A Closer Look at Teacher Moves in Mathematically Responsive Interactions

• In Event: Analyzing Teachers’ Responses to Student Mathematical Contributions During Whole-Class Interactions: Goals, Grain Sizes, and Coding Schemes

Abstract

Our approach to investigating teachers’ responses to student mathematical thinking grows out of a larger project studying what we call mathematically responsive interactions. Our stance is that participating in mathematical discourse is inherently a responsive act, for both listeners and speakers (Bahktin, 1986; Halliday, 1978). In that vein, we define responsiveness to students’ mathematical thinking as a characteristic of interactions wherein students’ mathematical ideas are present, valued, attended to, and taken up as the basis for instruction. This perspective is grounded in sociocultural theories of teaching, learning, and interacting and is consistent with the vision of instruction advocated for in policy and standards documents (NCTM, 2000; NCTM, 2014).

The framework we developed is comprised of two interrelated components that describe the responsiveness in teacher-student interactions during whole-class discussions: (a) students’ mathematical contributions and (b) the moves teachers enact in response to these contributions. Here, we focus on the second component, Teacher Moves. We created three categories of Teacher Moves (Confirming & Correcting, Probing & Publicizing, Engaging Others) that reflect the extent to which teachers take up, make public, and use students’ mathematical contributions as the basis for whole-class discussions. In Confirming & Correcting interactions, teachers do not use students’ mathematical contributions as the foundation for discussion; instead, the teacher’s ideas typically drive discussions. Teacher moves include brushing-off, evaluating, funneling, and acknowledging students’ contributions. In Probing & Publicizing interactions, teachers work to understand and highlight individual students’ thinking by asking probing questions or revoicing student ideas. In interactions defined as Engaging Others, teachers simultaneously focus on student thinking and direct students to engage significantly with peers’ mathematical ideas. Because the class is engaged with others’ mathematical ideas, student thinking drives instruction. And when student thinking is the basis for collective mathematical activity, conversations have greater potential to support deep mathematical understandings (Ing et al., 2015). Teacher moves in the Engaging Others category include requesting comparisons across student contributions, taking up a student-posed problem as a whole-class activity, asking students to restate or apply another’s strategy, and inviting students to ask questions of their peers. The unit of analysis for all coding is a segment, defined as a series of turns of talk with a common focus (e.g., activity or strategy). Note that a lesson might contain anywhere from 8–25 segments during whole-class instruction. Our goal, then, is to describe the overall responsiveness of Teacher Moves for an entire lesson. Another important point is our coding of Teacher Moves is holistic at the segment level; for example, a segment may be characterized as Engaging Others even if it contains individual turns of talk that would be described as Probing & Publicizing or Confirming & Correcting.

We have used this framework to analyze over 30 lessons in 10 middle-grades classrooms across 4 grades. By documenting different categories of teacher moves throughout an entire lesson (and across multiple lessons), we can describe variation in responsiveness both across and within mathematics classrooms and have seen multiple ways teachers use student thinking to drive instruction.

Authors

• Jessica Pierson Bishop, Texas State University

• Hamilton Hardison, University of Georgia - Athens

• Julia Przybyla-Kuchek, University of Georgia - Athens