Award Winning Problems

CW
by christine Willard9 views·Updated Feb 8, 2022
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  1. What separates one math problem from another math problem.
  2. It really has to do with a couple of things.
  3. Sometimes math problems have too much of what we call a cognitive load
  4. which means that inherently built into that are a lot of distractive,
  5. distracting types of information so that the student is left
  6. kind of frustrated with how to solve the problem.
  7. Teachers need to explicitly
  8. explain
  9. the vocabulary,
  10. the the discourse, the syntax, the function,
  11. the language that is used.
  12. All the language demands that are used in a word problem
  13. should be explicitly explained to students prior to starting the problem.
  14. This gives students a great advantage in the
  15. math class and here's an example of what I
  16. think is is a good um math problem put forth by the author of our text.
  17. I also added to it.
  18. Um
  19. Giselle says that 23 times 45 yields a greater amount than 1000.
  20. Do you agree or disagree
  21. with her conjecture,
  22. explain your thinking, demonstrate your proof,
  23. Why do I like this math problem?
  24. Well there are multiple entry points. A student could
  25. visually represent this problem in a number of different ways.
  26. The student could also derive multiple solutions to
  27. get to um the answer as well and explanations
  28. this word problem
  29. incorporates academic language
  30. and it does have academic demands but academic language demands.
  31. But if the teacher is careful to be very explicit with explaining
  32. the language in this word problem,
  33. the student will be all the better off and we'll be able to
  34. use math language when they're speaking and
  35. when they're explaining their own thinking,
  36. this language is more sophisticated.
  37. This language is more sasic inked and more math discipline based.
  38. So you have the discourse which would be having the student, you know?
  39. Do you agree or disagree?
  40. That is something that teachers might often say to students in a debate.
  41. In a discussion, You have the vocabulary, you have conjecture.
  42. You have
  43. proof. Those are two words that students may not know.
  44. They may know the word proof, but maybe not in this context. You know, syntax
  45. Which is symbolic words or phrases or images that
  46. students may not have encountered before the multiplication side.
  47. You have the symbolic representation of 1000
  48. and then you have
  49. function words
  50. explain,
  51. demonstrate,
  52. agree, disagree.
  53. So these are things that the teachers asking the student to do
  54. all of these when they're broken down,
  55. relieve the cognitive load for the student, but also enhances their
  56. academic
  57. language and their discourse in the math classroom. So it's a great problem