ABSTRACT
The goal of many of the chapters in this volume is to study directly the connections between teaching and learning rational numbers. The benefits of such efforts are significant but there are costs as well. The costs arise from the limitations that necessarily must be imposed on studies of enormously complex places like classrooms. I argue that complexity reduction is inevitable and that it can be understood by considering two dimensions of teaching-learning research — scope and specificity. Complexity can be increased and decreased along both dimensions through methodological decisions; such decisions do not sever the connections between teaching and learning. I illustrate the ways in which researchers reduce complexity by applying this analysis to my own work and to the studies reported in this volume by Ball, by Mack, and by Streefland. I conclude by proposing that the benefits of the new generation of teaching-learning research will be enhanced by making intentional decisions to reduce complexity and by making these decisions explicit for the reader.
Much recent work in mathematics education is concerned with the integration of teaching and learning. This is especially true of the work presented in the reports edited by the National Center for Research in Mathematical Sciences Education at the University of Wisconsin (e.g., Fennema, Carpenter, & Lamon, 1988). This volume represents a further contribution to the integrative literature by highlighting perspectives from teaching and learning within a particular content area.