Why, then, do students who "successfully" engaged in repeated practice of the division of fractions not retain their skill in this activity? Why do so many college graduates not recall how to divide 11/31 by -53/97?
Stigler et. al. have studied these classrooms, and the pedagogical practices in use there, for decades (and speak the local languages fluently.) I strongly urge you to read their work. Japanese teachers are extremely subtle in the influence they exert.
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Understanding their practices and the effects thereof is not easy; indeed, it can be quite a challenge just to see what is going on. Considerable attention to subtle detail is required, and fluency in the language is a must. Few mathematically knowledgeable Americans have his.
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it's also expected that kids have their basics mastered to automaticity. The cram schools are a huge aspect of this which, as we are all aware, insists on regular practice.
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Cram schools are a very small part of the picture at the elementary level.
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