Knowing And Teaching Elementary Mathematics

International studies of mathematics achievement find that students in some Asian countries, such as Japan and China, consistently outperform their counterparts in the United States. Researchers have described various factors that contribute to this learning gap (such as differences in cultural contexts, school organization, amount of time spent learning mathematics, content of mathematics curricula), but have not looked in much depth at the issue of teachers' mathematical and pedagogical knowledge. Could there be a parallel gap in teacher knowledge? If so, how does this affect mathematics teaching and learning? Liping Ma reports in this book on her study of the differences between Chinese and US teachers' knowledge of mathematics for teaching. She explores how Chinese teachers' understanding of mathematics and its teaching contributes to their student's success, documents some of the factors that support the growth of Chinese teachers' mathematical knowledge, and proposes that it seems difficult, if not impossible, for elementary teachers in the United States to develop a deep understanding of the mathematics they teach. In a series of case studies of teachers' knowledge, Ma interviewed elementary mathematics teachers in the US and China about the way they would handle various mathematics topics. She found that US teachers may seem to know more about mathematics (they may have taken more courses, and have some understanding of more advanced concepts), but their understanding of the mathematics they teach is, in fact, much more shallow. On the other hand, Chinese teachers have a much deeper understanding of both the mathematics and the relevant pedagogy for teaching it. This, Ma's study suggests, is what lies at the core of the Chinese teachers' competence, and perhaps at the root of the Chinese students' superior performance on international comparison studies. Given the release of the Third International Maths and Science Study (TIMSS), this book speaks to the debates over issues raised by TIMSS. It illuminates cross-cultural comparisons - and may well shift the debate on what counts as good teaching.