Download Knowing and Teaching Elementary Mathematics: Teachers' by Liping Ma PDF

By Liping Ma

Reviews of lecturers within the U.S. frequently rfile inadequate subject material wisdom in arithmetic. but, those reviews supply few examples of the data academics have to help educating, fairly the type of educating demanded by means of contemporary reforms in arithmetic schooling. Knowing and instructing uncomplicated Mathematics describes the character and improvement of the data that basic academics have to develop into entire arithmetic lecturers, and indicates why such wisdom turns out extra universal in China than within the usa, although chinese language academics have much less formal schooling than their U.S. opposite numbers.

The anniversary variation of this bestselling quantity comprises the unique reviews that examine U.S and chinese language user-friendly tuition teachers’ mathematical realizing and gives a strong framework for greedy the mathematical content material essential to comprehend and improve the taking into account university youngsters. Highlighting extraordinary alterations within the box and the author’s paintings, this new version comprises an up to date preface, creation, and key magazine articles that body and contextualize this seminal paintings.

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Additional resources for Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Anniversary Edition)

Sample text

Three kinds of mathematical knowledge are included in a fully developed and well-organized knowledge package of conceptual understanding: procedural topics, conceptual topics, and basic principles of the subject. Procedural topics are included to support the procedural learning, as well as the conceptual learning of the topic. For example, proficiency in composing and decomposing a 10 is such a procedural topic. Many Chinese teachers referred to it as a significant support for learning the addition and subtraction within 20, procedurally as well as conceptually.

There is still another way to regroup. We may want to regroup the subtrahend 26 as: € We first subtract one 3 from 53 and get 50. Then we subtract the other 3 from 50 and get 47. Finally we subtract 20 from 47 and get 27. (Tr. C) The teachers referred to three main ways of regrouping. One was the standard way: decompose a unit at a higher value place into units at a lower value place, combine them with the original units at the lower place, and then subtract. Another way was to regroup the minuend into three parts, rather than two parts, before subtracting.

The difference between the phrases “other number” and “the other part of the number” is subtle, but the mathematical meanings conveyed are significantly different. 4â•… Knowing and Teaching Elementary Mathematics Instructional Techniques: Manipulatives Teachers’ knowledge of this topic was correlated not only with their expectations about student learning, but also with their teaching approaches. When discussing how they would teach the topic, all except one of the teachers referred to manipulatives.

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