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.