Liping Ma : Knowing Mathematics 2

Department of Mathematics and Statistics WIKI Service présente :

 

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

In the following, I wish to share some of the work of Liping Ma – specifically, her findings and her ideas regarding the education and skills of elementary mathematics teachers. If you are interested, I would encourage you to read her book (relatively short and available in the York library).

Table of contents

1 The Study: Introduction and Motivation 2 Participants and Interview Questions2.1 The Perimeter-Area Question: Results and Analysis 2.1.1 Why were some teachers more successful than others? 3 Acculturation of Math teachers to the Mathematics Discipline – Thinking Mathematically 4 Knowledge Packages 4.1 Learning Paths – a linear progression? 5 Profound Understanding of Fundamental Mathematics (PUFM) 5.1 PUFM Characteristics 6 China & The U.S.: Differences In Teacher Education and Training 7 Current Trends 8 Reference Information 9 Relevant Links

The Study: Introduction and Motivation

As a graduate student at Michigan State University, Liping Ma served as a research assistant for the Teacher Education and Learning to Teach (TELT) study. In her classroom observations and review of TELT interview transcripts on the teaching of mathematics, Ma invariably compared these observations to her own experiences of being educated in China. Ma noticed that many of the U.S. teachers (ranging from student to experienced teachers) lacked a deep conceptual understanding of many areas covered in elementary mathematics. In addition, international studies of achievement showed that students in the United States are consistently “outperformed” by students in certain Asian countries, including China. While researchers have suggested potential reasons for this apparent gap (such as differences in number word systems – in Chinese, Ma explains, 20 means “two tens”, 30 means “three tens” etc), Ma hypothesized that teachers’ mathematical knowledge and training was a key factor in this equation. Thus, Ma, who was educated in China and familiar with the education system in the United States, decided to engage in comparative research into the knowledge of elementary teachers in China and the U.S.
As Ma explains, there is a clear difference between the training of teachers in China and the U.S. While most U.S. teachers complete at least a bachelor’s degree, Chinese teachers complete only between two and three years of formal training following the ninth grade. How, then, could it be possible that Chinese teachers have a better understanding of elementary mathematics? Ma hypothesizes that “elementary teachers in the two countries possess differently structured bodies of mathematical knowledge,” where pedagogical content knowledge (i.e. knowing how to represent the content in a comprehensible way) is central. The question of teachers’ mathematics subject matter knowledge – what does a teacher need to know to be well equipped to teach mathematics – has been a focus of mathematics education researchers since the late 1980’s.



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