en 3 an educational philosophy
DESCRIPTION
EN 3 An Educational Philosophy. Presented by Dr. Robert Mann Western Illinois University [email protected] http://www.wiu.edu/users/mfrrm1/ www.rsacmann.pbworks.com. Stickerzneezle. The number infected is a function of the time. Can lead to Powers. Grows very fast. - PowerPoint PPT PresentationTRANSCRIPT
ENEN33
AnAnEducational PhilosophyEducational Philosophy
Presented byPresented by
Dr. Robert MannDr. Robert MannWestern Illinois UniversityWestern Illinois University
http://www.wiu.edu/users/mfrrm1/
www.rsacmann.pbworks.com
StickerzneezleStickerzneezle
The number infected is The number infected is a function of the timea function of the time
TimeTime Number infectedNumber infected
00 11
11 33
22 99
33 2727
44 8181
55 243243
Can lead to PowersCan lead to Powers
TimeTime Number infectedNumber infected
00 11
11 3 =33 =311=3=3
22 3*3 = 33*3 = 322 =9 =9
33 3*3*3=33*3*3=333=27=27
44 3*3*3*3=33*3*3*3=344=81=81
55 3355 = 243 = 243
Grows very fastGrows very fast
TimeTime Number infectedNumber infected
55 243243
66 729729
77 21872187
88 65616561
99 1968319683
1010 5904959049
The longer it goes,The longer it goes,The faster it grows…The faster it grows…
TimeTime Number infectedNumber infected
00 11
55 243243
1010 5904959049
1515 14 million14 million
2020 3.5 billion3.5 billion
2121
How long to conquer How long to conquer the world???the world???
TimeTime Number infectedNumber infected
00 11
55 243243
1010 5904959049
1515 14 million14 million
2020 3.5 billion3.5 billion
2121 10 billion!!!10 billion!!!
StickersneezleStickersneezle
Ahhhh-Choo!!
Multiplicative Multiplicative patternpattern
PowersPowers Geometric Geometric
SequenceSequence Exponential Exponential
Growth functionGrowth function F(x)=1*3F(x)=1*3xx
ENEN33
Engage Engage Enlighten Enlighten EnrichEnrich
ENEN33
Engage: Grab the students' attention, Engage: Grab the students' attention, – hookhook their interest, make them their interest, make them – ""active learnersactive learners""
Enlighten: teach them something!Enlighten: teach them something!– Skills, concepts, connections, Skills, concepts, connections, objectiveobjective– Learn something new each dayLearn something new each day
Enrich: Make it Enrich: Make it meaningfulmeaningful– give reasons for learning that objectivegive reasons for learning that objective– connectconnect, extend, elaborate, extend, elaborate
Stickersneezle Stickersneezle example:example:
Engage: Kids are out of their seats, Engage: Kids are out of their seats, – get to sneeze on people! get to sneeze on people! – Can Can seesee the numbers forming from the physical the numbers forming from the physical
situationsituation Enlighten: Exponential FunctionsEnlighten: Exponential Functions
– Represented as Physical Represented as Physical – model, words, tables, graphs, equationsmodel, words, tables, graphs, equations– Geometric Sequence, recursive patternGeometric Sequence, recursive pattern
Enrich: where else is this phenomena seen?Enrich: where else is this phenomena seen?– World population, compound interest, AIDS….World population, compound interest, AIDS….– Real connectionsReal connections– ““The longer it goes, the faster it grows”The longer it goes, the faster it grows”
One example of a One example of a simple philosophy:simple philosophy:
EngageEngageEnlightenEnlighten EnrichEnrich The key is to EN^3 ALL learners..The key is to EN^3 ALL learners..
Extending Extending StickersneezleStickersneezle Triples every minute: y=1*3Triples every minute: y=1*3xx
Started with 5 and triples every Started with 5 and triples every minute: y=5*3minute: y=5*3xx
Triples every 10 minutes: Triples every 10 minutes: y=5*3y=5*3(x/10)(x/10)
Or y = 5*(1.116)Or y = 5*(1.116)xx
Or y = 5*eOr y = 5*e(.1099x)(.1099x)
Multiple Multiple RepresentationsRepresentations
Engagement doesn’t Engagement doesn’t have to be elaboratehave to be elaborate
A simple sheet of paper…A simple sheet of paper…– Cylinder volumeCylinder volume
– Lines of SymmetryLines of Symmetry
– FoldingFolding
EngageEngage
I believe in the power of young I believe in the power of young minds to engage in mathematics minds to engage in mathematics and the power of mathematics to and the power of mathematics to engage young minds.engage young minds.
A.G. AndrewsA.G. Andrews
Engagement?Engagement?
Interesting activities (Pascal)Interesting activities (Pascal)Exciting Experiments Exciting Experiments (technology)Silly StoriesSilly StoriesProvoking Problems Provoking Problems Perplexing PuzzlesPerplexing PuzzlesDismaying DisequilibriumDismaying DisequilibriumRelevant ReviewRelevant ReviewCurious CapersCurious Capers
Pascal’s Tree?Pascal’s Tree?
Related problem???Related problem???
In the song, “The Twelve Days of In the song, “The Twelve Days of Christmas”, how many total gifts Christmas”, how many total gifts are given by the ‘true love’?are given by the ‘true love’?
How is this related to Pascal’s How is this related to Pascal’s triangle?triangle?
What pattern emerges from the What pattern emerges from the sum of each row??sum of each row??
Engaging problems…Engaging problems…
Write a paragraph describing what you Write a paragraph describing what you will be doing 1 billion seconds from nowwill be doing 1 billion seconds from now
Jacey met her friends at the park. . Everyone was riding either a tricycle or a bicycle. Jacey counted seventeen wheels on the playground. How many friends could be riding at the playground and what are they riding?
Lots of others from NCTM resources, Lots of others from NCTM resources, this conference, the web,….this conference, the web,….
Solve the following:
•
046
096
043
04
2
2
2
2
xx
xx
xx
x
Engagement?Engagement?
Interesting activities Interesting activities Exciting ExperimentsExciting ExperimentsSilly StoriesSilly StoriesProvoking ProblemsProvoking ProblemsPerplexing PuzzlesPerplexing PuzzlesDismaying DisequilibriumDismaying DisequilibriumRelevant ReviewRelevant ReviewCurious CapersCurious Capers
Engage..Engage..
You have to reach them to teach them!You have to reach them to teach them!
ENEN3 Lesson Planning3 Lesson Planning
Engage:Engage:
How will I convince them that this is How will I convince them that this is important/meaningful?important/meaningful?
Enlighten:Enlighten:
What do I want the students to What do I want the students to learn?learn?
Enrich:Enrich:
Why do I want them to learn this?Why do I want them to learn this?
Connection to Connection to StandardsStandards
Enlighten:Enlighten: Number SenseNumber Sense MeasurementMeasurement GeometryGeometry AlgebraAlgebra Data AnalysisData Analysis
And ProbabilityAnd Probability
Enrich:Enrich: Problem-solvingProblem-solving ReasoningReasoning ConnectionsConnections RepresentationsRepresentations CommunicationCommunication
Lets try another example….
D
C
BA
EngageEngage
Personally invested (ALL can do)Personally invested (ALL can do)
Pick one that will be a cubePick one that will be a cube
Which face will be opposite the face with Which face will be opposite the face with the stickerthe sticker
EnlightenEnlighten
Net types that fold into a cube
Spatial visualization
Properties of a cube
6 faces
8 vertices
12 edges
•Net types that fold into a cube
•Spatial visualization
•Properties of a cube
6 faces
8 vertices
12 edges
EnrichEnrich
a. What do the nets of other a. What do the nets of other polyhedron look like?polyhedron look like?b. How many different cube nets are b. How many different cube nets are there?there?
(what is meant by different?)(what is meant by different?)c. If the side length is 3, what is the c. If the side length is 3, what is the surface area, what is the volume?surface area, what is the volume?d. Euler's formulad. Euler's formulae. Design a better, more useful 12-pack e. Design a better, more useful 12-pack pop cartonpop carton
EnrichmentEnrichment
ShapeShape FacesFaces VerticesVertices EdgesEdges
CubeCube 66 88 1212
TetrahedroTetrahedronn
44 44 66
GeneralGeneral FF VV
EnrichmentEnrichment
ShapeShape FacesFaces VerticesVertices EdgesEdges
CubeCube 66 88 1212
TetrahedroTetrahedronn
44 44 66
GeneralGeneral FF VV F+V-2F+V-2
A net ….
A net ….
A net ….
A net ….
A net ….
How many cube nets How many cube nets are there?are there?
See “Building a Box” problem in November, 2003
Teaching Children Mathematics and November, 2004 and March, 2009
The cube and The 4The cube and The 4thth dimension?dimension?
Dim.Dim. PointPointss
00 11
11 22
22 44
33 88
44
55
Multiple dimensionsMultiple dimensions
Dim.Dim. PointPointss
00 11
11 22
22 44
33 88
44 1616
55 3232
Enrichment??Enrichment??
One’s mind, once One’s mind, once stretched by a new idea, stretched by a new idea, never regains its original never regains its original dimensions.dimensions.
Oliver Wendell Oliver Wendell HolmesHolmes
ENRICHENRICH
To connect mathematical ideasTo connect mathematical ideas To connect math to other subjectsTo connect math to other subjects To connect to real-lifeTo connect to real-life To connect to studentsTo connect to students To expose students to the beauty To expose students to the beauty
and power of mathematicsand power of mathematics To stretch their mindsTo stretch their minds
Pythagorean TheoremPythagorean Theorem
Physically or Virtually showPhysically or Virtually show Prove (Garfield’s Proof)Prove (Garfield’s Proof) Connect to Distance FormulaConnect to Distance Formula Connect to Law of CosinesConnect to Law of Cosines Connect to Fermat’s TheoremConnect to Fermat’s Theorem
EnrichmentEnrichment
EnlighteningEnlightening students is an students is an integral part of good integral part of good instructioninstruction
butbut EnrichingEnriching students is an integral students is an integral
part of good part of good teaching!teaching!
ENEN3 3 : Engage, Enlighten, : Engage, Enlighten,
EnrichEnrich
But how many faces on the cube?But how many faces on the cube? EnergyEnergy
EnthusiasmEnthusiasm
Enjoy Enjoy
EnergyEnergy
Research Research shows that shows that active active learners learners learn betterlearn better
Awake Awake students students learn more learn more than than sleeping sleeping studentsstudents
EnthusiasmEnthusiasm
EnjoyEnjoy
SmileSmile Have funHave fun Enjoy the Enjoy the
rewards of rewards of teachingteaching
Keep your Keep your sense of sense of
humor!humor!You will need It!!!
6 Faces of EN6 Faces of EN33
ENGAGE the learnerENGAGE the learner ENLIGHTEN the learnerENLIGHTEN the learner ENRICH the learnerENRICH the learner ENJOY the phenomenal experienceENJOY the phenomenal experience
And do all this with And do all this with ENERGY and ENERGY and ENTHUSIASMENTHUSIASM
Don't just teach them, Don't just teach them, EN-cube them!!!EN-cube them!!!
Other EN words to Other EN words to consider:consider: EncloseEnclose
– Package, wrap a lesson—like the cube…Package, wrap a lesson—like the cube… Encourage?Encourage?
Of courseOf course Enspire?Enspire?
Spelled wrong but yes, definitelySpelled wrong but yes, definitely
Entertain?Entertain?
Maybe….Maybe….
EN…..EN…..
EncloseEnclose EncourageEncourage EnspireEnspire EntertainEntertain
Enpower?? Enpower??
Enpower?Enpower? Maybe this is our ultimate goal as Maybe this is our ultimate goal as
teachers--to empower our students… withteachers--to empower our students… with
KnowledgeKnowledge SkillsSkills ConfidenceConfidence ReasoningReasoning UnderstandingUnderstanding ThinkingThinking InsightInsight The Courage to dream The Courage to dream The Ability to achieve those dreams.The Ability to achieve those dreams.
One more One more Stickersneezle Stickersneezle extensionextension Pay it ForwardPay it Forward
"Enpower" our students with "Enpower" our students with the ability to "Enpower" others:the ability to "Enpower" others:
http://payitforward.warnerbros.com/Pay_It_Forward/http://payitforward.warnerbros.com/Pay_It_Forward/
ENEN33
toto
33ENEN
““en-cubed in order to enpower”en-cubed in order to enpower”
Empower them to Empower Empower them to Empower othersothers
YouYouAre OneAre One
Yet, You are ManyYet, You are ManyYour Impact seems small, but it is ImmenseYour Impact seems small, but it is Immense
You are the Sage and the Guide--you Reach, you Teach, you Instruct and you Inspire You are the Sage and the Guide--you Reach, you Teach, you Instruct and you Inspire You are not merely purveyors of information, but rather are instigators and facilitators of You are not merely purveyors of information, but rather are instigators and facilitators of
great deedsgreat deedsDaily, you engage, enlighten, and enrich young mindsDaily, you engage, enlighten, and enrich young minds
They are Empowered becauseThey are Empowered becauseYou areYou are
Empowered.Empowered.
Learning Mathematics Learning Mathematics does not have to be does not have to be fun,fun,
but, it can be!but, it can be!
Learning Mathematics Learning Mathematics does not have to be does not have to be fun,fun,
but, it can be!but, it can be!
Have we seen this Have we seen this pattern before?pattern before?
IterationIteration TrianglesTriangles
00 11
11 33
22 99
33 2727
44 8181
55 243243
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