An Analysis of Two Different Approaches for Studying Teacher Responses

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

Abstract

The objective of this paper is to better understand the nuances of the two teacher response coding schemes discussed in this symposium by applying the schemes to the same excerpts of whole‑class mathematics discussion. For blinding purposes, the two coding schemes are referred to here as CS1 and CS2. Both approaches describe aspects of whole-class mathematics instruction, in contrast with other frameworks that focus on one-on-one conversations between the teacher and student (e.g., Jacobs & Empson, 2015). The perspective towards instruction framing the analysis in this paper is consistent with theoretical frameworks from which the two schemes were developed: (a) students engage in sense-making; (b) students collaborate and participate in mathematical discourse; and (c) instruction incorporates student thinking.

The data for the analysis were excerpts of classroom discussion selected by the two research groups, either because they had experienced them as particularly exemplary or problematic. Each excerpt was then coded by the developers of the other coding schemes. I looked across the two sets of codes, and the developers’ rationales for them, to identify nuances in their approaches.

CS1 describes the extent of teacher responsiveness using three categories of Teacher Moves (Confirming & Correcting, Probing & Publicizing, Engaging Others), while CS2 is composed of four categories (Actor, Recognition, Mathematics, Move) that disentangle components of teacher responses. The unit of analysis for CS1 is a series of teacher turns of talk during a segment of dialogue that focuses on a common activity or strategy. In contrast, the unit of analysis for CS2 is a specific teacher turn of talk in response to a student mathematical contribution.

The different categories and unit of analyses of CS1 and CS2 made different aspects of the teacher responses salient. I focus on the unit of analysis for one excerpt here, but will address other excerpts and differences in the paper. In the excerpt in Figure 3, using CS1 enabled the examination of the nature of the teacher’s questions and statements collectively, and led to the assignment of one code for the segment. In contrast, CS2 treated each teacher turn as an individual teacher response, resulting in codes for five distinct teacher responses (see Figure 3 for coding). The different units of analyses also impacted the understanding of which student’s mathematical thinking the teacher response incorporated. In Figure 3, CS1 captured that the teacher response engaged a student with another’s thinking, while CS2 identified both the actor and the contributing student’s likely recognition of their thinking for each teacher response. This glimpse into the analysis illustrates the holistic nature of CS1 and the detailed nature of CS2. As mentioned earlier, other nuances will be discussed in the paper.

While it is clear that teacher responses to students’ mathematical thinking matter (e.g., Ing et al., 2015), the field is just beginning to investigate teacher responses. CS1 and CS2 are two options for investigating not only the nature and responsiveness of teacher responses, but trends and patterns across teacher responses during whole-class interactions.

Author

• Ben Freeburn, Western Michigan University