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Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States [Hardcover]

Liping Ma
4.9 out of 5 stars  See all reviews (10 customer reviews)
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Book Description

Jan. 25 2010 0415873835 978-0415873833 2

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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"Both sides in the math wars claim Dr. Ma as their own. Districts have distributed her book to teachers. Its broad appeal offers some hope for common ground in math education....we will continue fights over whether children should be taught arithmetic rules or theory. What Dr. Ma shows is that we need both."
—The New York Times

"Ma's book is a significant contribution to mathematics education because it begins to tackle the important and complex question of 'what is mathematical knowledge for elementary teaching'. In doing so, she helps us to understand elementary mathematics as a complex and demanding subject that is to be taken seriously."
—Contemporary Psychology

"Elementary school teachers need as deep an understanding of the mathematics they teach as high school teachers need of what they teach. Both need a deep knowledge of the mathematics which comes in later grades, at least three or four, for this knowledge should influence how topics are taught."
—Mathematicians and Educational Reform

"Must reading for those who call for more mathematics and those who champion reform pedagogy in teacher education."

"...Ma has done a masterful job of showing how the conceptual approach of Chinese elementary school teachers succeeds where the procedural approach of their American counterparts flounders....I highly recommend this brief volume to elementary school teachers who wish to improve their teaching of mathematics. I also recommend it to all university teacher educators who want their students to develop that 'profound understanding of fundamental mathematics' that allows Chinese students to outscore their American counterparts in international assessments."
—Mathematics Teaching in the Middle Schools

"The contributions of this book are multifaceted....This book is an excellent resource and will interest anyone involved in teaching preservice teachers, as well as researchers concerned with teachers' knowledge of content and methods."
—Teaching Children Mathematics

"Even beyond education, the book supports the need for, and indeed the educational benefits of, changing professional teaching conditions for U.S. teachers....it provides some food for thought for everyone involved in improving mathematics education. And it supports the necessity, highlighted in NCTM's Standards documents, that even at the elementary school level, students can, and should, learn challenging mathematics."
—NCTM News Bulletin

"For all who are concerned with mathematics education...Knowing and Teaching Elementary Mathematics is an important book. For those who are skeptical that mathematics education research can say much of value, it can serve as a counterexample. For those interested in improving precollege mathematics education in the U.S., it provides important clues to the nature of the problem. An added bonus is that, despite the somewhat forbidding educationese of its title, the book is quite readable....I recommend this book!"
—Notices of the AMS

"Ma's work has been well received on both sides of the so-called math wars....Supporters of the National Council of Teachers of Mathematics (NCTM) reform agenda are pleased by her stress on real understanding as opposed to mere computational competence."
—American Scientist

"...a book that is becoming a stealth hit for math junkies on both sides of the 'math wars,' and a must read for anyone interested in solving the problems of public schools."
—The Christian Science Monitor Electronic Edition

"The book is earning praise both from some of those who support changes proposed in the NCTM Standards and from some of those who oppose them, and it is sparking discussion. It is also helping to unify some disparate forces in mathematics education on at least a few ideas for continuing positive changes....[the book] provides some food for thought for everyone involved in improving mathematics education."
—NCTM News Bulletin

"Mathematical performance of children in countries in the west like the USA and the UK is a constant source of concern when comparisons are made with achievements in countries in the Far East and Eastern Europe. Liping Ma's book provides valuable insights into possible explanations for this disparity--and these have obvious implications for the training of mathematics teachers in any country."
—British Journal of Educational Technology

"Liping Ma's work has given me hope about what can be done to improve mathematics education."
—Richard Askey, University of Wisconsin-Madison

"This is indeed a valuable, enlightening book. It attests to the talent of its author, and to the Chinese and American learning environments that have nurtured that talent. It attests to the value of welcoming scholars from other nations to study in the United States. I urge all those who are seriously concerned about the quality of mathematics education in the United States to read this book, and to take its lessons seriously."
—Lee Shulman, President, Carnegie Foundation for the Advancement of Teaching, From the Foreword

"For all who are concerned with mathematics education in the U.S., Liping Ma has written an important book. It provides valuable clues to the nature of the problem of improving our K-12 mathematics education. An added bonus is that, despite the somewhat foreboding educationese of its title, it is quite readable. I recommend this book."
—Roger Howe, Yale University

"Must reading for those who call for more mathematics and those who champion reform pedagogy in teacher education."
—Anna O. Graeber, University of Maryland-College Park

"...both a graceful introduction (for mathematicians and other neophytes) to an important area of mathematics education and an interesting theoretical work in its own right. I recommend it highly."
—Judith Roitman, University of Kansas

About the Author

Liping Ma earned a Ph.D. from Stanford University, following a masters degree in education from East China Normal University. After a term as a senior scientist at the Carnegie Foundation for the Advancement of Teaching, she is now an independent scholar.

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Let's spend some time thinking about one particular topic that you may work with when you teach, subtraction with regrouping. Read the first page
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Customer Reviews

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Most helpful customer reviews
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.
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5.0 out of 5 stars An important read for all elementary teachers July 12 2001
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.
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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
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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Most recent customer reviews
5.0 out of 5 stars changes the way you view math
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. Read more
Published on Feb. 19 2004
5.0 out of 5 stars Just as promised. Fast deliverary in mint condition!
Excellent seller. Will definately buy from again!
Published on Sept. 16 2002
4.0 out of 5 stars Clear discussion of why math teaching in Asia is so good.
With exceptional clarity, Ma compares American and Chinese teachers by discussing their responses to four teaching situations. Read more
Published on Oct. 1 1999 by anonymous
5.0 out of 5 stars Highest recommendation to teachers and educators
This is education research at its best. It directly points the way to better classroom preformance, which is ultimately what education research is about. Read more
Published on Aug. 28 1999 by Hung-Hsi Wu (wu@math.berkeley.edu)
5.0 out of 5 stars A book that will change mathematics teaching/learning.
This book provides a starting place for an important and long overdue discussion. Teachers, mathematicians and preservice programs could come together to develop professional... Read more
Published on Aug. 24 1999
5.0 out of 5 stars This is a must read if you are interested in math education.
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 more
Published on June 7 1999 by Richard Askey
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