Knowing and Teaching Elementary Mathematics

The teacher book that really opened my eyes to the fact that many elementary teachers do not understand the mathematics they teach was Knowing and Teaching Elementary Mathematics by Liping Ma.  This book looks at teachers' understandings of fundamental mathematics concepts in the United States and China.

Knowing and Teaching Elementary Mathematics

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In this book, Ma examines the difference in conceptual understanding of math between US teachers and Chinese teachers.  Despite having less overall education than US teachers, Chinese teachers demonstrate a much deeper understanding of the mathematics they teach which may in part be why China outperforms the US in math over and over again.  According to Ma, "even expert teachers, experienced teachers who were mathematically confident, and teachers who actively participated in current mathematics teaching reform did not seem to have a thorough knowledge of the mathematics taught in elementary school."  

If you teach subtraction with re-grouping, or if you have kids who you think should be able to accomplish this important skill, you may want to look at chapter 1 which goes into great details about how US and Chinese methods on the subject vary and how you might help your students conceptualize this topic rather than trying to remember steps in a procedure.

If you teach multi-digit multiplication, chapter 2 is where you want to start.  Ma takes a deep look at how Chinese teachers use the concept of place value to help students understand multiplication.  This chapter can seriously make you a better teacher.

The chapter that changed my teaching practices the most was chapter 3 which is on fraction division.  Ma has some scary statistics about the number of US teachers who can not write a number story to go with a fraction division equation.  By generating representations and focusing on the reciprocal relationship between multiplication and division, Chinese teachers have a very different way of teaching and learning about fraction division.   

The book also includes ideas about the relationship between area and perimeter and how and when teachers attain profound understanding of mathematics.  

If you want to better understand the math you teach, or are curious about how to help your students who are struggling in subtraction, multiplication or fraction division, this might be a book you want for your own collection.

How does the way you learned math effect the way you teach math?