Fostering Flexibility Using Comparing Solution Strategies and Classroom Discussion: Effects of Two Professional Development Programs

Abstract

This article shows that enabling teachers to integrate comparing solution strategies into their teaching fosters student flexibility in algebra. We designed two professional development (PD) programs that either focused exclusively on comparing solution strategies, or additionally introduced the accountable talk approach to guiding productive classroom discussions. The effects of both PD programs were investigated in an experimental field study (N = 39 teachers, 739 students). In both experimental groups, student posttest gains in strategy flexibility and procedural knowledge were greater than in the control group. The accountable talk group also increased conceptual knowledge. Significant effects in strategy flexibility were still observed 2.5 months later. We discuss recommendations for PD programs to foster flexibility in algebra using comparing.

How Manuscripts Can Contribute to Research on Mathematics Education: Possibilities for Applied Research

“…Their contribution adds a field study component to earlier work by Rittle-Johnson and Star (2007) that documented the efficacy of contrasting cases in algebra in laboratory settings. Rüede et al (2023) found that when teachers were supported by professional development, students exposed to comparing solution strategies showed better gains in strategy flexibility and procedural fluency. The study contributes more evidence to the area of instructional improvement, suggesting that teacher professional development adds value to materials development.…”

“…The second pair of articles, Rüede et al (2023) and Clements et al (2023), could be described as cases of the documenting improvement efforts type, because they both assess the merit of approaches to improve aspects of the practice of mathematics education, albeit at different scales. Rüede et al (2023) situate their article in the context of algebra instruction and investigate the efficacy of an instructional approach that engages students in comparing solution strategies. Their contribution adds a field study component to earlier work by Rittle-Johnson and Star (2007) that documented the efficacy of contrasting cases in algebra in laboratory settings.…”

“…Furthermore, researchers often include in their limitations section the reductions in their assumptions about the system that their research design has necessitated. For example, though Rüede et al (2023) include an assessment of implementation fidelity of the teacher facilitation strategies, this was not done during the period in which they taught the unit on quadratic equations, when student gains from comparing cases were evaluated. Although this does need to be seen as a limitation, we would like to point out a way for us to see the proverbial glass half full: We think our field could productively consider that the identification of that limitation may move forward our understanding of what a pedagogy that is serviceable to comparing solution methods looks like and how to track it through observational research.…”

Orchestrating productive classroom talk in Swiss second grade mathematics classrooms

“…The talk sequence is only productive when the productive talk moves result in an interaction that meets the intended demands of the moves. However, various findings show that the number of productive talk moves can serve as a proxy for the productivity of classroom talk: The number of productive talk moves is positively related to the number, length, and content quality of student turns as well as to student performance (Chen et al, 2020;O'Connor et al, 2017;Pauli & Reusser, 2015;Rüede et al, 2023).…”

“…There are recent studies that have demonstrated the theoretically expected effects of orchestrating productive classroom talk on student performance in mathematics (Chen et al, 2020;O'Connor et al, 2015;Pauli & Reusser, 2015;Rüede et al, 2023), mostly in secondary school. However, there are also some studies that found no effects on student performance (in science and mathematics: Pehmer et al, 2015;in literature: Reznitskaya et al, 2012).…”