Thomas P. Carpenter Elizabeth Fennema Thomas A. Romberg University of Wisconsin-Madison
In the last few years there has been significant progress in integrating programs of research on student learning, teaching, curriculum, and assessment that has potential for influencing curriculum reform. The semantic analysis of rational number provides a common focus for the research discussed in this volume. There is some consensus that rational number can be characterized as a set of related subconstructs that share certain common features, but which aspects of the analysis will prove the most valuable to help us to better understand the teaching and learning of rational number concepts and skills is an open question. There is mounting evidence that students have a substantial body of informal knowledge about the basic principles underlying rational number that can serve as a basis for instruction, but successful instruction requires a great deal of content and pedagogical content knowledge on the part of the teacher. The research described in this volume focuses on the attempt to understand the effects of instruction rather than on the development of prescriptions for more effective instruction.
Until recently there had been relatively little integration of programs of research on teaching, learning, curriculum, and assessment ( Romberg & Carpenter, 1986). However, in the last few years it has become increasingly apparent that a more unified program of research is needed if we are to acquire an understanding of teaching and learning in schools that will inform curriculum development and assessment ( Carpenter & Peterson, 1988, Fennema, Carpenter, & Lamon, 1991). The chapters in this volume represent a first step toward an integration of research paradigms in one clearly specified mathematical domain.
Attempting to integrate a number of different research perspectives is a