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

by
Liping Ma

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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## Community Reviews

(showing
1-30
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309)

This book is a product of a thesis on comparison of the thinking patterns of teachers in USA and China who work with maths. The teachers in USA are drawn towards procedural thinking while those in China are drawn towards an integration of conceptual thinking and procedural in teaching of maths. She has displayed this fact by observing classes, interviewing sets of teachers of both countries and informal discussions. She has taken 4 base areas of maths for the same - subtraction with reg ...more

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 ...more

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 ...more

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 ...more

Jul 03, 2009
LauraW
rated it
5 of 5 stars
·
review of another edition

Shelves:
education-parenting,
non-fiction

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.

Apr 04, 2009
Matt
rated it
4 of 5 stars
·
review of another edition

Shelves:
only-have-read-certain-parts-of-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...

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