k-12 calculator usage and college grades

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K-12 Calculator Usage and College GradesAuthor(s): W. Stephen Wilson and Daniel Q. NaimanSource: Educational Studies in Mathematics, Vol. 56, No. 1 (2004), pp. 119-122Published by: SpringerStable URL: http://www.jstor.org/stable/4150266 .

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SHORTCOMMUNICATION

W. STEPHENWILSONand DANIELQ. NAIMAN

K-12 CALCULATORUSAGE AND COLLEGEGRADES*

ABSRTACT.We find that studentsin the big mathematics service courses at the JohnsHopkinsUniversitywho wereencouraged o use calculators n K-12 have somewhatlowergradesthan those who weren't.KEYWORDS:calculators,college grades

1. INTRODUCTIONWe teach ourelementarymathematics oursesCalculusI, II, III,andLinearAlgebra,in fairly large multi-sectioncourses. Calculatorsare certainlyabig improvementover the slide ruleand books of tables.However,none ofthe mathematicalconcepts andproblem-solvingskills we want to impartin these courses requirethe use of a calculator. Overuse of calculators,especiallyin the lowergrades,might carrysome risk with it. Studentsmaynot get the necessary feel for the numbersystem needed to progress inmathematics.Many of our studentswant to use their calculatorsin ourcourses.We began to wonderif therewere any connectionsbetween stu-dents' previous experiencewith calculatorsand theirperformance n ourbasic mathematicscourses.Studentsat JohnsHopkinsUniversityare all very good. Admission ishighly competitiveandastrongmathematicsbackgrounds fairlyuniversal.Manyof ourstudentshavehighscoreson standardizedestsin mathematics*This short communication, writtenby two universitymathematicians, s published inESM in the hope that it will start off a discussion among readerson several interestingissues. The authorsof thepaperstate a difference n achievement n universitymathematicscoursesrelatedto the use of calculators n pre-university tudyof mathematics.It would beinteresting o understand hereasons behindthis fact. Why this differencein achievement?How is the mathematical hinkingwith calculatorsdifferentfrom mathematical hinkingwithout them?What are the non-calculatormathematicscourses teachingthat calculatorcoursesdon't and vice-versa?The mathematicalknowledgeandwaysof thinkingdevelopedwithcalculatorsmaynot be veryusefulin succeedingin themathematicscourses offeredattheuniversity,butperhaps hisknowledgeis useful elsewhere.What is this knowledge andwherecould it be useful?ESMreadersare welcome to expresstheiropinions andproposalsin commentaryarticles andLettersto the Editor.(Editor'snote)

Educational Studiesin Mathematics56: 119-122, 2004.? 2004 KluwerAcademicPublishers. Printed in theNetherlands.


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120 W. STEPHENWILSON AND DANIEL Q. NAIMANandmanyhave advancedplacement n Calculus.We formedthehypothesisthatwith this groupof elite studentstheirpreviousK-12 calculatorexperi-ence wouldhaveno effect on theirgradesin theirelementarymathematicscourses.

2. THE SURVEYWe set out to test ourhypothesisby giving a small surveyto our studentsduringtheirfinalexam. We asked a very simple question:"InK-12, cal-culatorusage was (1) emphasizedandencouraged,(2) was taughtbutnotpushed,or (3) not muchat all."The survey was done in the fall of 2002. The courses surveyedwereas follows: 110.105, Introductionto Calculus, our pre-calculus course;110.106-7, CalculusI andII for Biological and Social Sciences; 110.108CalculusI forPhysicalSciencesandEngineering;110.201,LinearAlgebra;110.202, CalculusIII,Calculusof SeveralVariables.There were a total of 776 studentswho finished the surveyedcourseswith a grade.Of these, we had signed, completesurveysfrom 663 (85%).Ofthese 663 studentswe hadmathematicsSATscoresfor607 of them.Asit was possiblethatmathematicsSATscorewasakeyfactor n determininggrades, it was important o control for the effect of this variable in ouranalysis.

3. CONCLUSIONWecombinedthelast two answersfor thesurveyto createabinarycategor-ical variablethat,we feel, appropriately egregatesthe studentsinto highcalculatorand low calculatoremphasis groups.Thus each studenthad a 0ora 1for thevariableCALC.tis 0 if they picked(1) in the survey(InK-12,calculatorusagewasemphasizedandencouraged.)and I if they picked(2)or (3). (In K-12, calculatorusage was not emphasizedand encouraged.)The GRADEs the gradeat the end of the courseon the 4.0 scale (with B+a 3.3, B- a 2.7, etc). MSATs the students'mathematicsSATscore.

Regressionanalysis led to the following fit to the data:GRADE = CONSTANT+ CALC x .2046 + MSAT x .0036.

Thep-value forMSATis 0.0000 and thep-valueforCALCs 0.01. The CALCp-value is significant.Fromthis, it appearsthatcalculatorshave an effecton grades.Weproceedto quantifythe magnitudeof this effect.We first note that CALChas the same effect on the grade that 57 pointsof the mathematics SAT has. This, of course, does not make the result


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K-12 CALCULATORSAGE NDCOLLEGERADES 121

meaningful.It is the effect on gradesthatmakes it meaningful.Withplusandminusgrades,anotchon thegradescale is, onaverage,0.33. A notchonthegradescale is definitelymeaningful o ourstudents.Ofour 607 studentssurveyed,268 (44%)wereself-declared hat"InK-12,calculatorusagewasemphasizedand encouraged."On average, their grades were 0.20 lower.Onewayto achievethis outcomeis for 162 of these268 students ohaveonegradenotch lower. Thatis, 27% of all the students n the survey.Althoughthereare otherways to achievethis numericaloutcome, it is clearthat ourhypothesiswas wrong.Muchto oursurprise,we mustconclude that here s a(negative)connec-tion betweenourcollege mathematicsgradesatJohnsHopkinsUniversityandheavycalculatorusage in K-12.Calculatorsclearly have a place in the classroombut we suspect thatthey are sometimesmisused.

4. DISCussIoN

Mathematicseducationresearchis not our area of researchor expertise.This studyshould be considereda small pilot study.Oursurvey questionwas ratherblunt. If our studentsare asked if calculatorusage was encour-aged andemphasizedfor 1 yearor more (asked informallyin class), thenthe number hootswayupover the 44% obtainedhere.From hiswe deducethatthe students' nterpretationf thequestionwas one of prettyheavycal-culatorusage. A refinementof this questionwould be nice andgive moreinsightinto the results.JohnsHopkins Universityis a rather imited universe.It would not bedifficultto do similar studies at otherplaces. Giving the surveywith thefinalexam does guaranteea fairly captiveaudience. The majorityof highschool graduatesnow go on to college. Thus most K-12 programsarecollege preparatoryby default.The success of mathematicsprogramsinK-12 shouldbejudged by how well studentsdo in college. Gradesareonlyoneplaceto look. The firstthingenteringstudentsget is a placementexamin mathematics.So, to a largeextent, K-12 is preparingstudentsfor thisplacementtest as the next step in theircareers.Most college mathematicsdepartmentswould be happyto put a series of questionsabout calculatorusage on theirplacementtest. The results would be interestingno matterhow theyfell.

ACKNOWLEDGEMENTSWe want to thank Doris Entwisle for numerous suggestions and guidance.


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122 W. STEPHENWILSON AND DANIEL Q. NAIMANW. STEPHEN WILSONDepartmentof Mathematics,JohnsHopkinsUniversity,3400 N. CharlesStreet,Baltimore,MD 21218, USAE-mail:[email protected] Q. NAIMANDepartmentof AppliedMathematicsand Statistics,JohnsHopkinsUniversity,3400 N. CharlesStreet,Baltimore,MD 21218, USAE-mail:[email protected]

k-12 calculator usage and college grades

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