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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) [Paperback]

by Liping Ma
4.7 out of 5 stars  See all reviews (31 customer reviews)

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Book Description

May 3, 1999 0805829091 978-0805829099 1
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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Editorial Reviews


"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." -CHOICE "...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. 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 --This text refers to the Digital edition.

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. --This text refers to the Digital edition.

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 (31 customer reviews)
  • Amazon Best Sellers Rank: #106,687 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
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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57 of 59 people found the following review helpful
5.0 out of 5 stars An important read for all elementary teachers 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.
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38 of 39 people found the following review helpful
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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72 of 79 people found the following review helpful
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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Most Recent Customer Reviews
5.0 out of 5 stars 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 5 months ago by teddyjo26
5.0 out of 5 stars 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 9 months ago by Lynne Kenney
5.0 out of 5 stars 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
5.0 out of 5 stars 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
5.0 out of 5 stars 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
5.0 out of 5 stars 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
5.0 out of 5 stars 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
2.0 out of 5 stars China vs US
This book compares Chinese math teachers to US math teachers. Many of the US teachers seem incompetent. Read more
Published on March 3, 2010 by Waltzing Matilda
5.0 out of 5 stars Knowing and teaching math
The condition of the book was very good and the shipment was in the appropriate time. Thank you.
Published on October 11, 2009 by Eva B. OBrien
5.0 out of 5 stars Excellent
As a resource teacher having taught middle school, it is shocking to find so many middle school students who cannot add or subtract fractions, or correctly solve other forms of... Read more
Published on August 17, 2009 by Francine B. Mcdermott
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