Day 03: Heart of Mathematics

Our mission today: consider solutions of #1, 3, 4, 5, 7, 8.
Okay, be honest: how many of you have peeked at the solutions?
Any dramatic changes in perception following our discussion from last time? Favorites? Least Favorites?
What questions remain?
Any "lessons for life" which were helpful?:
1. Just do it.
2. Make mistakes and fail, but never give up.
3. Keep an open mind.
4. Explore the consequences of new ideas.
5. Seek the essential.
6. Understand the issue.
7. Understand simple things deeply.
8. Break a difficult problem into easier ones.
9. Examine issues from several points of view.
10. Look for patterns and similarities.
Observations, solutions, and strategies:
- We drew a tentative conclusion from the data last time, that I told you I want to test:
  Students tend to like problems they can solve and dislike problems they can't solve.
  Observation: correlation coefficients measure this, and in your case, the correlation between liking problems and solving them is .62 (positive), whereas the correlation between disliking problems and solving them is -.62 (negative).
- Solutions and strategies:
  - Dodge can always be won by player two, using a process of reversing the diagonal element chosen by player one. It's a fixed game.
    - Consider modifications to the original game? (Some modification of an existing problem might make a good project....)
      - Constrain choices (e.g. must use 3x and 3o)
      - Whoever starts loses...
    - Consider extreme cases? (What's special about 6?)
  - Let's make a deal" problem
  - Trou - demonstration using model
  - Genie
  - Fountain
  - the "Dot" problem
  - Problems #2 and 6?

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