ENEN33

AnAnEducational PhilosophyEducational Philosophy

Presented byPresented by

Dr. Robert MannDr. Robert MannWestern Illinois UniversityWestern Illinois University

rr-mann@wiu.edu

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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