Beyond the "Move": A Scheme for Coding Teachers' Responses to Student Mathematical Thinking

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

Abstract

Our objective was to develop a coding scheme to capture teachers’ in-the-moment responses to instances of student mathematical thinking (SMT). Our theoretical perspective is grounded in four core principles of quality mathematics instruction that we see embedded in NCTM (2014): (1) mathematics is at the forefront, (2) students are positioned as legitimate mathematical thinkers, (3) students are engaged in sense-making, and (4) students work collaboratively. Our examination of existing research revealed three important components to attend to in teacher responses: (1) student engagement in classroom communication, (2) responsiveness to students, and (3) attention to mathematics. We also found that existing research typically incorporated combinations of these components into their definition of “move.” To develop a more nuanced coding scheme, we disentangled these three components of a teacher’s response from the teacher move (Figure 1 includes our coding categories, their descriptions, and their connection to the literature). This disentanglement allows us to measure teacher responses against the core principles of our theoretical perspective, and provides a structure for other researchers to investigate teacher responses from their theoretical perspectives.

The resulting coding scheme includes four categories: (1) who is publicly asked to consider the SMT (Actor), (2) the degree to which the SMT is honored (Recognition), (3) the alignment between the mathematical focus of the teacher response and the mathematics that can be learned from the instance of student thinking (Mathematics), and (4) what the actor is doing or being asked to do with response to the SMT (Move). To flesh out our coding scheme (Figure 2), we analyzed over 600 instances of SMT and the corresponding teacher responses, where an instance is an observable student action or small collection of connected actions (e.g., verbal expression with a gesture) and a teacher response is the collection of observable teacher actions that begins as a given instance of student mathematical thinking ends and concludes when that instance of student mathematical thinking is no longer the focus of the observable teacher actions. The result was a set of carefully-defined, comprehensive codes for the four categories that coordinate to provide a nuanced understanding of teacher responses to SMT. Relevant to this presentation is the fact that the grainsize of both our instance and our teacher response is very precise. This precision supports our goal of capturing teachers’ in-the-moment responses to individual students’ thinking.

Our scheme is applicable across grade levels and mathematics content. It has descriptive power because it disentangles the teacher move from the actor, the degree to which the student thinking is honored, and the extent to which the response focuses on the mathematics of the student thinking. Thus, it paints a rich picture of the teacher response without being evaluative in nature. The researcher applying this coding scheme decides which combination of codes might be more or less productive based on their own perspective. The scheme’s flexibility makes it useful for a broad range of researchers interested in better understanding the teacher’s role in shaping meaningful mathematical discourse in their classrooms.

Authors

• Laura R. Van Zoest, Western Michigan University

• Blake E. Peterson, Brigham Young University

• Shari L. Stockero, Michigan Technological University

• Keith R. Leatham, Brigham Young University