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

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

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

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

Synopsis

Although Chinese students typically outperform U. S. students on comparisons of mathematics competency, Chinese teachers receive far less education than U. S. teachers. This book describes the development of the profound understanding of fundamental mathematics that elementary teachers need.

Excerpt

Chinese students typically outperform U.S. students on international comparisons of mathematics competency. Paradoxically, Chinese teachers seem far less mathematically educated than U. S. teachers. Most Chinese teachers have had 11 to 12 years of schooling--they complete ninth grade and attend normal school for two or three years. In contrast, most U.S. teachers have received between 16 and 18 years of formal schooling--a bachelor's degree in college and often one or two years of further study.

In this book I suggest an explanation for the paradox, at least at the elementary school level. My data suggest that Chinese teachers begin their teaching careers with a better understanding of elementary mathematics than that of most U.S. elementary teachers. Their understanding of the mathematics they teach and--equally important--of the ways that elementary mathematics can be presented to students continues to grow throughout their professional lives. Indeed, about 10% of those Chinese teachers, despite their lack of formal education, display a depth of understanding which is extraordinarily rare in the United States.

I document the differences between Chinese and U.S. teachers' knowledge of mathematics for teaching and I suggest how Chinese teachers' understanding of mathematics and of its teaching contributes to their students' success. I also document some of the factors that support the growth of Chinese teachers' mathematical knowledge and I suggest why at present it seems difficult, if not impossible, for elementary teachers in the United States to develop a deep understanding of the mathematics they teach. I shall begin with some examples that motivated the study.

In 1989, I was a graduate student at Michigan State University. I worked as a graduate assistant in the Teacher Education and Learning to Teach Study (TELT) at the National Center for Research on Teacher Education (NCRTE) coding transcripts of teachers' responses to questions like the following:

Imagine that you are teaching division with fractions. To make this meaningful for kids, something that many teachers try to do is relate mathematics to other things. Sometimes they try to come up with real- world situations or story-problems to show the application of some particular piece of content. What would you say would be a good story or model for 1 3/4 ÷ 1/2 ?

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