School mathematics reform : Implications for mathematics teacher preparation

In the past four decades, attention in research in teaching has turned from the content of teaching and learning to the context in which they occur. Many researchers now view learning as active construction rather than passive absorption, and teaching as facilitation rather than transmission. A similar shift has occurred in the view of the school curriculum, now less a collection of topics than a set of experiences. In mathematics, the National Council of Teachers of Mathematics publication The Agenda for Action (1980) opened a new dimension to how many educators view teaching. The recommendations in the Agenda emphasized problem solving and applications; a reexamination of basic skills; incorporation of calculators, computers, and other technology into the mathematics curriculum; and more mathematics for all students. As a response to the Agenda, in 1986, the Board of Directors of the National Council of Teachers of Mathematics NCTM) established the Commission on Standards for School Mathematics to help improve the quality of school mathematics (NCTM, 1989). Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989), which established a framework to guide reform in school mathematics, is the product of the Commission. This document, along with the Professional Teaching Standards (NCTM, 1991) and the Assessment Standards for Teaching Mathematics (NCTM, 1995), set forth a vision of school mathematics curriculum and teaching and a view of evaluation different from what most teachers experienced in their mathematical education and what they found in most textbooks. If the mathematics curriculum changes as proposed, the need for competent teachers will become more acute. Teachers will need more and better preparation, for teaching for better mathematics (Begle, 1972) demands better teaching of mathematics. The recommendations of the current reform for school mathematics focus attention on teaching. They require that teacher education programs play an integral role in familiarizing teachers with current recommendations and preparing them with the professional knowledge base for realizing those visions. Research on mathematics teachers and teacher education indicate that this process is neither straightforward nor simple. The National Council of Teachers of Mathematics standards for content, pedagogy, and evaluation provide the direction, but not the mechanism, for reform in school mathematics. A mechanism for reform must be developed; without it even current guidance will not affect the teaching of mathematics. This mechanism must take into account the challenges of preparing teachers to teach in accord with the proposed visions and provide a perspective on how to deal with the complexities of teacher change. This mechanism must serve as the vehicle for improving teaching as well as teacher education. The mathematics teacher education community has recognized this need for some time. Bruner (1966) indicated that a theory of instruction must specify how a body of knowledge should be structured so that learners can most readily grasped it. A theory of instruction should identify the most effective ways in to facilitate learning. Cooney and Brown (1985) argue that a theory or theories in mathematics education must ultimately provide a basis for improving the teaching and learning of mathematics. Recent researchers on mathematics teacher education have examined four reform areas in educating mathematics teachers: teacher beliefs, content knowledge, pedagogical content knowledge, and pedagogical reasoning. In this article, I synthesize research on these areas and provide several recommendations for the reform in teacher education. Beliefs I believe teachers make decisions about students and curriculum in rational ways according to conceptions they hold. To design teacher education programs without understanding those conceptions and their role creates a context where teacher educators believe that their insights into the teaching/learning cycle are synonymous or even consistent with those of the teachers they teach (Cooney, 1994, p. …