Building on the work of teachers: Augmenting a functional lens to a teacher-generated framework for describing the instructional practices of responding

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Abstract

We offer a framework for analyzing teachers’ practice of responding to students’ mathematical contributions. This work builds on a framework developed by secondary mathematics teachers that we then augmented with one developed by linguists to create a modified framework that addresses pedagogic responding moves in detail. We show, through in-depth transcript analysis, along with commentary by a teacher and researcher, how the modifications support teachers and researchers to better understand how the dual focus on particular moves and their functional organization shapes discourse to support learning. The resulting framework is situated in the efforts toward building a common language of practice useful for enabling teachers to see and intervene on their own practice while supporting researchers to build theory about how teachers’ instructional practices shape classroom discourse.

Introduction

The longstanding interaction pattern of IRE (Initiation-Response-Evaluation), first identified by Mehan (1979), is pervasive (Stigler & Hiebert, 2009) and problematic in mathematics classrooms in the U.S (Edwards & Mercer, 1987; Borasi, 1990). Specifically, researchers have noted problematic patterns in the way that mathematics teachers in the U.S. respond to students’ mathematical contributions (e.g., Son & Crespo, 2009). For example, mathematics teachers often handle correct answers by moving on, praising, or repeating the students’ contribution for the benefit of the class (Ball, 1988). Similarly, teachers frequently handle incorrect answers by ignoring and identifying another student to answer or reinterpreting the incorrect answer to fit the teacher's expectation (Stigler, Fernandez, & Yoshida, 1996). These largely evaluative methods for responding to students are problematic because they fail to be responsive to students’ mathematical thinking (Ball, Lubienski, & Mewborn, 2001; Jacobs & Empson, 2016).

Research suggests that one way to improve instructional practice, is to develop a common language and framework for examining practice that can aid both research on teaching and teaching practice (e.g., Ball, 2010; Lortie, 1975). According to Grossman and McDonald (2008), Such a framework for teaching would require a careful parsing of the domain, an effort to identify the underlying grammar of practice, and the development of a common language for naming its constituent parts (p. 186).

If our hope is that such a framework would make a difference for practice, it must also make incisions at the places that make a meaningful difference in the interaction and be sensitive to the needs of practitioners. Presently, research on teaching parses instructional practice in ways that are still relatively inaccessible to teachers, describing practice at a much larger scale (e.g., avoid lecturing, build on student's ideas) than is useful for teachers’ actual practice as enacted minute-by-minute in the classroom (e.g., Grossman, Brown, Schuldt, Metz, & Johnson, 2013; Herbel-Eisenmann, Drake, & Cirillo, 2009). The field of education has not yet “developed extensive knowledge of the detailed pedagogical practices that are helpful for teachers to learn, yet the difference between effective and ineffective teaching probably rests in the details of moment-to-moment decision making” (Boaler & Humphreys, 2005, p. 53). Furthermore, many have documented the ways that tools from research need adaptation to take into account discursive practices specific to the kinds of things teachers do (e.g., Herbel-Eisenmann et al., 2009; Pimm, 1994).

In this paper, we offer a framework for parsing teachers’ instructional practices of responding to students’ contributions, that we and others have identified as critical for teacher's practice (e.g., Milewski & Strickland, 2016; Brodie, 2011; Franke et al., 2009). The framework developed from a bi-directional research-practice partnership—originally drafted by a group of secondary mathematics teachers (with help from educational researchers) interested in analyzing and improving their own instructional practices. In that work, teachers developed a list of moves to account for the variety of things a teacher could say to respond to students’ mathematical contributions (Milewski & Strickland, 2016). In our prior work, we describe how that framework, made up of 20 discursive moves, proved useful in supporting those teachers to analyze and shift their instructional practices. However, we noticed ways that the teachers would have benefited from more explicit connections between the moves and the ways those moves shaped the discourse.

We build on that work here—describing how we have adapted the Teachers' Framework by comparing it with a similarly-purposed framework from linguistic research using the process of comparative analysis. The results of that analysis organize the teachers’ list of discursive moves into functional categories, resulting in a framework describing teachers’ practices of responding in a way that is accessible for practitioners by attending to particular discursive moves and the larger functional categories useful for building theory about how teachers’ instructional practices shape classroom discourse. We illustrate that modified framework's potential for illuminating aspects of practice that resonate with both teachers and researchers.

Section snippets

Background & research purpose

The original framework this work is based on was drafted by a set of secondary teachers in the context of a research-practice partnership. That partnership, facilitated by the first author, supported a district-team of secondary mathematics (n=3) and science (n=2) teachers who were interested in working on shifting their discursive practices to better support students’ engagement in mathematics (Milewski, 2012). Embedded in that partnership, the first author conducted a research study focused

Literature review: Examining frameworks for responding from educational research

When choosing a framework to compare with the teachers’ work, we began by considering some of the similarly-purposed frameworks from educational research. We found those frameworks, however, difficult to compare to the teachers’ work. Rather than comprehensively describing all of those frameworks, we elect to illustrate the kinds of difficulties we found in locating a framework from educational research.

Some of the frameworks were difficult to compare to the teachers’ work because they were

Theoretical framework: Looking beyond educational research for an analytic framework for comparison

The challenges we faced in comparing the Teachers' Framework to similarly-purposed educational frameworks suggested we needed to look beyond educational research. In recent years, educational researchers have looked to Systemic Functional Linguistics to locate tools for describing the structure of discourse in mathematics classrooms (e.g., González & DeJarnette, 2012; Herbel-Eisenmann & Otten, 2011; Mesa & Chang, 2010; Schleppegrell, 2007). Though none of the above-cited educational

Research questions

As described earlier, our purpose was to both take up the teachers’ ways of parsing practice while leveraging resources from research in order to modify the Teachers’ Framework so that it could better inform the teachers’ work (where by better inform, here we insist on the importance of including moves that might be considered aspirational as well as ones a teacher may want to use more sparingly), maintain respect for their contributions, (and thus attend to maintaining a focus on reacting

Research question 1: How do the frameworks compare?

To answer research question one, we compared the Eggins-Slade Framework to the Teachers' Framework to develop a Modified-Responding Framework which retained elements from the teachers’ work, but also attended to the functional affordances of the Eggins-Slade Framework. Using comparative analysis, we identified 26 overlapping and 24 non-overlapping moves across the frameworks. Of those 24 latter moves, we (a) added six moves that the Eggins-Slade Framework offered, which the teachers had not

Research question 1: How do the frameworks compare?

In our first round of comparison, we noticed some of the Eggins-Slade Framework moves (n=9) did not have matches in the Teachers' Framework because they are uncharacteristic for the pedagogic exchanges teachers examined. For example, even with shifts toward reform, it would be abnormal for a teacher to react to a student's mathematical contribution using a withhold—"I have no idea what a quadratic equation is". If a teacher elected to use such a move (perhaps with playful sarcasm), its purpose

Conclusion

In this section, we review some of this article's contributions and then situate the Modified-Responding Framework in the larger body of research on studying instruction. We also provide some ideas for using the tool towards those ends. Related to research question 1, the analytical framework we present here adds a new dimension to the ways the field presently accounts for teachers’ instructional practices of responding, namely a functionally-linguistic perspective. This would not have been

Acknowledgments

We would like to express our appreciation to Dr. Mary Schleppegrell, Dr. Patricio Herbst, and many members of the GRIP lab at the University of Michigan School of Education for their valuable and constructive suggestions during the early development of thismanuscript. Their willingness to give their time so generously is very much appreciated. We would also like to thank the editors and anonymous reviewers (particularly Reviewer 1) of Linguistics and Education for their careful reading of our

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