Reflections on a portrait of our field

Abstract

After providing summaries of the seven core chapters that follow, I discuss some common themes that run through them. As a framework I use the four-component model of teacher, student, content, and environment, which continues to provide a useful way to talk about meta-issues in mathematics education. Chapters in this volume emphasize both the centrality of the acts of teaching that lie where the teacher and student components meet, and the importance of better understanding the ways in which students come to understand the content. These emphases and the educational problems that gave rise to them help paint a portrait of our field, and strongly suggest some necessary next steps. Although the seven core chapters place less emphasis on the need for careful attention to content and environment, they too need to play an important role as we move forward in our scholarly efforts.