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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) 1st Edition
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More About the Author
Top Customer Reviews
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.
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.Read more ›
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.Read more ›
Most Recent Customer Reviews
This book has the form of a comparison of math teacher content knowledge between US and China, but it is actually a discourse on the kind of mathematical knowledge and attitudes... Read morePublished 5 months ago by Robert Root
This book is a product of a thesis on comparison of the thinking patterns of teachers in USA and China who work with maths. Read more
I have owned this book for quite a while now, but still look at it. Whenever I loan it to colleagues, I always make sure I get it back. Read morePublished 14 months ago by Jubilee
This book changed my life. I read it summer of my sophomore year of college and was absolutely riveted. Read morePublished on October 30, 2013 by teddyjo26
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 morePublished on July 27, 2013 by Lynne Kenney
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 morePublished on September 29, 2011 by Jane M. Batchelder
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 morePublished on June 29, 2011 by Lukas Halim
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 morePublished on April 10, 2011 by Christie P
I read this book to improve my teaching skills, and to prepare myself to teach Singapore math at home. Read morePublished on January 1, 2011 by kalanamak