Having FUN Engaging Future Teachers in Mathematical Thinking

1. Having FUN Engaging Future Teachers in Mathematical Thinking Teacher Prep Committee

2. Friday 4:15 – 5:15 Teacher Preparation Committee Meeting

3. Presenters: Kendall Jacobs – Aha Moments Joyce Lindstrom – Exploring Divisibility Observation and Proof – Puppies & Kittens Judith Sallee – Where Should I hide the Prize Jake McIntyre – Algebra Tiles Anthony Piccolino – Preparing Teachers

4. “Aha”Math is SooooCool!

5. Students need to experience the satisfaction of discovering mathematics for themselves This session will focus on strategies and activities that help pre-service teachers experience the sometimes elusive “Aha” moment.

6. The first “Aha” moment I had was when we were finding sums to sequences. It literally took me two weeks to figure it out and when I finally did I was extremely happy. I never thought getting excited about math would ever happen for me……. ……..This class is still fairly frustrating and challenging for me, so when I do finally understand something I am super excited and happy! …..Student comments Fall 2013

7. Find the sum of 3+5+7+….+303

8. I don’t know what’s the matter with people….They do not learn by understanding…They learn by some other way – by rote, or something.... Their knowledge is so FRAGILE! Richard Feynmen

9. Find the 500th term 3,5,7,9,…….. Hey wait….what is an arithmetic sequence? 3,3+2,3+2+2,3+2+2+2, ……

10. When you make the finding yourself—even if you’re the last person on Earth to see the light—you’ll never forget it….Carl Sagan

13. Finding patterns where I did not realize they could be found, and even coming to realize why the class is called “Numbers and Operations” - all of these have been “aha” moments for me. …..Student comments Fall 2013

15. They must FEEL the Mathematics flowing And UNLEARN what they have learned

16. How do our students approach this problem? They have been “well trained”

18. The Story of an Exam Question……

19. Don’t just “memorize” mathematics….. EXPERIENCE IT!!!!!!

20. ….before I took this class I probably would've gotten really frustrated with the problem and it would've taken me a lot longer to figure out but …[now]… I feel like I am a stronger math student because I can try to problem solve on my own and create those "AHA" moments…

21. Proof and Reasoning Exploration Inductive and Deductive Reasoning • 1. Write down any “non-palindromic” 3 digit number • 2. Reverse the number and then subtract the smaller from the larger • 3. Tell me the last digit of the number in the difference and I AMAZE you by telling you the entire difference.

22. For example

24. 99 198 297 396 495 594 693 792 891

25. Deductive Reasoning

26. Angela Duckworth: TED talk …..Mathematical Grit http://www.ted.com/talks/angela_lee_duckworth_the_key_to_success_grit.html Dan Meyer: Math Class needs a Makeover http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html Grant Wiggins: Problem of Problems - Exercises verses Problems http://www.carnegielearning.com/webinars/designing-math-curricula-with-true-problem-solving-capabilities-for-the-common-core-state-standards-around-mathematics/

28. What has been the most mind-opening for me, however, is learning about different bases, and how they work. Math 1100 student Fall 2013

29. when we were learning different algorithms for multiplication in different bases. I kept carrying the 'left overs" instead of the "long" of the "regrouped" part because I wasn't really understanding why we were doing what we were at first. I was never told in grade school why we carried, just to do it because that's how multiplication works. With the different algorithms and by exploring it on my own, I finally had it click -Student Comments Fall 2013

30. It was confusing and frustrating at first, but one moment it hit me and I totally understood it. I now feel confident in adding, subtracting, and multiplying in any base. I feel like I truly understand it  now instead of just going with it. 

33. I have had several “aha” moments during this class. The whole idea of the definition of “problem solving” and what a problem is, wow. The fact that we can use different algorithms to solve problems in all operations, wow. Some of the algorithms: Egyptian math – Russian Peasant – lattice - wow! Finding patterns where I did not realize they could be found, and even coming to realize why the class is called “Numbers and Operations” - all of these have been “aha” moments for me.

34. Math didn't have to be so difficult if I just tried a little harder to understand it! Student Comment Fall 2013

36. Puppies and Kittens For this game, two players alternate turns. We start with a pile of 7 kittens and 10 puppies. A legal move is one of the following three possibilities: 1. Removing any positive number of puppies (but no kittens), 2. Remove any positive number of kittens (but no puppies) 3. Remove an equal number of both puppies and kittens. The winner is the last player who makes a legal move. Which player has a winning strategy? For what starting values of k kittens and p puppies will player 1 win? Player 2?

37. How to Win at Puppies and Kittens Finding an Oasis Find values of k and p for which you win Puppy and Kitten Grids