How and Why Do Teachers Explain Things the Way They Do?

Abstract

Like jazz, teaching is both planned and improvisational. Many explanations come as planned parts of lessons, for example, when a teacher introduces a new topic and lays out its structure for students. But many also occur on the fly, in response to what students say, as the teacher realizes that what students say and do call for deeper, or different, understandings. One goal of this chapter is to address the question, “What causes teachers to elaborate or explain, and what shapes the ways they do so?” I argue that a teacher’s choice of which explanations to make, and when and how, can be modeled as a function of that teacher’s knowledge, goals, and orientations. That is, in-the-moment explanatory or elaborative choices made by teachers are shaped in very specific ways by the teacher’s beliefs and orientations regarding the content, the student(s), and what constitutes appropriate pedagogy; by planned and emergent goals as the lesson unfolds; and by the content and pedagogical knowledge the teacher has available and his or her perception of its relevance and utility in this context. In this chapter I outline a theoretical framework characterizing the relationship between teachers’ knowledge, goals, and orientations as they play out in the classroom and exemplify the framework with discussions of teachers’ explanations and elaborations of mathematical ideas. I also expand on Leinhardt’s framing of explanations to include not only the clarification of content matter, but various process goals including the establishment of classroom norms intended to help students develop productive habits of mind.