Editorial - January 2008 - Volume 108 (1)

Teachers' Mathematics Knowledge

Gerald Kulm, Texas A&M University

The issue of elementary and middle school teachers' mathematics knowledge has been the focus of attention in recent years. Significant effort and funding has been directed at developing assessments that would reveal both the level of mathematical content and pedagogical knowledge of teachers. The original idea of “pedagogical content knowledge” that was first studied by Shulman (1987), has been extended by researchers (e. g., Hill, Rowan, & Ball, 2005). Now, we have the results of a study that compared the mathematics knowledge of U. S. teachers with those in six other countries (Schmidt, et al., 2007). Not surprisingly, U. S. teachers ranked somewhere in the middle, providing further explanation for the similar international ranking of 8th grade students. These results provide an overall picture that student achievement is the result of the curriculum they study and the teachers in their classrooms. Although home environment, economic issues, and other extracurricular effects can detract or enhance learning, the teacher and instructional materials in the classroom are what make the real difference in children's achievement.

Most mathematics educators are painfully aware of the issues and the system that produces, in spite of our best efforts, teachers who are likely to lack sufficient mathematics knowledge. Until recently, the issue of teacher preparation, especially the importance of content knowledge, was the “800 pound gorilla” in the room that few people were willing to acknowledge. Research on teacher learning was not a central concern of the mathematics education community. Funding for the development of instructional approaches, course materials, or other strategies to enhance teacher preparation have been a low priority. The development of mathematical knowledge, in many teacher preparation programs, is the responsibility of mathematics departments where the assignment to teach “mathematics for teachers” courses is often a burden. In many cases, two or three of these courses represent the entire content preparation for teachers who will be certified to teach in grades K through 8.

So what is to be done? A major step has been taken by identifying the issue and developing the means to assess specific areas of knowledge. The necessary changes and reforms could take place at systemic levels, or in targeted and specific ways. The former is very difficult to achieve, as we learned in the case of making systemic change in school mathematics and science education. Many other countries have a system of normal colleges that specialize in teacher preparation. Students in these colleges study mathematics and science for teaching throughout their undergraduate work, taking many courses that focus on fundamental concepts of mathematics and science that comprise the K-12 curriculum. Recent research has revealed the in-depth level of mathematics understanding that results from this type of preparations (e. g., An, Kulm, & Wu, 2004; Ma, 1999). Without this profound understanding by our teachers, it is unlikely that we can expect much more from our students.

Changing back to normal colleges for teacher preparation, as is the practice in most other countries, will not happen here. It is even difficult to expect that teacher preparation will allow for significant increases in the number of mathematics courses that are required for certification. The alternative is to find more specific yet powerful approaches that can make a difference. Two strategies are available and within mathematics educators' ability to effect change. Together, these approaches could provide contexts and opportunities to improve teachers' mathematics knowledge. Both require building bridges and lines of communication that have seems difficult to achieve in the past. Neither of these ideas are entirely new, but perhaps the time has come to revisit and try once again, aided by what we now know about the nature of teacher knowledge and how to enhance it.

The first strategy is for mathematics educators and mathematicians to connect, or reconnect, around the issue of teacher preparation. Too often, the few required courses in mathematics and teaching methods are not coordinated, or at worst, work nearly in opposition to each other in building mathematics knowledge. There are many possible approaches for coordinating and strengthening these courses, from their content, to scheduling, to who teaches them. Research on effective approaches to addressing any of these would help. However, simply sitting down together and developing a workable and plan with specific goals for improving teacher knowledge would go a long way toward a solution.

References

An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education, 7, 145-172.

Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 371-406.

Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum.

Schmidt, W., Tatto, M. T., Bankov, K., Blomeke, S., Cedillo, T., Cogan, L., Han, S. I., Houang, R., Feng, J. H., Paine, L., Santillan, M., & Schwille, J. (2007). The preparation gap: Teacher education for middle school mathematics in six countries. East Lansing, MI: Michigan State University.

Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.