EN 3 An Educational Philosophy

1. EN3AnEducational Philosophy Presented by Dr. Robert Mann Western Illinois University rr-mann@wiu.edu http://www.wiu.edu/users/mfrrm1/ www.rsacmann.pbworks.com

2. Stickerzneezle

3. The number infected is a function of the time

4. Can lead to Powers

5. Grows very fast

6. The longer it goes,The faster it grows…

7. How long to conquer the world???

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

9. EN3 • Engage • Enlighten • Enrich

10. 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

11. 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”

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

13. 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)

14. Multiple Representations

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

16. 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

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

18. Pascal’s Tree?

19. 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??

20. 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,….

21. Solve the following:

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

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

24. 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?

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

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

28. 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

29. 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

30. Enrichment

31. Enrichment

32. A net ….

33. A net ….

34. A net ….

35. A net ….

36. A net ….

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

38. The cube and The 4th dimension?

39. Multiple dimensions

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

41. 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

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

43. Enrichment • Enlightening students is an integral part of good instruction but • Enriching students is an integral part of good teaching!

44. Energy Enthusiasm Enjoy EN3 : Engage, Enlighten, EnrichBut how many faces on the cube?

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

46. Enthusiasm Attitude is contagious Make Yours Worth Catching!!

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

48. 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!!!

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

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