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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) 1st Edition

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Liping Ma (Author)
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Liping Ma (Author)
4.7 out of 5 stars 34 customer reviews
ISBN-13: 978-0805829099
ISBN-10: 0805829091
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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: 8.5 x 6.9 x 0.5 inches
  • Shipping Weight: 11.4 ounces
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (34 customer reviews)
  • Amazon Best Sellers Rank: #393,094 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

69 of 71 people found the following review helpful
insight into math education
By Charles R. Williams on June 22, 2000
Format: Paperback
I 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.
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58 of 60 people found the following review helpful
An important read for all elementary teachers
By Daryl Anderson VINE VOICE on July 12, 2001
Format: Paperback Verified 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.Read more ›
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39 of 40 people found the following review helpful
Clear discussion of why math teaching in Asia is so good.
By Judy on October 1, 1999
Format: Paperback
With exceptional clarity, Ma compares American and Chinese teachers by discussing their responses to four teaching situations. The Chinese teachers, despite less formal education, have a much deeper understanding of the elementary mathematics they are teaching. Ma explores the components of what she calls "profound understanding of fundamental mathematics," and also the professional conditions that encourage it. Highly recommended for anyone involved in the preparation or professional development of teachers. Also highly recommended for educational policy makers.
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73 of 80 people found the following review helpful
Page 31 made me CRY!!!!!!!!!!!
By The Accidental Reader on June 21, 2002
Format: Paperback
Interviews teachers and displays the difference between procedural understanding of math and conceptual understanding of math. Delves into how and why US and Chinese teaching of math are so different.
An American teacher with only a procedural understanding said this about teaching regrouping with manipulatives:
"I would have them start some subtraction problems with maybe a picture of 23 things and tell them to cross out 17 things 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."
What? Dinosaurs are the key to effective teaching of math? This approach does not explain why we regroup! It does not even touch on place value. You have got to read this book to believe what goes on in way too many American classrooms!

An American teacher with a conceptual understanding of math had a much better way to use manipulatives in teaching regrouping. She used single sticks and bundles of ten sticks to show the mathematical principle of equality. She said she would stress that when you have 53 sticks, the total is still 53 sticks whether arranged in 5 bundles of ten, plus three sticks; or 4 bundles of ten, plus 13 sticks. THIS is a manipulative approach that actually works to teach the concept of regrouping because it draws on the fundamentals of math. One has to demonstrate to the children the idea that you can change the FORM of the number without changing the number itself.
Watch out for page 31! You may CRY when you see that many American elementary teachers don't recognize the implied zeroes in multi-digit multiplication.Read more ›
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Most Recent Customer Reviews

but because the exposition on the nature of mathematics needed to...

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... Read more

Published 3 months ago by Robert Root
Liping Ma This book is a product of a thesis ...

Liping Ma

This book is a product of a thesis on comparison of the thinking patterns of teachers in USA and China who work with maths. Read more

Published 12 months ago by monica
Whatever your math curriculum suggests, this book guides teachers to...

I have owned this book for quite a while now, but still look at it. Whenever I loan it to colleagues, I always make sure I get it back. Read more

Published 12 months ago by Jubilee
Must read, especially for mathematicians

This book changed my life. I read it summer of my sophomore year of college and was absolutely riveted. Read more

Published on October 30, 2013 by teddyjo26
If you teach elementary math this book is a must

Liping Ma has written a bright and easy to read book on how teachers think mathematically. She compares Asian and American teaching styles, non-judgmentally with many... Read more

Published on July 27, 2013 by Lynne Kenney
Revealing!

If you've ever wondered what's wrong with US math students, here's your answer. I won't spoil it by telling you the answer, but if you're an elementary teacher who teaches math, I... Read more

Published on September 29, 2011 by Jane M. Batchelder
Awesome

This book is fantastic - I need to reread it and spend more time thinking about the examples. If you are interested in math education, this is essential reading. Read more

Published on June 29, 2011 by Lukas Halim
Absolutely a Must-Read for all Math Teachers and esp Homeschoolers

I purchased this book on a recommendation from a homeschooling forum - and I am absolutely thrilled that I did! It is a fascinating comparison between U.S. Read more

Published on April 10, 2011 by Christie P
Cult Classic for Homeschoolers, Too.

I read this book to improve my teaching skills, and to prepare myself to teach Singapore math at home. Read more

Published on January 1, 2011 by kalanamak
Great Look at elementary Math

Just more evidence that our preservice elementary school teacher need more exposure to elementary math. Read more

Published on June 10, 2010 by Mr. Nice

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