Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Anniversary Edition)
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Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts.
The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.
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Daniel Chazan Associate Professor, Mathematics Education, College of Education, Michigan State University (Currently Associate Professor, Department of Curriculum and Instruction, College of Education, University of Maryland) Glenda Lappan Former President of National Council of Teachers of Mathematics, Professor, Department of Mathematics, Michigan State University Helen Featherstone Associate Professor, Teacher Education Department, College of Education, Michigan State University Jinfa
subtraction problems with maybe a picture of 23 things and tell them to cross out 17 and then count how many are left… I might have them do some things with dinosaur eggs or something that would sort of have a little more meaning to them. Maybe have them do some concrete subtraction with dinosaur eggs, maybe using beans as the dinosaur eggs or something. Problems like 52−25 or 23−17 are problems of subtraction with regrouping. However, what students would learn from activities involving
10, etc. Interestingly, as in the case of subtraction with regrouping, the Chinese teachers thought that the interview topic was not the key piece of the package. The multiplication of twodigit numbers, where the rationale for the topic is introduced for the first time, was considered as the key piece that deserves most effort from teachers, as well as from students. For the topic of subtraction with regrouping, the key piece was subtraction within 20. Chinese teachers tend to pay significant
similar in some ways to the National Council of Teachers of Mathematics’ Standards for School Mathematics (NCTM, 1989) or state documents like Mathematics Framework for California Public Schools (California Department of Education, 1985, 1992). In China, the textbooks are intended to interpret and embody the Teaching and Learning Framework. The National Department of Education once published only 112â•… Knowing and Teaching Elementary Mathematics one set of textbooks for all its public schools.
of Fundamental Mathematics 121 Most members of the mathematical community—it is a remarkably worldwide community, possessing a universality uncommon in other areas of human enterprise— would prefer to do mathematics, not concern themselves excessively with the question of what it is that they are doing. (p. 51) While mathematicians may “not concern themselves with the question of what it is that they are doing,” teachers who teach mathematics cannot ignore the question of what it is that they