Review of “Learning to Think Mathematically: Problem Solving, Metacognition, and sense-making in Mathematics,” by Alan Schoenfeld

I really enjoyed reading Mr. Shoenfeld’s article. The focus this past week of our class has been on problem solving vs. “exercising” if you will. Mr. Shoenfeld gave a great example that I believe sums up his article nicely. He said that knowing how to use the tools in a shop does not make a person a craftsman, and simply working exercises at the end of a chapter in a mathematics textbook, for example, does not make one good at math. He went on to say that math should focus in the following three areas:
• Seeking solutions, not just memorizing procedures;
• Exploring patterns, not just memorizing formulas;
• Formulating conjectures, not just doing exercises.
I agree with Mr. Schoenfeld to a degree, but isn’t it in doing these exercises that one gains the skills needed to “think mathematically” and move on “seeking solutions?”

Check out this article and let me know what you think.

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1 Response to Review of “Learning to Think Mathematically: Problem Solving, Metacognition, and sense-making in Mathematics,” by Alan Schoenfeld

  1. I have a lot of respect for Alan Schoenfeld’s work on problem solving, as well. Is gaining skills a prerequisite for problem solving? People fight over what they think is the right answer, a lot.

    My take: “You can’t get there from here.” You can’t get to problem-solving skills by ONLY developing exercise-solving skills. The skills do not transfer easily among different contexts. However, one can exercise more mundane skills within the context of higher-order tasks. A good juicy problem can involve a lot of little exercises as you go along in solving it – while providing a context and a frame for the exercises.

    Another way is to invite students to reflect on what skills they need, as they are doing more complex tasks. For example, if a student realizes remembering times tables would be exceedingly nice for doing long division, she can find some piece of software or other means of drilling – for that PURPOSE. Without the purpose, the drill has a very different flavor.

    I hope it makes sense.

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