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

4.22 of 5 stars 4.22  ·  rating details  ·  150 ratings  ·  27 reviews
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 ...more
ebook, 221 pages
Published January 21st 2010 by Routledge (first published May 1st 1999)
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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
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
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
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. Conceptua
Jun 23, 2007 Ben rated it 5 of 5 stars  ·  review of another edition
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
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
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
Dec 19, 2012 Jaclyn rated it 5 of 5 stars
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
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
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
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.
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.
Aug 31, 2008 Barb rated it 4 of 5 stars  ·  review of another edition
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.
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.
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!
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.
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.
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.
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!
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...
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.
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.
Vitally important read for anyone involved in math education in the US.
Dry. Awful. Not sure why so many people think this is a good book.
A must have for any teacher whether teaching math or not.
Michael Tallman
A must read for any elementary teacher.
Susan Lee
Jul 14, 2007 Susan Lee is currently reading it  ·  review of another edition
Frightening so far.
Anne E.
Anne E. marked it as to-read
Aug 26, 2015
Cutzinas marked it as to-read
Aug 20, 2015
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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)

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