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Teaching as Problem Solving


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Apply Polya's heuristics for problem solving to the "problem" of teaching.

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Teaching as Problem Solving

  1. 1. + Problem Solving Dr. Mary Pat Sjostrom Bear with me… this is relevant to this module.
  2. 2. + Why teach problem solving?  “Learning to solve problems is the principal reason for studying mathematics.” (NCSM, 1977)  “Problem solving is not only a goal of learning mathematics but also a major means for doing so.” (NCTM, 2000)
  3. 3. + Problem or Exercise?  A problemis a task for which one has no ready strategy for solving; there are no memorized or prescribed methods.  Most of the “problems” posed in U.S. mathematics classrooms are really exercises. The purpose of an exercise (like the purpose of exercises done in a physical workout) is to develop skill with a particular method or algorithm.  Exercise (like working out) is important, but it should not be the primary goal of the curriculum. Some research has found that as much as 90-95% of time spent in mathematics classroom is devoted to exercises – learning specific algorithms and practicing them through exercise.
  4. 4. + Devise a Plan Look Back Problem Solving Heuristics Understand the Problem Carry out the Plan Polya, 1945 Remember these?
  5. 5. Can we view teaching as + problem solving?
  6. 6. + Devise a Plan Look Back Teaching as problem solving Understand the Problem Carry out the Plan We can approach and solve teaching as we approach and solve a mathematics problem: heuristically, rather than algorithmically. How do Polya’s heuristics apply to teaching?
  7. 7. + Understand the Problem  What are your goals for students?  What concept do you want students to understand?  What is the Big Idea of the mathematics?  What are the real world connections?  What do you expect students to already know about this concept?  What misconceptions might students have?  Where would you like student thinking to be at the end of this lesson?
  8. 8. + Devise a plan  How do you usually teach this lesson?  What problem (or what coherent sequence of problems) can you pose that will engage students in developing this mathematical concept?  What resources are available to you? For the students?  How do you expect students to respond to __________?  How will you know students understand?
  9. 9. + Carry out the plan  Teach the lesson.  Listen to student thinking.  Students should do the mathematics. (You don’t need the practice, they do!)  Monitor and reflect on your teaching.  You may have to modify the plan as the lesson progresses.
  10. 10. + Look Back  How do you think the lesson went?  What worked? What didn’t work?  Did students learn what you wanted them to learn? How do you know?  What would you do differently if you could teach the lesson again?  Based on what happened today, what will you do when the class meets again?
  11. 11. + References Hiebert, J., et al. (1997). Making Sense: Teaching and Learning Mathematics with Understanding. Portsmouth, NH: Heinemann. National Council of Supervisors of Mathematics. (1997). Position paper on basic mathematical skills. Retrieved Feb. 9, 2011, from National Council of Teachers of Mathematics. (2000). Principles and standards of school mathematics. Reston, VA: NCTM. Polya, G. (1945). How to solve it. Princeton, NJ: Princeton University Press. Posamentier, A. S., Smith, B., &Stepelman, J. (2010). Teaching secondary mathematics: Techniques and enrichment units (8th Edition). Upper Saddle River, NJ: Merrill Prentice Hall. Van De Walle, J. A, Karp, K, & Bay-Williams, J. M.. (2010). Elementary and middle school mathematics (7th edition). Boston: Pearson Education.