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Who'll Fill the Gap: continued
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I'm pretty sure that TIMSS was not the primary driving force behind the move to standards-based teaching in California. In spite of that, the new California mathematics standards do require algebra much earlier in the school curriculum. However, beyond mathematical concepts, the idea of students doing critical thinking during lessons was also investigated.
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In mathematics, deductive reasoning is often found in proofs. As it turns out, there were no mathematical proofs in U.S. lessons. In contrast, there were proofs in 52 percent of Japanese lessons and 10 percent of German lessons. Whatever students in the United States were doing with the definitions [they had learned], they clearly were not using them to develop proofs of mathematical relationships... We found that one-fifth of the topics in U.S. lessons contained developed concepts, while four-fifths contained only stated concepts… this distribution was nearly reversed in Germany [77% developed:23% stated] and Japan [83%:17%]. (p. 59-60)
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Not a flattering place to be as an American math [or science?] teacher is it? Why do you think that American lessons generally seem to move in the same low-level morass?
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We have learned that students in Germany and the United States learn mathematics by following the teacher's lead... on average, there is a balance in Japan. Mathematical work is shared by the teacher and the students. (p. 71)
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"Mathematical work is shared by the teacher and the students." What a concept. How much work do you do for your students? How much do they do? How equal is the sharing, or do you do way more than your share? Stigler and Hiebert don't point fingers, but they do point out that American math [science?] teachers tend to do more than their share of the work during lessons.
| When we watched a Japanese lesson, we noticed that the teacher presentss a problem to the students without first demonstrating how to solve the problem. We realized that U.S. teachers almost never do this, and we saw a feature...that is perhpas one of the most important features of U.S. lessons - that the teacher almost always demonstrates a procedure for solving problems before assigning them to students. (p.77) |
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Science Education Reform Index
