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Knowing and Teaching Elementary Mathematics: Teachers' Understandng Fundamental Mathematics in China and the United States
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Knowing and Teaching Elementary Mathematics: Teachers' Understandng Fundamental Mathematics in China and the United States

4.23  ·  Rating Details ·  197 Ratings  ·  31 Reviews
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 ex
Paperback, 192 pages
Published May 1st 1999 by Routledge
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May 24, 2011 Jacob rated it really liked it
This book is someone's dissertation, and although it's been "dressed up" it still reads like one. However, if you're able to read that kind of dryer content, and especially if you have young children, this book can be valuable on a couple of levels. First of all, it's a good argument for certain changes in our education system. Through interviews with American and Chinese math teachers on four specific math topics, the author demonstrates that a large reason for the disparity in student scores s ...more
Mar 16, 2011 Emily rated it it was amazing
I realized reading this book that my understanding of arithmetic is very incomplete. I was taught arithmetic in a very procedurally focused way, without a lot of insight into the "why" behind arithmetic operations. The descriptions of the depth of understanding of the Chinese teachers into various ways of presenting and teaching basic concepts of arithmetic was astounding to me. I was never taught this way and although I went on to get a bachelor's and master's degree in statistics, never realiz ...more
May 14, 2013 Ilib4kids rated it really liked it  ·  review of another edition
372.70973 MA(166p)
dividend ÷ divisor = quotient
Multiplier(factor, number of group ) * multiplicand(factor: number in a group) = Product,
google search : devlin on multiplication(Keith Devlin): multiplication is not repeated addition., no mention in this book.
Worth reading for parents try to help their children and teachers try to teach elementary arithmetic(addition, subtraction, multiplication, division). A great insight of elementary math teaching, procedural perspective teaching vs. Conceptu
Jan 20, 2016 Aurora rated it it was amazing
This book is a comparison of how teachers from the US and China understand various basic concepts in elementary mathematics. What is shocking is that the US teacher do not understand how to effectively teach these concepts, even though they have had more training than the average elementary school teacher in China. One reason for this discrepancy is the focus on the US on procedural knowledge. We want to rely so much on simple formulas and algorithms, handed to us to memorize and then "plug and ...more
Jun 23, 2007 Ben rated it it was amazing
Recommends it for: math teachers
This is a really interesting investigation into the differences between Chinese and American math teaching and teacher preparation. For me, this book opened up and excited me about the nuances of teaching arithmetic. There are a huge amount of analogies, comparisons, and various mental models in play when we teach even simple math, and they are strongly affected by language. The teacher's deep level of understanding of the math is critical to sorting through the possible misconceptions and guidi ...more
Apr 16, 2012 Laura rated it it was amazing
Shelves: 2014
For anyone who doesn't understand why our children are learning "new math", this is a must-read. I spent a Saturday morning intently reading this dissertation on elementary mathematics education. I was interested in this book as a homeschool parent who uses Singapore Math curriculum for my first grader.

Liping Ma's research shows the difference in how we teach math for a conceptual verses a procedural understanding. I had several aha! moments where I realized that my memory of certain mathematica
Feb 09, 2011 M rated it it was amazing
Shelves: teaching, nonfiction
This book was fantastic. Every elementary math teacher should read it. In China, elementary math teachers only teach math. They have discussions and shared planning time. They actually spend a lot of time studying math. They don't assume they know it and are done. Because American elementary teachers teach all subjects, we don't have time to do what they do, which is a shame. We are so worried about math scores and international competition, but we don't make the changes that would truly make a ...more
Aug 15, 2015 Brian rated it really liked it
Deeply insightful. Helped me realize that although I have some strengths as a math teacher, I have so, so much to learn! So many of Ma's insights, or really, the insights of the teachers she interviewed, are directly applicable to my work with struggling mathematicians. Favorite quote - "The reason that one problem can be solved in multiple ways is that mathematics does not consist of isolated rules, but connected ideas. Being able to and tending to solve a problem in more than one way therefore ...more
Dec 09, 2012 Jaclyn rated it it was amazing  ·  review of another edition
Shelves: rm
Well, this was excellent. My anger at Mathematics education in the states is melting into sadness and despair. When almost 20% of elementary school math teachers surveyed don't know the formulas for area and perimeter of a rectangle, we face a more deeply ingrained, entrenched, intractable problem than I ever could have imagined.

It also pained me to hear the Chinese teachers describe learning from their colleagues, solving problems together and spending time discussing pedagogy. If teachers her
Feb 24, 2012 Alicia rated it it was amazing
Shelves: education
Liping Ma's research (the book is based on her dissertation at Standford University), shows how math teachers in the US consistently demonstrate a fragmented, shallow understanding of math concepts in comparison to their Chinese counterparts. This knowledge gap is likely a significant contribution to the perpetual lag in US public school math performance. Very compelling and highly recommended for teachers, homeschoolers, teacher educators and parents fed up with public school mathematics educat ...more
Mar 04, 2011 Sue rated it liked it
Shelves: educational
I know of many teachers who could have explained this math with more conceptual understanding than the teachers who were presented for the United States in this book. This book has made me look differently at my teacher's editions, and I have noticed how limited the instruction is and the strong focus on procedure. I am more aware of how I present math lessons now. I was especially interested in the end chapter comparing U.S. teachers prep time with that of their Chinese counterparts. I'm a litt ...more
Jul 28, 2016 Joe rated it really liked it  ·  review of another edition
This reads very much like the dissertation it was originally, but that doesn't take away from it's great content. There is a clear distinction between the process based American math teacher perspective and the conceptual based Chinese math teacher perspective. The process dependent approach sadly leaves many students (and teachers) unable to explain, expand, understand the concepts behind the process. The conceptual based approach leads students and teachers to develop a wide variety of process ...more
Aug 31, 2008 Barb rated it really liked it
Recommends it for: Teachers of Math
It was both enlightening and discouraging to read this book which compares the teaching of mathematics in the US and China. It was written almost 10 years ago and I'd like to think US teachers have improved their teaching of math in that time. Still, many of the quotes from teachers in the discussion groups sounded real and could have come from me. It was interesting to see the different ways of thinking about how teachers do what they do.
Apr 27, 2011 Evan rated it really liked it
The author has done extensive interviews of American and Chinese math teachers concerning 4 or 5 fundamental topics in math. The chapter on subtraction with "borrowing" is really great--full of good ideas about teaching. She finds that many many (75%) of American teachers don't really understand why the subtraction algorithm works, in contrast to about 75% of Chinese teachers who do. She goes much beyond those statistics though, by providing the meat of the interview transcripts.
Jun 09, 2009 LauraW rated it it was amazing
It is fascinating to see the degree of understanding of fundamental math processes and the differences between Chinese and US teachers. I think some of the curricula I have dealt with are trying to address this problem (Everyday Math, in particular), but too often the teachers teaching EM lack the understanding that the curriculum is attempting to impart, so they skip over or slight the fundamental understandings. It is hard to pull yourself up by your own bootstraps.
Feb 09, 2013 Carol rated it it was amazing  ·  review of another edition
Shelves: unfinished
Surprisingly engaging and incisive, for a rather academic book. As a new math teacher, I was alternately horrified by the knowledge gaps of the U.S. teachers portrayed in this book, as well as intrigued by the lessons to be learned from the history of Chinese math education. I also found it to be practical in providing numerous examples of particular problems!
Apr 29, 2012 Amy rated it really liked it
Shelves: 2012
Excellent read for anyone who teaches or tutors math. I will be referring back to the first few chapters a lot, especially the chapter on dividing fractions. Four stars because it is a study, and a hard read. Which is why it's taken me a year to finish this book: the first chapters required time to reflect, the last ones I had to push through. It has really opened my eyes to the beauty of math.
Heather Seeber
Sep 17, 2015 Heather Seeber rated it it was amazing
This is a must read for parents of elementary school students who don't understand why schools are spending more time on the conceptual understanding behind mathematics topics as a baseline for the procedural calculations. It is also quite horrifying to see some of the U.S. teacher quotes as they work through four simple arithmetic problems. Highly recommend to both parents and teachers.
Nov 12, 2010 Lynne rated it really liked it  ·  review of another edition
I don't think it's just the math geek in me -- this book is really fascinating. It examines the differences between teaching methods in the U.S. and China, but also explores a sampling of math concepts with very clear language.
Jul 01, 2011 Darin rated it really liked it
This book is based on the author's dissertation. She compared Chinese to American teachers of elementary mathematics and found that overall the Chinese teachers had a better understanding of the underlying concepts.
Jan 20, 2013 Manda rated it it was amazing
I have only just started this. But I think it is a must read -especially for people who are home schooling their children -but really whether you are "good" at math or "bad" at math, you need to read this!
Jul 01, 2007 Laura rated it really liked it
This book began as a doctoral thesis and reads like one. It was very helpful, though, as it clearly showed how and why Chinese teachers think more mathematically, and are thus able to teach math more thoroughly.
Jun 14, 2012 Ceri rated it it was amazing
A startling look into mathematics education in America. It's been very helpful in helping me define and realize my goal in teaching my kids math.
Apr 04, 2009 Matt rated it really liked it
Never had to read it for a class, but heard good things about it...Browsed through it on a couple of occasions, especially the chapter on dividing by fractions...Interesting stuff...
Sep 23, 2012 Melissa rated it it was amazing
A must have for any teacher whether teaching math or not.
Jul 22, 2012 Arron rated it really liked it
Shelves: math
Vitally important read for anyone involved in math education in the US.
Michael Tallman
Sep 23, 2012 Michael Tallman rated it really liked it
A must read for any elementary teacher.
May 07, 2009 Betty rated it liked it
I have been meaning to read this book for years. This summer I assigned it to a student, so I had to read it myself. It's very good.
Susan Lee
Jul 14, 2007 Susan Lee is currently reading it
Frightening so far.
Jan 07, 2015 Lindsay rated it did not like it  ·  review of another edition
Dry. Awful. Not sure why so many people think this is a good book.
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