An Analysis of the Research on K-8 Teachers' Mathematical Knowledge.

This paper provides a summary and a critique of the empirical literature on elementary teachers' mathematical knowledge. The empirical evidence addresses four major issues surrounding teachers' mathematical knowledge: 1) What is the nature of teachers' content knowledge, particularly with regard to the domain of number? 2) How does teachers' knowledge impact their instructional practice? 3) How does teachers' knowledge impact student' learning? and 4) How do teachers develop appropriate mathematical knowledge? For each question, major findings are summarized, exemplars of studies that have addressed the question are provided, and the contribution of these studies to our understanding of teachers' mathematical knowledge is critiqued. The paper concludes that there is no clearly definable body of knowledge that informs teaching; rather, teachers need multiple types of knowledge, each of which is somewhat ill-defined and amorphous. (Contains 65 references.) (ASK) Reproductions supplied by EDRS are the best that can be made from the original document. PERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIAL HAS BEEN GRANTED BY TO THE EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) U.S. DEPARTMENT OF EDUCATION Office of Educational Research end Improvement UCATIONAL RESOURCES INFORMATION CENTER (ERIC) hi document has been reproduced as received from the person or organization originating it. Minor changes have heen made to improve reproduction quality. o Points of view or opinions stated in this document do not necessarily represent uiiiciai GERI posilior: or policy. An Analysis of the Research on K-8 Teachers' Mathematical Knowledge Denise S. Mewborn Mathematics Education Department University of Georgia 105 Aderhold Hall Athens, GA 30602-7124 Paper presented at the Annual Meeting of the American Educational Research Association. , New Or lean, April 28, 2000. An earlier version of this paper was prepared for the Mathematics Learning Study conducted by the National Research Council of the National Academy of Sciences, Washington, DC. I gratefully acknowledge the contmibutions of Deborah Loewenberg Ball, University of Michigan, Jeremy Kilpatrick, University of Georgia, and Jane 0. Swafford, National Research Council. The many stimulating discussions I had with therm and theirconstructive feedback on earlier drafts were immeasurably helpful to me. 2 BEST COPY MAILABLE An Analysis of the Research on K-8 Teachers' Mathematical Knowledge Every study or subject thus has two aspects: one for the scientist as a scientist; the other for the teacker as teacher. These two aspects are in no sense opposed or conflicting. But neither are they immediately identical. (Dewey, 1990/1900, p. 200) The issue of what types of knowledge are essential for teaching mathematics in the elementary school has been the subject of numerous conceptual essays and empirical studies for the last 40 years. Research upholds Dewey's claim that' knowledge for teaching is different from knowledge for "doing" in a discipline. Merely "knowing" more mathematics does not ensure that one can teach it in ways that enable students to develop the mathematical power and deep conceptual understanding envisioned in current reforms documents (e.g., National Council of Teachers of Mathematics, 1989). Five major research genres are distinguishable in the literature on teachers' knowledge, and these genres follow a roughly chronological pattern. The earliest studies, conducted in the 1960s and 1970s were quantitative studies that sought to demonstrate a connection between teachers' knowledge and student achievement. These studies failed to find any statistically significant correlation between measures of teacher knowledge (such as number of mathematics courses taken, major in mathematics, grade point average) and student achievement. Although these studies have been roundly criticized for taking a naive and simplistic view of teachers' knowledge by using such gross measures as number of courses taken, there has been little effort in the intervening 20 years to develop more appropriate research methods to answer the question about the relationship between teachers' knowledge and students' knowledge. The 1960s, 1970s, and 1980s saw a flurry of descriptive studies that attempted to characterize the strengths and weaknesses in teachers' knowledge of particular content areas,