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Reflective mathematical homework#

See also: teaching-mathematics

Boaler (2015) citers working with two teachers to develop "a set of home reflection questions that they choose from each day to help their students process and understand the mathematics that they have met that day" (p. 46)

As an alternative to the common long list of exercises indicative of a practice-approach-to-mathematics, with this reflective approach resonating more strongly with a conceptual-approach-to-mathematics. An approach more likely to develop a mathematical-mindset

Questions#

  1. What were the main mathematical concepts or ideas that you learned today or that we discussed in class today?
  2. What questions do you still have about ______________? If you don't have a question, write a similar problem and solve it instead.
  3. Describe a mistake or misconceptuion that you or a classmate had in class today. What did you learn from this mistake or misconception?
  4. How did you or your group approach today's problem or problem set? Was your approach successful? What did you learn from your approach?
  5. Describe in detail how someone else in class approached the problem. How is their approach similar or different to the way you approached the problem?
  6. What new vocabulary words or terms were introduced today? What do you believe each new word means? Given an example/picture of each word.
  7. What was the big mathematical debate about in class today? What did you learn from the debate?
  8. How is ______ similar or different to _________?
  9. What would happen if you changed _______________?
  10. What were some of your strengths and weaknesses in this unit? What is your plan to improve in your areas of weakness?

References#

Boaler, J. (2015). Creating Mathematical Mindsets: The Importance of Flexibility with Numbers. In Mathematical Mindsets: Unleashing Students' Potential Through Creative Math, Inspiring Messages and Innovative Teaching (pp. 33--56). John Wiley & Sons, Incorporated.