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

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

by Liping Ma

But, they give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education.This book describes the nature and development of the "profound understanding of fundamental mathematics" that elementary teachers need to become accomplished mathematics teachers, and suggests why such teaching knowledge is much more common in China than the United States, despite the fact that Chinese teachers have formal education than their U.S. counterparts.The studies described in this book suggest that Chinese teachers begin their teaching careers with a better understanding of elementary mathematics than that of most U.S. elementary teachers.

The concluding chapter of the book suggests changes in teacher preparation, teacher support, and mathematics education research that might allow teachers in the United States to attain profound understanding of fundamental mathematics.

  • Language: English
  • Category: Education
  • Rating: 4.26
  • Pages: 192
  • Publish Date: May 1st 1999 by Routledge
  • Isbn10: 0805829091
  • Isbn13: 9780805829099

What People Think about "Knowing and Teaching Elementary Mathematics: Teachers' Understandng Fundamental Mathematics in China and the United States"

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 stems from the teachers in the US not having a good conceptual understanding of the material. The Chinese teachers, in contrast, demonstrate a deep conceptual understanding of the math behind the procedures, and tend to teach to that. The second way this book is helpful is that it explains the conceptual understanding of the four specific math topics: subtraction with borrowing, multidigit multiplication, division by fractions, and the relationship between the area and perimeter of a shape.

I realized reading this book that my understanding of arithmetic is very incomplete.

This book came out in the late '90s, when lots of energy in the United States was devoted to comparing our educational approach (especially in fields we now call STEM) to that of other nations. Part of me suspects I just don't bump into those circles any more; part of me suspects the competitive feelings underpinning that research still exists but is now increasingly focused on differentiating groups within the US.) The majority of the book is devoted to comparing the pedagogical approach of American and Chinese teachers in four specific topics from grade school mathematics. It is difficult not to be appalled at the state of some of the American teachers' mathematical knowledge.

A deeper reason for the methods is the lack of knowledge inculcated in US teachers with regard to what Ma calls the "Profound Understanding of Fundamental Mathematics." In short, we simply do not give elementary math the credence it deserves. Key to Chinese instructors is an understanding of the interconnectedness of math concepts as well as the calling-upon of mathematical laws even among the youngest students.

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. My reading note: 1)Chapter1 subtraction with regrouping A:decomposing a higher value unit p7 B:the rate of composing a higher value unit:10, which is 10 lower place value = 1 higher place value and the place value system addressing in chapter 2 are theories underneath addition, subtraction standard carrying or borrowing procedural algorithm, you always deal with number under 20. to justification move algorithm, you can also think as unit is multiplicand D: Borrowing traditional term will illustrate standard subtraction procedure. Decomposing emphasis the "no value change" idea, borrowing illustrate subtraction procedure, they are 2 faces of the same thing. That my daughter does whenever doing addition and subtraction, she has a strong concept with carrying and borrowing concept, keeping change value when she found carrying or borrowing happen, she figure out her idea's math operation rule when playing monopoly game. Neuroscience study shows our brain (cortex) dealing with abstract number operations not fully mature until adolescence. rate of higher place value of 10 underline carry, borrowing procedure 3.

What is shocking is that the US teacher do not understand how to effectively teach these concepts, even though they have had more training than the average elementary school teacher in China.

So, the book is kinda dorky, but pretty interesting if you are into math, cultural differences, or thinking about the role of analogies in learning.

I would highly recommend this book to any parent who wants to help their child develop a greater conceptual understanding of basic math.

In China, elementary math teachers only teach math. Because American elementary teachers teach all subjects, we don't have time to do what they do, which is a shame.