Preservice Secondary Mathematics Teachers' Learning of Communicative Actions That Elicit and Extend Student Thinking

• In Event: Responding to Student Thinking in Secondary Mathematics Classrooms: Studying and Supporting Teaching Practice

Abstract

Objectives and Perspectives

While researchers have examined design issues (e.g., Authors, 2015) and PTs’ learning opportunities (e.g., Ghousseini & Herbst, 2016) in secondary mathematics method courses using a pedagogies of practice perspective (Grossman et al., 2009), little is known about what preservice secondary mathematics teachers (PSMTs) actually learn during these courses. The objective of this study is to examine what PSMTs, enrolled in a methods course designed using pedagogies of practice, learned about communicative actions that elicit and extend student thinking. Two theoretical constructs informed this study. The study uses a radical constructivist perspective on learning (von Glasersfeld, 1995) to model the PSMTs’ conceptions and the decomposition of practice construct from Grossman and colleagues to frame the object of the PSMTs’ learning. Specifically, a core practice of teaching, eliciting and extending student thinking, was decomposed into three communicative actions – asking assessing and advancing questions (Smith, Bill, & Hughes, 2008) and telling (Lobato, Clarke, & Ellis, 2005).

Methods and Data

Using qualitative data collection and analysis techniques, I constructed case studies (Merriam, 2009) of four secondary PSMTs’ learning of the communicative actions. The setting was a 15-week secondary methods course at a large mid-Atlantic university. Course activities were designed within a pedagogies of practice perspective and framed using the three aforementioned communicative actions. The data sources were classroom observations of twenty-eight course sessions (video-recordings, audio-recordings, classroom artifacts, and student assignments) and three audio-recorded interviews (beginning, middle, and end of the semester) with each participant about their thinking and learning of mathematics pedagogy. Since I did not have direct access to the PSMTs’ thinking, I created models of the PSMTs’ constructed conceptions using comparative analysis techniques. Then, cross-case analysis strategies (Miles, Huberman, & Saldaña, 2013) were used to search for themes across PSMTs’ conceptions.

Results

Findings were that the four PSMTs constructed conceptions of the communicative actions that built on and expanded the characteristics in the initial course descriptions. On one hand, the PSMTs’ conceptions described ways that communicative actions respond to student thinking. For example, the PSMTs’ conceptions were that advancing questions incorporate and build on student mathematical thinking. Another example, the PSMTs' constructed conceptions of telling involved a number of ways that telling may respond to students (e.g., repeating, inserting terminology). On the other hand, the extent to which the responsiveness honored and/or built on student thinking varied among the PTs’ conceptions. For example, two of the PSMTs’ conceptions of advancing questions involved asking these types of questions that guided students in a manner similar to funneling (Wood, 1998). The full paper will more thoroughly report the nuances of the PTs’ conceptions.

Scholarly Significance

In order to keep pedagogical approaches for methods courses from becoming fad-like, scholars need to investigate learning outcomes and the impact of course activities (McDonald et al., 2013). A contribution of this study is an illustration of the nuanced conceptions of communicative actions responsive to student thinking that PSMTs construct during a mathematics methods course designed using pedagogies of practice.

Author

• Ben Freeburn, Western Michigan University