Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning Series) Review

Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning Series)
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Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning Series) ReviewI am working on certification in secondary mathematics. This one book has given me more insight into what is wrong with mathematics education in the USA and what needs to be done than anything else I have read or discussed in class.
The author's key point is that even the best elementary school math teachers in this country have only a shallow, cookbook knowledge of arithmetic and are not trained to think mathematicaly.
One consequence is that the emphasis in mathematics teacher training on new instructional practices: use of manipulatives, "authentic assessment" collaborative learning, etc. is at best misplaced.
There is much interesting information on Chinese educational practices. Math at all levels is taught by specialists who have only the equivalent of a Chinese high school education. Classes are very large but teachers have about an hour of time for preparation, grading homework, and student conferences for every hour of instruction. Chinese math teachers spend many, many hours working with the curriculum as learners both individually and in groups.
The book is a rich source of ideas that might be adapted to the American environment to improve math instruction.Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning Series) Overview

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