» Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning.)

Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning.) Reviews

Customer Rating:
Summary: Makes so much sense
Comment: I am not a formal educator. I'm not a math lover In fact growing up I refered to my self as mathmatically retarded (please excuse my congnitive reference). I have begun homeschooling my 3 children and am piecing together, what I feel is an appropriate curriculum. I'm trying to avoid the drill and kill approach in all subjects. I was really struggling with finding or creating a math curriculum. I was concerned with my ability to teach a subject that I only understand at a very basic level. I came upon this book and thought perhaps it would help me make sense of things and guide me in choosing a math curriculum for the kids. I have to say that I really struggled in the beginning of the book where the U.S. teachers explain subtraction with borrowing. I was lost. I still remember the process from my days in school, but their explanations were absolutely alien to me. I then got to the chinese way of teaching subtraction with regrouping and all the lights came on. It made so much more sense to me. I may not be an idot after all. I'm gaining understanding and finding direction. This book is not a curriculum in itself, but has greatly helped me in the process of choosing an appropriate way of learning math for the kids. It's truly helping me make sense of math for myself. I recommend this book to anyone teaching math and for parents who want to help their kids and themselves understand math in a natural and logical way.

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Customer Rating:
Summary: Important for all math teachers to read
Comment: While this text focuses on topics covered in elementary school arithmetic, I think this is an important text for all math teachers to read. Having an understanding of how our students are taught at the elementary level will illuminate why our students' minds are so inflexible and so shallow when it comes to mathematics. I also think it is good to read to get a flavor for the rigor used to approach mathemtics at the elementary level in China. We can use this as secondary teachers to design review or remedial material, or to provide alternative ways to approach arithmetic while solving other types of problems.

This book is a bit dry to get through, but the material itself is excellent. The reviewer who gave the book one star - I don't think you understand how research is planned. You cannot take all variables into account. It just isn't possible. For the scope of the work, Ma's work is right on. I suppose Ma could have surveyed the teachers about their attitudes towards math, expectations on useage of math in the real world, etc. But that's not her field! Other people are doing research on that already!

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Customer Rating:
Summary: Guess the Profession of the Only Person Thus Far to Give this Book a One-Star Rating
Comment: That's right: a teacher (undoubtedly an American teacher), and even worse, one working on a master's degree in education. And yet, she (to pick a gender to use) is unable to see any worth in this great book. Furthermore, her review illustrates one of the problems with many teachers today in the US: the lack of critical thinking skills, not to mention an apparent ignorance about research methodologies.

That reviewer complained that the author "neglects to even mention any cultural differences between the two societies that she is comparing" and saw that failure as a fallacy that undermined everything said in the entire book. How cultural differences would alter any of the valuable lessons that we can learn from this book about a better way of teaching mathematics in elementary school and the importance of teachers having an in-depth knowledge of the subjects that they are teaching is completely lost on me. Maybe that's because they would not make any difference!

Math is a universal language, and we should be able to learn something from other cultures who we already know are producing children who consistently outscore American children by a wide margin.

And guess what: one of the basic goals of cross-cultural studies is to find out if others are doing something better and, if so, whether their methods can be applied successfully to help us do something, like teaching mathematics, better. Of course there are some cultural differences between the US and China, but so what? The point is to examine other societies who are apparently doing a better job in some area and see what they are doing differently and what can we learn from them.

The fact that a teacher found this book "boring and not worth the paper that it is printed on" should tell those of you not working in the field of education how bad it already is in our schools and how much worse it is probably going to get in the future. I teach remedial mathematics at the college level. In case any of you reading my comments did not know it, many of our schools are, and for some time now have been, graduating kids from high school who cannot add and subtract integers because they do not understand the most basic facts about our number system and how it works. None of my students have even heard the term "base 10," which is what the "composing" and "decomposing" concepts used by the Chinese teachers relies so heavily upon, and is what determines the value of every number in the system that we use in everyday life (computers, of course, use base 2).

Is there any hope for improvement in the future? Frankly, I don't think so because we just keep throwing money at the problem (giving it to the same people who helped cause the problems), rather than doing those things that are necessary to bring about meaningful changes.

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Customer Rating:
Summary: Highly Recommended for Early Ed. Teachers
Comment: I am a college student who purchased this book for a class project. It was VERY HELPFUL. I used the chapter on division by fractions to teach my class ways to make it easier, and the reasoning behind the methods. It was so accurate on how American teachers teach, that anyone who will be teaching math to students should really review this book to learn helpful methods for students. I aced my lesson plan for the class I taught.

Topics in this book range from subtraction, to multiplication, division, representations of fractions, and more.
The case study comparisons between the Chinese teachers and the American teachers was shocking. A must read for anyone going into Elementary Education, or working in an Elementary School system.

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Customer Rating:
Summary: shows how important a profound understanding of fundamental mathematics is for teaching
Comment: Knowing and Teaching Elementary Mathematics is a book that compares and contrasts American and Chinese approaches to teaching elementary mathematics ie arithmetic and elementary geometry. The author argues that Chinese teachers have a more profound understanding of elementary mathematics than their American counterparts and provides pretty good evidence of this. While this aspect of the book is useful, the authors explanation of just what profound understanding of fundamental mathematics amounts to is much more useful. For example rather than using the technique of borrowing to subtract, the author recommends using something called decomposing a number which means understanding that, for example, the 2 in 23 is two tens so in 23 - 15 you move one ten from the 20 part and carry it over to the ones as a ten so 10 + 3 = 13 then you proceed to subtract 5 from 13. Of course the end result is the same but the student learns about the structure of numbers in the process ie that 23 = 2* 10 + 3 * 1. Anyway this is a very useful book. It is also a little bit embarrassing as I was not fully knowledgeable about some of the examples she used. For instance although I knew the process for computing (1 and 3/4 )/ (1/2) I couldn't for the life of me come up with a story to explain why you would want to do that. Anyway, this is a very eye opening book about the state of mathematics education in America and also just what it means to be proficient in elementary mathematics.

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