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5.0 out of 5 stars Page 31 made me CRY!!!!!!!!!!!, June 21 2002
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. One actually said you could use apples, oranges, or even ELEPHANTS to help you remember to move the columns over. Fruit? Animals? What about TENS? This experienced math teacher did not know that 237 shifted over a column stands for 237 tens. Chinese math teachers would not think of dressing up the process with fruit and animals. They simply teach the mathematical principles behind the procedure.
Parents and teachers alike need to gobble this book right up, right now, despite its high price. We must work towards more conceptual understanding of math by elementary school teachers or we shall never climb out of the morass. Buy a copy and share it around---it is a crucial work.
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5.0 out of 5 stars An important read for all elementary teachers, July 12 2001
By 
Daryl Anderson (Trumansburg, NY USA) - See all my reviews
(REAL NAME)   
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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5.0 out of 5 stars insight into math education, June 22 2000
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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5.0 out of 5 stars Wow!, Jan. 3 2004
By 
J. M. Dunn (Nagoya, Japan) - See all my reviews
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Never did I think that I would be interested... heck... excited... about a math book... but this is a great book, and good reading for anyone interested in education... It has given me a great deal to think about as a EFL teacher, a field where most "schooling" consists of teaching procedurally...
This excerpt from an editorial review of an entirely different book (The Teaching Gap) but summarizes Liping Ma's research nicely... "American teachers... tend to emphasize terms and procedures, thinking of math as a set of tedious skills... In contrast, [Chinese] teachers are more likely to emphasize ideas, expecting the concepts alone to stir students' natural curiosity."
It doesn't matter what field you are teaching, teaching a "procedural understanding" is like giving the students a fish; it will feed them for a day... a "conceptual understanding" will feed them for a lifetime...
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4.0 out of 5 stars Clear discussion of why math teaching in Asia is so good., Oct. 1 1999
By 
anonymous (Lawrence, KS United States) - See all my reviews
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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5.0 out of 5 stars Highest recommendation to teachers and educators, Aug. 28 1999
This is education research at its best. It directly points the way to better classroom preformance, which is ultimately what education research is about. It gives a very persuasive argument that good mathematics teaching must start with a total command of the relevant mathematics. Its implications on the professional development of mathematics teachers should be taken to heart by educators, state agencies, and administrators.
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5.0 out of 5 stars A book that will change mathematics teaching/learning., Aug. 24 1999
By A Customer
This book provides a starting place for an important and long overdue discussion. Teachers, mathematicians and preservice programs could come together to develop professional development programs around this one book. Understanding our own misunderstandings in mathematics will help to change instructional practice. Every school should have at least one copy.
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5.0 out of 5 stars changes the way you view math, Feb. 19 2004
By A Customer
Excellent book for anyone interested in math. This should be mandatory reading for all future and current teachers! I see math in a new light. This book will inspire you to re-evaluate your own knowledge of elementary math, and to work from a procedural understanding of math to conceptual.
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5.0 out of 5 stars This is a must read if you are interested in math education., June 7 1999
By 
Richard Askey (Madison, Wisconsin) - See all my reviews
Liping Ma has shown us what it means to know elementary school mathematics deeply, and has suggestions about what can be done to help our teachers acquire this knowledge. Read and share this book with anyone who cares about the education of elementary school children.
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5.0 out of 5 stars Just as promised. Fast deliverary in mint condition!, Sept. 16 2002
By A Customer
Excellent seller. Will definately buy from again!
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Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States
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