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Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States Hardcover – Jan 25 2010

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Product Details

  • Hardcover: 232 pages
  • Publisher: Routledge; 2 edition (Jan. 25 2010)
  • Language: English
  • ISBN-10: 0415873835
  • ISBN-13: 978-0415873833
  • Product Dimensions: 15.5 x 1.8 x 22.9 cm
  • Shipping Weight: 476 g
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Product Description


"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. 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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Most Helpful Customer Reviews on (beta) 4.7 out of 5 stars 11 reviews
5.0 out of 5 stars Excellent resource! Oct. 1 2016
By elanorh - Published on
Format: Paperback
I recommend this book often. My cousin, who is a math professor, recommended it to me. The author wrote it as her doctoral dissertation, so despite being a brief book, it can be a little dense at first (especially if math is not your strong suit - it is not mine!).

It is a wonderful book, though, to help parents (and teachers) move from procedural approaches to math, into conceptual approaches. I think the way we teach math in schools today is emphasizing conceptual approaches, but many of the parents (and teachers) don't know why or how that is happening. For those of us who learned "recipes" to solve math problems, this can be confusing (also, for our kids while we're trying to help them).

Reading this book, and discussing it aloud with my husband as I went through the book, was a real eye-opener to me about how I'd learned math - the things I'd understood intuitively, and the things which I'd learned by rote (and how that affected my later lack of mathematical skill/confidence).

I have used this book with both of our kids, as they encountered math stumbling blocks, to help them understand concepts well. Using the case studies in each chapter as my "guides," I have been able to help my kids understand the concept; and it is almost miraculous, how much more quickly and smoothly the math problems go for them after that point.

I really can't recommend this book enough.
3 of 4 people found the following review helpful
5.0 out of 5 stars for teachers of mathematics Oct. 21 2013
By A Reader - Published on
Format: Paperback Verified Purchase
We used this book in a state-sponsored course designed to improve the way mathematics is taught in the public schools.

Mathematics teaching in the US has traditionally focused on teaching and memorizing procedures rather than understanding the underlying concepts and relationships - this book encourages teachers to question that.

It may be a bit dry, but it is an excellent resource for those looking to improve their understanding of the important ideas in mathematics in order to improve the way they teach.
5.0 out of 5 stars The meaning of rigorous Sept. 26 2016
By El Asmar - Published on
Format: Paperback
A fantastic study. It's ironic that the US maths teachers here compare so unfavourably with the Chinese teachers, yet the essential academic reference is to Jerome Bruner's monumental thinking. Also wondered how the author used the city map analogy on p123 without crediting Richard Skemp who first proposed this in his 1976 paper on Relational Understanding and Instrumental Understanding: [...]
5.0 out of 5 stars The single best book on understanding the math you teach May 18 2015
By valerie hartmann - Published on
Format: Paperback
The single best book on understanding the math you teach. Over my fifteen years of teaching I often revisit the book to sharpen my presentations to my struggling sixth graders
5.0 out of 5 stars Conceptual Learning at its Best Jan. 22 2016
By NC teacher - Published on
Format: Paperback Verified Purchase
Love this book. I have learned so much about conceptual knowledge as opposed to procedural that lacks complete understanding.