A conceptualization of the teaching practice of building

In this theoretical paper, we present a conceptualization of the teaching practice of building—a teaching practice that takes advantage of high-leverage student contributions we call Mathematical Opportunities in Student Thinking (MOSTs). Specifying this complex teaching practice is important because it provides the detail needed for mathematics education researchers to study the nuances of teachers’ in-the-moment use of student thinking and for mathematics teacher educators to support teachers in developing such use. We describe key aspects and teacher actions associated with the four elements of building: Establish, Grapple Toss, Conduct, and Make Explicit. Throughout the paper we compare and contrast this decomposition with teaching moves and practices from the literature to illustrate the contribution of this work to understanding responsive teaching practices.