickMoment,The(Johansson),144–45clock,problemsreading,1Coffitivity,139coinsandtriangleexercise,23,23“collaborativeteaching”technique,218conceptmapping,71concretevs.abstractapproach,210,212contextandchunking,58–59,71continentaldriftexample,55cortisol,244Coulton,Jonathan,203counterintuitivecreativity,19Cowart,Aukury,130Coyne,Joseph,105CPR,184cramming,24,38,38,85,87–88,111,145,185,254,259cranialbonesmnemonic,176creativevs.nonimaginativescientists,66creativityandlearning,6,29–50,254–55brickwallmetaphor,38,38,39,43,85,254chunkingand,66–67,67diffusemodeofthinkingand,32–33,40Einstellungeffect(gettingstuck),17,25,26,27–28,36–39,38,52,146,170,186,243failure,33,41,110–11,219harnessing,extendingabilities,32–33keepingupwiththeintellectualJoneses,36

memoryand,179–80neuralstructures,building,32,38,38,45,46summary,46–47talkingwithothersforhelp,40,92,260togglingbetweenthinkingmodes,29–32,31,33–35,36–39,38,46,48Seealsodiffusemodeofthinking;mathandscience,learning;memory

Crick,Francis,xv–xvicriticism,50,232Crotchety,Mr.,3,70cue(trigger)partofzombies(habits),88,94,95,96,107,109,129,153

Dalí,Salvador,31,31,32Daniel,DavidB.,261–63Darwin,Charles,66,208,213Day,Thomas,63daybeforeatest,246–47daydreaming,101,187,190Dechant,Jason,73,177,210–11decimalsystemmnemonic,176deep-breathingandtesttaking,245,248,249deepchunking,196–99,198defaultsettingsofbrain,256DefenseLanguageInstitute,53“deliberatepractice,”chunking,114,188Dell,Michael,216densityexample,173depression,45Derman,Emanual,199developingthemind’seyethroughequationpoems.Seemind’seye,developingthroughequationpoems“Devil’sAdvocate,”228Seealsorighthemisphereofbrain

Dickens,Charles,30differentlocationandrecall,90,182differentproblemsandtechniques,interleaving,75diffusemodeofthinking,11,12activatorsfor,35“aha!”insights,30,227background,workingonaproblem,44big-pictureperspective,12,18,19,20,30,226,227,228,247,248brickwallmetaphor,38,38,39,43,85,254chunklibraryand,117coinsandtriangleexercise,23,23creativityand,32–33,40flashlightmetaphor,18–19,26frustrationsignal,39hard-start–jump-to-easytechnique,241–44,245–46,248,249intuitionproblemsolving,67,67,236–37,247magicalmathmarination,142–43pinballmetaphor,13,13,14,15,15restingstatenetwork,11righthemisphereofbrain,20,225–27,227,228sentenceerrorsexercise,33spiritualityand,189trianglesandsquaresexercise,21,21Seealsocreativityandlearning;focusedmodeofthinking;togglingbetweenthinkingmodes

disadvantages,turningintoadvantages,193,194,195,196,197,200“disagreeableness”andcreativity,50discomfortandprocrastination,85–86,90,101,102,107distractionsmemoryand,156,260

procrastinationand,84,105,107,150–51,151,154double-checkingyourwork,228,233,236,247,248,249Dragone,DebraGassner,60Drozd,Trevor,38Duhigg,Charles,93

Earl(lamb),3easydoesit,9–28,253Seealsodiffusemodeofthinking;focusedmodeofthinking

eBay,124Edison,Thomas,29,30–31,31,32,33,111Einstein,Albert,189,206,206,230,230Einstellungeffect(gettingstuck),17,25,26,27–28,36–39,38,52,146,170,186,243electricity,168electromagneticwaves,202Ellison,Larry,216Emmett,Rita,85emotionaltone-deafness,226empathy,220encryptednessandcomplexity,16–17energysavingsfromhabits,93–94engines,invention,112enhancingyourmemory.Seememoryepidermislayers,162equationpoems,201–5Seealsomind’seye,developingthroughequationpoems

“equationsheetbingo,”229“EquationWhisperer.”SeechunkingEvernote,138evolution,213exerciseandmemory,108,178–79,182experimentalnotebook,107expertisefrommemorytricks,179–81expertise(increasingyour)andreducinganxiety.Seechunkingexplanatoryquestioning(simplifyingstudymaterial),79,207–8,255,258

failureandlearning,33,41,110–11,219FAQs,procrastination,148–52fearandcreativity,49–50fears,facingyour,244–46,248,250–51Felder,Richard,239,239–41Feynman,Richard,202,207,229–30,232,252–53,255,256FieldsMedal,70Fiore,Neil,129fishingtechniques,211flashcards,64,138,174,257flashlightmetaphor,18–19,26focusedattention,52–54,53,54,57,78,254,255focusedmodeofthinking,11–12,12attentionaloctopus,14–15,16,52,53,53,57brickwallmetaphor,38,38,39,43,85,254chunklibraryand,117coinsandtriangleexercise,23,23flashlightmetaphor,18–19,26highlyattentivestatenetwork,11lefthemisphereofbrainand,20,226,228,233overconfidenceand,20,226,228,233pinballmetaphor,13,13–14,15,15prefrontalcortex,12,12,14–15,187procrastinationand,24

sentenceerrorsexercise,33sequentialproblemsolving,67,67trianglesandsquaresexercise,21,21willpowerand,34Seealsodiffusemodeofthinking;togglingbetweenthinkingmodes

Foer,Joshua,155–57,156,163foolingyourself,easeof,148,229,234Fortenberry,Norman,92,9243Things,139Freedom,138“frogs,”eatingfirst,131,140,153,258frustration,diffusemodeofthinking,39furosemidememorytrick,181

Gabora,Liane,32Galois,Évariste,224Gamache,RobertR.,72Gashaj,Michael,137Gates,Bill,66,216Gazzaniga,Michael,228generation(recalling)effect,chunking,115genetictransposition(“jumpinggenes”),206geniusenvy,185–89,190GIBill,5goals,setting,136,137,141,152GoldenAppleAward,208GoldmanSachs,199Google,27,127,138Gordon,Cassandra,41Granovetter,Mark,231Gray-Grant,Daphne,131groupwork,120,130,231–33,234,235,239,240,241,255,259Gruber,Howard,30

habits.Seezombieshandbonesmnemonic,176handwriting.Seewritingbyhandhard-start–jump-to-easytechnique,241–44,245–46,248,249hardtasks,114,116,122,148–49Hardy,G.H.,223harnessing,extendingabilities,32–33harnessingyourzombies(habits),84,95–101,97Hasan,Yusra,96Hebert,SusanSajna,246hiddenmeaningsinequations,203–5,211,212highlightingtext,62,125,178,259highlyattentivestatenetwork,11hittingthewall(knowledgecollapse),chunking,118,123homeworkandtestpreparation,240hostagenegotiation,147

illusionsofcompetence,61–68,64,67,77,79,117,125“impostorphenomenon,”188indexcardsexample,75–76Inspire!program,124intellectualsniperscaution,219–21,222intentiontolearnandlearning,62interleavingvs.overlearning,74,74–78,113,173IntermediatePhysicsforMedicineandBiology(Roth),236internalizingconceptsandsolutions,6,73

introvertsandteamwork,233intuitionproblemsolving,67,67,236–37,247intuitiveunderstanding,183–85,185,190inventions,enhancing,112,113Iraq,80isolation,126,130,139,153

James,William,119Jeshurun,Weston,150jingles,163Jobs,Steve,216Johansson,Frans,144–45Johnson,Steven,66Jordan,168“jumpinggenes”(genetictransposition),206“justthisonetime”phenomenon,135–36juveniledelinquents,193–94,199

Kamkwamba,William,215Kanigel,Robert,223Karpicke,Jeffrey,xvii–xviii,61–62Kasparov,Garry,9–10,10,37keepingupwiththeintellectualJoneses,36keystobecomingan“EquationWhisperer.”Seechunking“keystone”badhabit,procrastination,86knowledgecollapse(hittingthewall),chunking,118,123knowledgevs.memorytrick,176Koehler,William,180–81Kruchko,Paul,80,80–82

labelsandconfidence,192language-learningskills,1,4,5,6,14,16,53,63,70,118,145,198,209,210LawofSerendipity,ix,66,116,122,137,256learnedindustriousness,99learningmoreeffectively,6–7Seealsomathandscience,learning

learningonyourown,213–16,214,218,221,222learningtoappreciateyourtalent.SeeappreciatingyourtalentLeechBlock,139lefthemisphereofbrain,20,226,228,233Leopold,KennethR.,22libraryofchunks,66–68,67,113,115,117,120,121,122,147,186LimitedTimeStudy,81–82limitingcasesandunderstandinganequation,237Lisa,Allen,93Lisi,Garret,104,104lists,enlisting,130–31,131,132,133,134,137,140,141,149,152littlegoesalongway,89long-termmemory,41,43,47,64,65,69,74–75,157,179

magicalmathmarination,142–43Seealsodiffusemodeofthinking

“magicofcreativity,”32Magrann,Tracey,162,164,244Mandelbrot,Benoit,203“MandelbrotSet”(Coulton),203ManhattanProject,229,252ManWhoKnewInfinity:ALifeoftheGeniusRamanujan(Kanigel),223Manzi,Mr.,201–2markingtheobjective,102

markinguptext,62,125,178,259Marx,Chico,136mathandscience,learningappreciatingyourtalent,183–92,221challengesofmathandscience,16–18easydoesit,9–28,253mind’seye,developingthroughequationpoems,201–12overconfidence,avoiding,20,225–37,247,248,254paradoxesoflearning,41,255renaissancelearning,213–24sculptingyourbrain,193–200testtaking,238–51unlockingyourpotential,252–60Seealsochunking;creativityandlearning;diffusemodeofthinking;focusedmodeofthinking;memory;procrastination

maturityofbrain,195,199McClintock,Barbara,206–7,207McCormick,Jonathon,136meaningfulgroups,memory,175–76,181meditation,126–27MeeTimer,139memory,155–82creativityand,179–80distractions,greatestenemy,156,260exerciseand,108,178–79,182expertisefrommemorytricks,179–81jingles,163long-termmemory,41,43,47,64,65,69,74–75,157,179meaningfulgroups,175–76,181memorypalacetechnique,160–63,161,164,165metaphors,168–71,171,175,181,182,255,258mnemonics,160,175–76musclememory,173,177,178–79,181,182namesofpeople,174neuralstructures,building,159,161,162,170,173,179,182senses,invoking,159,163,164short-termmemory,43songs,162,181,257spacedrepetition,43,47,69,172,172–74,257spatialmemory,157–58,161,166–67storiesand,177,181summary,164,181talkingtoyourself,178,181visualization,156,171,171visualmemory,157–58,158,158–59,159,161,164,165visualmetaphors,168–71,171,175,181,182,255,258workingmemory,15,41,42,42–43,47,64,64,65,119,121,122,157,179,186,187writingbyhand,173,177,178,181Seealsochunking;creativityandlearning;mathandscience,learning

memorypalacetechnique,160–63,161,164,165memorytraces,53–54,54,58,68,69,79,185MenofMathematics(Bell),223–24mentalcontrastingtechnique,99–100,108,258mentors,valueof,216–18,221“metabolicvampires,”172,172,174metaphorsmemory,168–71,171,175,181,182,255,258sculptingyourbrain,198–99,258Seealsospecificmetaphors

Microsoft,144–45microtasks,148

mimickingsolutions,avoiding,77–78mindfulnessandtesttaking,245mind’seye,developingthroughequationpoems,201–12“MindWell”initiative,UCLA,49mineralhardnessscale,160mini-testing,chunking,119–20MIT,134Miyoshi,Dina,178mnemonics,160,175–76“mobile”phoneinvention,112monkeysinabenzenering,171,171months(thirty-onedays),159,159morningsandrecall,165,182motivatingtechnique(mentalcontrasting),99–100,108,258multiple-choicetests,246multitaskingcaution,106,108,211,212musclememory,173,177,178–79,181,182musicians,116myelinsheaths,195

namesofpeople,memory,174negativefeelings,dealingwith,127,139,140negativeself-talk,250neuralstructures,buildingchunking,52–53,53,54,54–55,67,67,68,69,71,78,93,113,121creativityandlearning,32,38,38,45,46easydoesit,11,14–15,16,18,24memory,159,161,162,170,173,179,182sculptingyourbrain,195–96,197,198Seealsobrain

neurologicalcravings,93,98NewHabit,The(Fiore),129Newman,Forrest,102,157Newport,Cal,134Newton’ssecondlaw,158,158,159,172,204NewYorkTimes,223nightly,creatingto-dolist,130,131,152NobelPrizewinners,194,202,206,207,219,252NobleSavages(Chagnon),223Noesner,Gary,147Nolta,Kathleen,208“notmyfault,”151–52,153,154Noui-Mehidi,Nadia,27,27–28“NowYouTry!”challenges,11,23,23,24–25,33,39,41,44,65,68,101,107,121,135,141,152,162,175,181,209,221numbers,associatingwithevents,175

Oakley,Barbara,xix–xx,1–8,3Seealsomathandscience,learning

“obvious,”strugglingwith,219–20,221–22occipitallobe,52“Oh,ThemGoldenSlippers,”163opiatereceptors,216organizationandchunking,73,118–19Orrell,Mike,100,117overconfidence,avoiding,20,225–37,247,248,254overlearningvs.interleaving,74,74–78,113,173

panic,103–4,244–46,248,250–51paradoxesoflearning,41,255Pariseau,Michael,130

passion,followingyour,147–48,154passiverepetition,119pauseandrecall,26,79,90,108,122,140,153,165,182,190,199,212,222,234,249,257,260pauseandreflect(wisewaiting),146–48,154Pavri,Vera,177persistencevs.intelligence,101,213–14,221,255personalizingstudymaterial,205–7,206,207,208,211,212,214–15Pert,Candace,215–16photon,206,206“picturewalking,”11,61,61,81,113,260Pietro,William,176pinballmetaphor,13,13–16,15,16–17,18planner-journal,130–37,131,140,149,152Plath,Sylvia,201,202“playtime”planning,132,134,140Ploughman,Elizabeth,128poetryandmathematics,202–5,211Pomodorotechnique,24–25,97,99,103,103–7,104,108,132,138,149,151,151,253,258Porter,Mark,189PowerofHabit,The(Duhigg),93powerofteamwork(avoidingoverconfidence),20,225–37,247,248,254practicemakespermanent,68–72,69,74,74,78,82,120,188,257–58,259practicetests,246,250prefrontalcortex,12,12,14–15,187Prentis,Jeffrey,203–4PresidentialMedalofFreedom,214primingyourmentalpump,11,61,61,81,113,260prioritizingandprocrastination,146problemsolving,chunking,62–63,65,71processvs.product,101–2,104,104,106,107,109procrastination,83–92,144–54addictionand,87,88–89attentiondifficulties,149,150brainand,86–89,87challengeof,17,24,26change,possibilityof,88cramming,24,38,38,85,87–88,111,145,185,254,259discomfortand,85–86,90,101,102,107distractionsand,84,105,107,150–51,151,154FAQs,148–52focusedmodeofthinkingand,24“justthisonetime”phenomenon,135–36smartpeopleand,188summary,90,139–40,152–53tools,tips,andtricks,126–43transferand,211willpower,84,91,95,97–98,107,150wisewaiting(pauseandreflect),146–48,154zombies(habits),93–111“zone,the,”workingin,144–46,154Seealsomathandscience,learning;zombies(habits)

ProcrastinationEquation,The(Steel),96pseudoscienceasscience,229puzzlepiecesmetaphor,61,61,74,74Pythagoreantheorem,32

qualitativeunderstandingofanequation,236–37questions,asking,217,260quirkytestquestions,218,221quittingtime,planning,132,134,141

Quizlet.com,138

Ramachandran,V.S.,228Ramanujan,Srinivasa,223random-accessmemory(RAM),43Ranjan,Apara,32RateMyProfessors.com,110recallandchunking,61–68,64,67,72–73,78,78,90,116,117,123,125recheckingyourwork,228,233,236,247,248,249Reddit.com,208redosandcreativity,50reducinganxietyandincreasingyourexpertise.Seeanxiety,dealingwithreframingyourfocus,127,139,140refrigeratorinvention,112rehearsalandworkingmemory,42–43relativity,206renaissancelearning,213–24repetitionofproblem,chunking,114rereading,xvii–xviii,61–62,65,71,116,117,123,125restingstatenetwork,11retellingstudymaterial,79,207–8,255,258retrainingthebrain,5–6reviewingmaterial,48,58rewardingyourself,98,99,101,106,107,108,140,152,153rewardpartofzombies(habits),88,95,97,98–99,107rewritingnotes.Seewritingbyhand“ReykjavíkRapid”in2004,10,10righthemisphereofbrain,20,225–27,227,228Roberts,Seth,128–29Rohrer,Doug,76Rosenthal,Mike,77–78ROTC,4rotememorization,113,254Seealsomemory

Roth,Brad,236,236–37routinepartofzombies(habits),84,88,94,95,96–97,97,107,109,129rulefollowingcaution,184

safecracking(Feynman),252–53,256“safeenvironment”forcriticism,232Sandburg,Carl,30Saucedo,Oraldo“Buddy,”110,110–11schedule,freedomofa,133“schooldreams,”169Schwalbe,Paul,46Science,70ScienceOlympiad,189Sciuto,Anthony,169Scoggin,Patrick,211sculptingyourbrain,193–200secondnature,makingknowledge,63seekinggoodadvicefrompeersandteachers,92,260Sejnowski,TerrenceJ.,xv–xviself-control,40,48,101self-experimentation,128–30sensesandmemory,159,163,164sensorycortex,187sentenceerrorsexercise,33sequentialproblemsolving,67,67setbacks,procrastination,153,154

settinggoals,136,137,141,152Shereshevsky,Solomon,51,52,54,55,58Sheridan,Tai,127Sherrington,SirCharles,205–6short-termmemory,43simplifyingstudymaterial(explanatoryquestioning),79,207–8,255,258SkillsToolbox.com,163Skinner,B.F.,146sleep,32,34,39,44–46,47,60,114,153,169,182,241,248,249,260“slower”students,219–20,221–22“slowhunch,”66smartpeopleandprocrastination,188Smith,DavidEugene,202snacksandmemory,164songsandmemory,162,181,257Sorby,Sheryl,166,166–67SovietUnionandjournalists,51spacedrepetition,43,47,69,172,172–74,257spatialmemory,157–58,161,166–67spirituality,diffusemodeofthinking,189sportsandmathandscience,183StallingforTime(Noesner),147starting,zombies(habits),105,137,141,143,152StayFocusd,139Steel,Piers,96StickK,139“stickystudent”syndrome,217storiesandmemory,177,181“StrengthofWeakTies,The”(Granovetter),231stress,103–4,244–46,248,250–51stuck,getting(Einstellungeffect),17,25,26,27–28,36–39,38,52,146,170,186,243StudyBlue,138studygroups,120,130,231–33,234,235,239,240,241,255,259studyingrules,257–60strategies,6–8,261–63Seealsomathandscience,learning

success,desiretopractice,moresuccess,4,6,86,99successvs.GREscores,187Sundaresan,Neel,124,124–25synapse,206Syria,168

talent,appreciatingyour.Seeappreciatingyourtalenttalkingtoyourself,memory,178,181talkingwithothersforhelp,40,92,260Tan,FabianHadipriono,174TBI(traumaticbraininjury),80–81TeacheroftheYearAward,105,187teachers,valueof,92,216–18,221,260teamwork,225–37,247,248,254technologytips,studying,137–39TEDtalk,163teenagersandimpulsivebehavior,195television,problemsusing,1–2TenRulesofBadStudying,259–60TenRulesofGoodStudying,257–58testingeffect,chunking,119–20,122,238testingyourself,257TestPreparationChecklist,239–41,248,249

testtaking,238–51tetracyclineandacne,128–29thalamus,52thinkingmodes.Seediffusemodeofthinking;focusedmodeofthinking30/30,138Thompson,Silvanus,169thoughts,visualaswellasverbal,202threeB’s(bed,bath,bus),30Thurston,William,70timetolearn,givingyourself,6,36Titanic(ship),223togglingbetweenthinkingmodescreativityandlearning,29–32,31,33–35,36–39,38,46,48easydoesit,10,20–23,21,22,23,25,253Seealsodiffusemodeofthinking;focusedmodeofthinking

tools,tips,andtricks,126–43Seealsoprocrastination

top-downbig-picturechunkingprocess,59,60,61,61,70,79transfer,59,209–11,212transitionmetals,176traumaticbraininjury(TBI),80–81Treacher-Collinsmutant,105trianglesandsquaresexercise,21,21trigger(cue)partofzombies(habits),88,94,95,96,107,109,129,153tryingtoohardcansometimesbepartoftheproblem.Seeeasydoesittwenty-five-minutetimer(Pomodorotechnique),24–25,97,99,103,103–7,104,108,132,138,149,151,151,253,258

underestimatingyourself,189underliningtext,62,125,178,259understandingbasicideaforchunking,58,78,79unitsofmeasurement,friendly,236,247unlockingyourpotential,252–60“upkeep”repetitions,63U.S.Army,4–5,142U.S.MemoryChampionships,156,157

visualization,156,171,171visualmemory,157–58,158,158–59,159,161,164,165visualmetaphors,memory,168–71,171,175,181,182,255,258

Wade,Nicholas,223,223–24walkingandrecall,30,72–73,90Wassell,Shaun,19Wegener,Alfred,55Weierstrass,Karl,204weighttraining,34–35WhereGoodIdeasComeFrom(Johnson),66Whitehouse,Malcolm,163whyvs.how,183–84,185,185Williamson,Alexander,30willpower,34,84,91,95,97–98,107,150wisewaiting(pauseandreflect),146–48,154workingaproblemthrough,chunking,56–57,58,82,114,259workingmemory,15,41,42,42–43,47,64,64,65,119,121,122,157,179,186,187workinphysics,204–5WorldWideWeb,66Wozniak,Steve,216writingaboutnegativethoughts,250writingbyhandchunkingand,63,76–77,118,125–26,173,257

memoryand,173,177,178,181

Young,Scott,208YouTube,27

Zettler,Bill,105,187zombies(habits),93–111beliefpartof,88,95,99–100,107cue(trigger)partof,88,94,95,96,107,109,129,153energysavingsfromhabits,93–94harnessingyour,84,95–101,97markingtheobjective,102mentalcontrastingtechnique,99–100,108,258multitaskingcaution,106,108,211,212neurologicalcravings,93,98Pomodorotechnique,24–25,97,99,103,103–7,104,108,132,138,149,151,151,253,258processvs.product,focus,101–2,104,104,106,107,109rewardpartof,88,95,97,98–99,107routinepartof,84,88,94,95,96–97,97,107,109,129startingand,105,137,141,143,152summary,107–8zombiealliance(planner-journal),130–37,131,140,149,152Seealsoprocrastination

“zone,the,”workingin,144–46,154Zuckerberg,Mark,216

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