Launchings from the CUPM Curriculum Guide:
Preparing K-8 Teachers

David M. Bressoud March, 2006

B.4: Pre-service elementary (K-4) and middle school (5-8) teachers.

Among students who are not majoring in but are required to take mathematics, pre-service K-8 teachers form a very distinctive group with special needs. These are often students with weak math skills and weak understanding. These are also the people who are charged with laying the mathematical foundations for future generations. The mathematical education that they need is elementary mathematics, but elementary mathematics taught at a conceptually deep level. Liping Ma makes this point very clear when she says, “In the United States, it is widely accepted that elementary mathematics is `basic,’ superficial, and commonly understood. The data in this book explode this myth. Elementary mathematics is not superficial at all, and any one who teaches it has to study it hard in order to understand it in a comprehensive way.”[1]

No one should teach mathematics to pre-service K-8 who has not read Liping Ma’s Knowing and Teaching Elementary Mathematics. As she illustrates through many examples, the knowledge base needed to teach elementary mathematics is very sophisticated. Fortunately, this realization is spreading. A lot of work is being done to determine what teachers need to know, to learn how to help them to use this knowledge effectively in the classroom, and to support these teachers through continuing in-service training. The CUPM Illustrative Resources is rich in links to this work.

Probably the most important starting point for any mathematician who will teach pre-service K-8 teachers is the MAA’s program, Preparing Mathematicians to Educate Teachers (PMET). It runs workshops, supports collaborations and regional networks, provides mini-grants, and provides a rich collection of resources.

The Illustrative Resources include links to relevant reports: NCTM’s Professional Standards for Teaching Mathematics (1991) and the CBMS Mathematical Education of Teachers (2001). There are links to four statewide initiatives, in Michigan, Oregon, Virginia, and Indiana. The Michigan program, Michigan Mathematics Teacher Educators, formed to facilitate communication and collaboration among mathematics teacher educators, is especially noteworthy as both a resource and model.

The Illustrative Resources also links to a dozen programs at specific universities and to several research and training projects including Integrating Mathematics and Pedagogy at San Diego State University and the Institute for Mathematics and Science Education at the University of Illinois at Chicago. There is a section of links on the use of classroom video in the preparation of teachers.

One of the resources I find most interesting is the US Department of Education’s Teacher Preparation Research: Current Knowledge, Gaps, and Recommendations [2], written by Suzanne Wilson, Robert Floden, and Joan Ferrini-Mundy in 2001. It is a survey of the research literature, identifying and summarizing the reliable studies that provide answers to five questions, starting with “What kinds of subject matter preparation, and how much of it, do prospective teachers need?”

In her conclusion, Liping Ma speaks of the virtuous cycle of mathematics education in China. Future teachers get a solid grounding in mathematics when they are students. In their in-service training, they have the opportunity to deepen this understanding and learn how to draw upon it in their own teaching. As teachers, they are part of network in which they are constantly receiving peer review and support, constantly learning how to teach more effectively. In the United States, this virtuous cycle fails at all three points. The in-service training, by itself, cannot correct the ills that we now face. But it does have an important role to play.

[1] Ma, Liping, Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States, Lawrence Erlbaum Associates, London, 1999.

[2] Wilson, Suzanne, et al, Teacher Preparation Research: Current Knowledge, Gaps, and Recommendations, Research Report prepared for the US Dept. of Education, Center for the Study of Teaching and Policy, University of Washington, 2001.

Do you know of programs, projects, or ideas that should be included in the CUPM Illustrative Resources?

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We would appreciate more examples that document experiences with the use of technology as well as examples of interdisciplinary cooperation.

David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul, Minnesota, he was one of the writers for the Curriculum Guide, and he currently serves as Chair of the CUPM. He wrote this column with help from his colleagues in CUPM, but it does not reflect an official position of the committee. You can reach him at