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EN 3 An Educational Philosophy Presented by Dr. Robert Mann Western Illinois University rr-mann@wiu.edu http://www.wiu.edu/users/mfrrm1/ www.rsacmann.pbworks.com

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Stickerzneezle

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The number infected is a function of the time Time Number infected 01 13 29 327 481 5243

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Can lead to Powers Time Number infected 01 1 3 =3 1 =3 2 3*3 = 3 2 =9 3 3*3*3=3 3 =27 4 3*3*3*3=3 4 =81 5 3 5 = 243

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Grows very fast Time Number infected 5243 6729 72187 86561 919683 1059049

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The longer it goes, The faster it grows… Time Number infected 01 5243 1059049 15 14 million 20 3.5 billion 21

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How long to conquer the world??? Time Number infected 01 5243 1059049 15 14 million 20 3.5 billion 21 10 billion!!!

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Stickersneezle Ahhhh-Choo!! Multiplicative pattern Multiplicative pattern Powers Powers Geometric Sequence Geometric Sequence Exponential Growth function Exponential Growth function F(x)=1*3 x F(x)=1*3 x

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EN 3 Engage Engage Enlighten Enlighten Enrich Enrich

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EN 3 Engage: Grab the students' attention, Engage: Grab the students' attention, –hook their interest, make them –"active learners" Enlighten: teach them something! Enlighten: teach them something! –Skills, concepts, connections, objective –Learn something new each day Enrich: Make it meaningful Enrich: Make it meaningful –give reasons for learning that objective –connect, extend, elaborate

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Stickersneezle example: Engage: Kids are out of their seats, Engage: Kids are out of their seats, –get to sneeze on people! –Can see the numbers forming from the physical situation Enlighten: Exponential Functions Enlighten: Exponential Functions –Represented as Physical –model, words, tables, graphs, equations –Geometric Sequence, recursive pattern Enrich: where else is this phenomena seen? Enrich: where else is this phenomena seen? –World population, compound interest, AIDS…. –Real connections –“The longer it goes, the faster it grows”

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One example of a simple philosophy: Engage Engage Enlighten Enlighten Enrich Enrich The key is to EN^3 ALL learners.. The key is to EN^3 ALL learners..

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Extending Stickersneezle Triples every minute: y=1*3 x Triples every minute: y=1*3 x Started with 5 and triples every minute: y=5*3 x Started with 5 and triples every minute: y=5*3 x Triples every 10 minutes: y=5*3 (x/10) Triples every 10 minutes: y=5*3 (x/10) Or y = 5*(1.116) x Or y = 5*(1.116) x Or y = 5*e (.1099x) Or y = 5*e (.1099x)

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Multiple Representations

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Engagement doesn’t have to be elaborate A simple sheet of paper… –Cylinder volume –Lines of Symmetry –Folding

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Engage I believe in the power of young minds to engage in mathematics and the power of mathematics to engage young minds. I believe in the power of young minds to engage in mathematics and the power of mathematics to engage young minds. A.G. Andrews A.G. Andrews

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Engagement? Interesting activities (Pascal) Exciting Experiments (technology) (technology) Silly Stories Provoking Problems Perplexing Puzzles Dismaying Disequilibrium Relevant Review Curious Capers

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Pascal’s Tree?

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Related problem??? In the song, “The Twelve Days of Christmas”, how many total gifts are given by the ‘true love’? In the song, “The Twelve Days of Christmas”, how many total gifts are given by the ‘true love’? How is this related to Pascal’s triangle? How is this related to Pascal’s triangle? What pattern emerges from the sum of each row?? What pattern emerges from the sum of each row??

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Engaging problems… Write a paragraph describing what you will be doing 1 billion seconds from now Write a paragraph describing what you will 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, this conference, the web,…. Lots of others from NCTM resources, this conference, the web,….

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Solve the following:

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Engagement? Interesting activities Exciting Experiments Silly Stories Provoking Problems Perplexing Puzzles Dismaying Disequilibrium Relevant Review Curious Capers

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Engage.. You have to reach them to teach them!

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EN 3 Lesson Planning Engage: Engage: How will I convince them that this is important/meaningful? Enlighten: Enlighten: What do I want the students to learn? Enrich: Why do I want them to learn this?

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Connection to Standards Enlighten: Number Sense Number Sense Measurement Measurement Geometry Geometry Algebra Algebra Data Analysis Data Analysis And Probability Enrich: Problem-solving Problem-solving Reasoning Reasoning Connections Connections Representations Representations Communication Communication Lets try another example….

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Engage Personally invested (ALL can do) Pick one that will be a cube Which face will be opposite the face with the sticker

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Enlighten 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

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Enrich a. What do the nets of other polyhedron look like? b. How many different cube nets are there? (what is meant by different?) c. If the side length is 3, what is the surface area, what is the volume? d. Euler's formula e. Design a better, more useful 12-pack pop carton

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Enrichment ShapeFacesVerticesEdges Cube6812 Tetrahedron446 GeneralFV

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Enrichment ShapeFacesVerticesEdges Cube6812 Tetrahedron446 GeneralFVF+V-2

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A net ….

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How many cube nets are there? See “Building a Box” problem in November, 2003 Teaching Children Mathematics and November, 2004 and March, 2009

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The cube and The 4 th dimension? Dim.Points 01 12 24 38 4 5

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Multiple dimensions Dim.Points 01 12 24 38 416 532

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Enrichment?? One’s mind, once stretched by a new idea, never regains its original dimensions. One’s mind, once stretched by a new idea, never regains its original dimensions. Oliver Wendell Holmes

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ENRICH To connect mathematical ideas To connect mathematical ideas To connect math to other subjects To connect math to other subjects To connect to real-life To connect to real-life To connect to students To connect to students To expose students to the beauty and power of mathematics To expose students to the beauty and power of mathematics To stretch their minds To stretch their minds

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Pythagorean Theorem Physically or Virtually show Physically or Virtually show Prove (Garfield’s Proof) Prove (Garfield’s Proof) Connect to Distance Formula Connect to Distance Formula Connect to Law of Cosines Connect to Law of Cosines Connect to Fermat’s Theorem Connect to Fermat’s Theorem

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Enrichment Enlightening students is an integral part of good instruction Enlightening students is an integral part of good instructionbut Enriching students is an integral part of good teaching! Enriching students is an integral part of good teaching!

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Teaching…. We are not just purveyors of information, But rather sculptors of humanity ???

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EN 3 : Engage, Enlighten, Enrich But how many faces on the cube? Energy Energy Enthusiasm Enthusiasm Enjoy Enjoy

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Energy Research shows that active learners learn better Research shows that active learners learn better Awake students learn more than sleeping students Awake students learn more than sleeping students

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Enthusiasm

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Enjoy Smile Smile Have fun Have fun Enjoy the rewards of teaching Enjoy the rewards of teaching Keep your sense of Keep your sense of humor! humor! You will need It!!!

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6 Faces of EN 3 ENGAGE the learner ENGAGE the learner ENLIGHTEN the learner ENLIGHTEN the learner ENRICH the learner ENRICH the learner ENJOY the phenomenal experience ENJOY the phenomenal experience And do all this with ENERGY and ENERGY and ENTHUSIASM ENTHUSIASM Don't just teach them, EN-cube them!!!

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Other EN words to consider: Enclose Enclose –Package, wrap a lesson—like the cube… Encourage? Encourage? Of course Enspire? Enspire? Spelled wrong but yes, definitely Entertain? Entertain? Maybe…. Maybe….

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EN….. Enclose Enclose Encourage Encourage Enspire Enspire Entertain Entertain Enpower?? Enpower??

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Enpower? Maybe this is our ultimate goal as teachers--to empower our students… with Knowledge Knowledge Skills Skills Confidence Confidence Reasoning Reasoning Understanding Understanding Thinking Thinking Insight Insight The Courage to dream The Courage to dream The Ability to achieve those dreams. The Ability to achieve those dreams.

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One more Stickersneezle extension Pay it Forward Pay it Forward

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"Enpower" our students with the ability to "Enpower" others: http://payitforward.warnerbros.com/Pay_It_Forward/ http://payitforward.warnerbros.com/Pay_It_Forward/ http://payitforward.warnerbros.com/Pay_It_Forward/

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EN 3 to 3 EN “en-cubed in order to enpower” “en-cubed in order to enpower”

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Empower them to Empower others You Are One Yet, You are Many Your 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 not merely purveyors of information, but rather are instigators and facilitators of great deeds Daily, you engage, enlighten, and enrich young minds They are Empowered because You are Empowered. You Are One Yet, You are Many Your 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 not merely purveyors of information, but rather are instigators and facilitators of great deeds Daily, you engage, enlighten, and enrich young minds They are Empowered because You are Empowered.

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Learning Mathematics does not have to be fun, but, it can be!

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Learning Mathematics does not have to be fun, but, it can be!

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Have we seen this pattern before? IterationTriangles 01 13 29 327 481 5243 Back

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Dr. Bob Mann Western Illinois University

Dr. Bob Mann Western Illinois University

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