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

I’m sorry, I have not read the book. But I want to recommend the Singapore math curriculum US edition. It’s amazing, it teaches exactly what everyone is saying the book emphasizes. We are using it in our homeschool.

Interviews teachers and displays the difference between procedural understanding of math and conceptual understanding of math. Delves into how and why US and Chinese teaching of math are so different. 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. One actually said you could use apples, oranges, or even ELEPHANTS to help you remember to move the columns over. Fruit? Animals? What about TENS? This experienced math teacher did not know that 237 shifted over a column stands for 237 tens. Chinese math teachers would not think of dressing up the process with fruit and animals. They simply teach the mathematical principles behind the procedure.Parents and teachers alike need to gobble this book right up, right now, despite its high price. We must work towards more conceptual understanding of math by elementary school teachers or we shall never climb out of the morass. Buy a copy and share it around---it is a crucial work.

Elementary school teachers are expected to teach almost everything: math, reading, science, social studies, and writing; along with nurturing, soothing, and encouraging. It's not an easy job. It's also hard to be an expert in any one piece of the job. But now, many are hearing that we're losing the "math race" to other countries. The drums of "teacher competency" are booming... and any wise teacher knows where the drum sticks will be landing next!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." Division of fractions actually represents two or three fundamentally different processes which, confused, can be at the center of students (and teachers) uncertainty. Imagine that!These are thought provoking ideas, well presented. In the face of a growing national debate about "competency", we would do well to add this element to the discussion of math teaching. Otherwise, the politicians will provide their inevitably simplistic answers.

I am working on certification in secondary mathematics. This one book has given me more insight into what is wrong with mathematics education in the USA and what needs to be done than anything else I have read or discussed in class.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.

This is education research at its best. It directly points the way to better classroom preformance, which is ultimately what education research is about. It gives a very persuasive argument that good mathematics teaching must start with a total command of the relevant mathematics. Its implications on the professional development of mathematics teachers should be taken to heart by educators, state agencies, and administrators.

Liping Ma has shown us what it means to know elementary school mathematics deeply, and has suggestions about what can be done to help our teachers acquire this knowledge. Read and share this book with anyone who cares about the education of elementary school children.