Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning Series) 1st Edition

by Liping Ma (Author)

33 customer reviews

ISBN-13: 978-0805829099

ISBN-10: 0805829091

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Knowing and Teaching Elementary Mathematics Teachers' Understanding of Fundamental Mathematics in China and the United States
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Chinese students typically outperform U.S. students on international comparisons of mathematics competency. Paradoxically, Chinese teachers receive far less education than U.S. teachers--11 to 12 years of schooling versus 16 to 18 years of schooling.

Studies of U.S. teacher knowledge often document insufficient subject matter knowledge in mathematics. But, they give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education.

This book describes the nature and development of the "profound understanding of fundamental mathematics" that elementary teachers need to become accomplished mathematics teachers, and suggests why such teaching knowledge is much more common in China than the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts.

The studies described in this book suggest that Chinese teachers begin their teaching careers with a better understanding of elementary mathematics than that of most U.S. elementary teachers. Their understanding of the mathematics they teach and--equally important--of the ways that elementary mathematics can be presented to students, continues to grow throughout their professional lives.

Teaching conditions in the United States, unlike those in China, militate against the development of elementary teachers' mathematical knowledge and its organization for teaching. The concluding chapter of the book suggests changes in teacher preparation, teacher support, and mathematics education research that might allow teachers in the United States to attain profound understanding of fundamental mathematics.

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Product details

Series: Studies in Mathematical Thinking and Learning Series
Paperback: 192 pages
Publisher: Routledge; 1 edition (May 3, 1999)
Language: English
ISBN-10: 0805829091
ISBN-13: 978-0805829099
Product Dimensions: 6 x 0.5 x 9 inches
Shipping Weight: 11.4 ounces
Average Customer Review: 33 customer reviews
Amazon Best Sellers Rank: #258,981 in Books (See Top 100 in Books)
- #264 in Books > Science & Math > Mathematics > Study & Teaching
- #536 in Books > Education & Teaching > Schools & Teaching > Instruction Methods > Mathematics
- #629 in Books > Textbooks > Education > Elementary Education

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J. Li

Important for all math teachers to read

March 12, 2008

Format: PaperbackVerified Purchase

While this text focuses on topics covered in elementary school arithmetic, I think this is an important text for all math teachers to read. Having an understanding of how our students are taught at the elementary level will illuminate why our students' minds are so inflexible and so shallow when it comes to mathematics. I also think it is good to read to get a flavor for the rigor used to approach mathemtics at the elementary level in China. We can use this as secondary teachers to design review or remedial material, or to provide alternative ways to approach arithmetic while solving other types of problems.

This book is a bit dry to get through, but the material itself is excellent. The reviewer who gave the book one star - I don't think you understand how research is planned. You cannot take all variables into account. It just isn't possible. For the scope of the work, Ma's work is right on. I suppose Ma could have surveyed the teachers about their attitudes towards math, expectations on useage of math in the real world, etc. But that's not her field! Other people are doing research on that already!

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Pearl E Gates

Makes so much sense

September 9, 2008

Format: PaperbackVerified Purchase

I am not a formal educator. I'm not a math lover In fact growing up I refered to my self as mathmatically retarded (please excuse my congnitive reference). I have begun homeschooling my 3 children and am piecing together, what I feel is an appropriate curriculum. I'm trying to avoid the drill and kill approach in all subjects. I was really struggling with finding or creating a math curriculum. I was concerned with my ability to teach a subject that I only understand at a very basic level. I came upon this book and thought perhaps it would help me make sense of things and guide me in choosing a math curriculum for the kids. I have to say that I really struggled in the beginning of the book where the U.S. teachers explain subtraction with borrowing. I was lost. I still remember the process from my days in school, but their explanations were absolutely alien to me. I then got to the chinese way of teaching subtraction with regrouping and all the lights came on. It made so much more sense to me. I may not be an idot after all. I'm gaining understanding and finding direction. This book is not a curriculum in itself, but has greatly helped me in the process of choosing an appropriate way of learning math for the kids. It's truly helping me make sense of math for myself. I recommend this book to anyone teaching math and for parents who want to help their kids and themselves understand math in a natural and logical way.

Comment 11 people found this helpful. Was this review helpful to you?

Yes

An important read for all elementary teachers

July 12, 2001

Format: PaperbackVerified Purchase

Elementary school teachers are expected to teach almost everything: math, reading, science, social studies, and writing; along with nurturing, soothing, and encouraging. It's not an easy job. It's also hard to be an expert in any one piece of the job. But now, many are hearing that we're losing the "math race" to other countries. The drums of "teacher competency" are booming... and any wise teacher knows where the drum sticks will be landing next!
Liping Ma's book comes at an opportune time for those teachers and should be read by all. It dives into a central problem that elementary teachers face when we consider improving our math programs: How could going off and learning more math help, for instance, in a 4th grade fractions unit? Furthermore, having, typically, been taught mathematics, ourselves, as a process of memorizing and applying procedures, we often teach it that way as well, thinking "how much more can I study the `flip and multiply' rule for fraction division?"
This book answers those and many other questions, while opening many new ones. There's more to math, even "kids math" than meets the eye.
Ma demonstrates that American teachers do not necessarily suffer from a lack of breadth or extensiveness of mathematical training. Adding more `higher math' to our training really would not help us teach arithmetic. We lack deep knowledge of "fundamental mathematics." Ma's claim is that what we need to do is to dig deeper into the underpinnings of "elementary" math - to discover that there is much more to understand about such fundamental concepts. There really is much more to subtraction than remembering when to "regroup." Division of fractions actually represents two or three fundamentally different processes which, confused, can be at the center of students (and teachers) uncertainty. Imagine that!
These are thought provoking ideas, well presented. In the face of a growing national debate about "competency", we would do well to add this element to the discussion of math teaching. Otherwise, the politicians will provide their inevitably simplistic answers.

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Rob Root

but because the exposition on the nature of mathematics needed to teach elementary students is brilliant.

August 17, 2015

Format: PaperbackVerified Purchase

This book has the form of a comparison of math teacher content knowledge between US and China, but it is actually a discourse on the kind of mathematical knowledge and attitudes that lead to successful teaching of elementary school students. Anyone interested in teaching elementary mathematics should give this book a careful look, not because American teachers fare so poorly in comparison with their Chinese counterparts, but because the exposition on the nature of mathematics needed to teach elementary students is brilliant.

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kalanamak

Cult Classic for Homeschoolers, Too.

January 1, 2011

Format: PaperbackVerified Purchase

I read this book to improve my teaching skills, and to prepare myself to teach Singapore math at home. If one has a burning passion to teach better, this short book will be extra oxygen for your fire. I encourage all homeschoolers teaching elementary and middle school math to read this book. The cultural comparisons are not important to those of us not involved with policy, but just reading it to see in the minds of various teachers is plenty worthwhile. Consider the question at the beginning of the first four chapters, and think of what YOU'D do to teach this topic--then compare with what Ma found. A wonderful book to "stretch the mind on the rack of thought", and your children will benefit, too.

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