THE PREPARATION OF TEACHERS OF MATHEMATICS: CONSIDERATIONS AND CHALLENGES
A letter report of the Mathematical Sciences Education Board, prepared for the National Science Foundation Review of Undergraduate Education in Science, Mathematics, Engineering, and Technology
The National Science Foundation (NSF), through its ongoing Review of Undergraduate Education in Science, Mathematics, Engineering and Technology (SME&T), is seeking input and testimony about the current state and future needs of undergraduate education in the United States in science, mathematics, engineering, and technology. Members and staff of the Mathematical Sciences Education Board (MSEB) have been involved in this process as individuals and in their roles with various professional societies. Given the MSEB's long-standing interest in the preparation of teachers of mathematics, we are pleased to answer NSF's request for a letter report on this topic.
The MSEB has been central to the development of several reports raising issues about mathematics teacher preparation, including Everybody Counts (National Research Council [NRC], 1989), Moving Beyond Myths (NRC, 1991), and The Teacher of Mathematics: Issues for Today and Tomorrow (NRC, 1987). The most recent and major documents prepared by professional societies on teacher preparation, A Call for Change (Leitzel, 1991) and the Professional Standards for Teaching Mathematics (National Council of Teachers of Mathematics [NCTM], 1991), are consistent with MSEB findings, as well as with the sentiments of many MSEB discussions. Recently, MSEB members and staff provided input for the report, Mathematical Preparation of Elementary School Teachers: Issues and Recommendations (AMATYC, AMS, MAA, NCTM, and SIAM, 1994), which makes recommendations to the mathematics professional societies.
This MSEB letter report begins with a set of considerations which ground our thinking on mathematics teacher preparation and which the reader should bear in mind throughout the report. We then discuss five challenges, as a way of addressing the questions posed by the NSF for its undergraduate review: “What are the specific innovations, as well as the evidence that their adoption represents a superior practice of education? What are the unresolved requirements for those who are already receiving SME&T instruction? What infrastructure needs must be supported for institutions to implement the best instructional practice?” (Boylan & Yankwich, p. 6). Clearly teacher preparation is a critical SME&T issue. The majority of the future teachers of this nation experience much of their mathematics content preparation as undergraduates, often before they have identified themselves as prospective mathematics teachers. Further, the effectiveness and competence of the nation 's K-12 teachers of mathematics directly bear upon the
health of the undergraduate SME&T enterprise. There will not be enough students who choose to, and are adequately prepared to, participate in SME&T, without an effective K-12 teaching force.
This report is about the preparation of teachers of K-12 mathematics. It raises questions about directions for future work in critical areas of mathematics education. It does not address more general topics in teacher preparation and development, such as school reform, the reform of teacher preparation, teacher learning and program philosophy, and the professional education of prospective teachers. In some cases the assumptions and issues raised are equally relevant to the preparation of teachers of science, and to the preparation of the professoriate more generally.
Below we explicitly highlight some considerations to be kept in mind while reading this report.
Teacher preparation—the formal undergraduate and graduate experience of prospective teachers —is only one part of a continuum of experiences which contribute to the process of learning to teach. Prospective teachers are deeply influenced by their own background as K-12 students (Lortie, 1975). Their professional development continues through the field experience, the induction years into teaching, and in ongoing formal and informal staff development throughout their careers (Loucks-Horsley et al., 1987). The undergraduate preparation of a teacher provides a bridge from the prospective teacher's precollege experiences to beginning teaching, and a foundation for subsequent professional development. Preservice experiences at the undergraduate level need to be coordinated, in both a practical and theoretical sense, with teachers' initiation into the profession in schools, as well as with their continuing education.
Educational research, about K-12 mathematics teaching and learning, and about the preparation and continuing education of teachers, is a critical component in the improvement of mathematics teacher preparation. There is an increasingly coherent body of research about mathematics teaching and learning (Grouws, 1992), and about the preparation and development of teachers of mathematics (Brown & Borko, 1992; Grouws & Schultz, 1996). Reform of K-12 mathematics teacher preparation programs can be based on such investigations. Dewey (1910/91) commented on the limitations of unanalyzed empirical impression, and we are positioned in teacher preparation to move beyond this (Lampert, 1988). Scholarly inquiry in a field not only challenges assumptions and beliefs, it is essential to systematic change.
Many of the mathematical preparation issues for prospective elementary school teachers, middle school teachers, and secondary school specialists differ considerably. Preparation programs differ substantially depending on whether they are for generalist teachers in elementary and middle schools, or for specialists in middle and secondary schools (National Center for Education Statistics [NCES], 1993, 1995; Nelson, Weiss & Conaway, 1992). This is partly because of the organization of schools, of universities, and of state credentialling and certification programs. Moreover, K-8 teachers face a need to integrate mathematics with other content areas that their secondary school colleagues do not face to the same degree. There is some evidence that people