EN3AnEducational Philosophy Presented by Dr. Robert Mann Western Illinois University firstname.lastname@example.org http://www.wiu.edu/users/mfrrm1/ www.rsacmann.pbworks.com
Stickersneezle • Multiplicative pattern • Powers • Geometric Sequence • Exponential Growth function • F(x)=1*3x Ahhhh-Choo!!
EN3 • Engage • Enlighten • Enrich
EN3 • Engage: Grab the students' attention, • hook their interest, make them • "active learners" • Enlighten: teach them something! • Skills, concepts, connections, objective • Learn something new each day • Enrich: Make it meaningful • give reasons for learning that objective • connect, extend, elaborate
Stickersneezle example: • Engage: Kids are out of their seats, • get to sneeze on people! • Can see the numbers forming from the physical situation • Enlighten: Exponential Functions • Represented as Physical • model, words, tables, graphs, equations • Geometric Sequence, recursive pattern • Enrich: where else is this phenomena seen? • World population, compound interest, AIDS…. • Real connections • “The longer it goes, the faster it grows”
One example of a simple philosophy: • Engage • Enlighten • Enrich • The key is to EN^3 ALL learners..
Extending Stickersneezle • Triples every minute: y=1*3x • Started with 5 and triples every minute: y=5*3x • Triples every 10 minutes: y=5*3(x/10) • Or y = 5*(1.116)x • Or y = 5*e(.1099x)
Engagement doesn’t have to be elaborate A simple sheet of paper… • Cylinder volume • Lines of Symmetry • Folding
Engage • I believe in the power of young minds to engage in mathematics and the power of mathematics to engage young minds. • A.G. Andrews
Engagement? • Interesting activities (Pascal) • Exciting Experiments (technology) • Silly Stories • Provoking Problems • Perplexing Puzzles • Dismaying Disequilibrium • Relevant Review • Curious Capers
Related problem??? • 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? • What pattern emerges from the sum of each row??
Engaging problems… • 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,….
Engagement? • Interesting activities • Exciting Experiments • Silly Stories • Provoking Problems • Perplexing Puzzles • Dismaying Disequilibrium • Relevant Review • Curious Capers
Engage.. • You have to reach them to teach them!
EN3 Lesson Planning • Engage: How will I convince them that this is important/meaningful? • Enlighten: What do I want the students to learn? Enrich: Why do I want them to learn this?
Enlighten: Number Sense Measurement Geometry Algebra Data Analysis And Probability Enrich: Problem-solving Reasoning Connections Representations Communication Connection to Standards Lets try another example….
Engage • Personally invested (ALL can do) • Pick one that will be a cube • Which face will be opposite the face with the sticker
Net types that fold into a cube Spatial visualization Properties of a cube 6 faces 8 vertices 12 edges Enlighten • Net types that fold into a cube • Spatial visualization • Properties of a cube • 6 faces • 8 vertices • 12 edges
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
How many cube nets are there? See “Building a Box” problem in November, 2003 Teaching Children Mathematics and November, 2004 and March, 2009
Enrichment?? • One’s mind, once stretched by a new idea, never regains its original dimensions. Oliver Wendell Holmes
ENRICH • To connect mathematical ideas • To connect math to other subjects • To connect to real-life • To connect to students • To expose students to the beauty and power of mathematics • To stretch their minds
Pythagorean Theorem • Physically or Virtually show • Prove (Garfield’s Proof) • Connect to Distance Formula • Connect to Law of Cosines • Connect to Fermat’s Theorem
Enrichment • Enlightening students is an integral part of good instruction but • Enriching students is an integral part of good teaching!
Energy Enthusiasm Enjoy EN3 : Engage, Enlighten, EnrichBut how many faces on the cube?
Research shows that active learners learn better Awake students learn more than sleeping students Energy
Enthusiasm Attitude is contagious Make Yours Worth Catching!!
Smile Have fun Enjoy the rewards of teaching Keep your sense of humor! Enjoy You will need It!!!
6 Faces of EN3 • ENGAGE the learner • ENLIGHTEN the learner • ENRICH the learner • ENJOY the phenomenal experience And do all this with • ENERGY and • ENTHUSIASM Don't just teach them, EN-cube them!!!
Other EN words to consider: • Enclose • Package, wrap a lesson—like the cube… • Encourage? Of course • Enspire? Spelled wrong but yes, definitely • Entertain? Maybe….
EN….. • Enclose • Encourage • Enspire • Entertain • Enpower??