Mathematical Argumentation in Small-Group Discussions of Complex Mathematical Tasks in Elementary Teacher Education Settings

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Mathematical argumentation is widely considered an important disciplinary practice, and teachers play critical roles in establishing opportunities in elementary school classrooms for students to develop, share, and evaluate mathematical arguments. In this chapter, we describe an ongoing project in which prospective teachers gain experiences participating in and facilitating small-group discussions centered on co-constructing mathematical arguments in response to complex mathematical tasks. We share our conceptualization of the primary components of mathematical argumentation in classrooms by characterizing the claims, evidence, and reasoning that individuals use as they construct arguments individually and collectively. Recognizing that traditional classroom discourse patterns limit efforts to promote mathematical argumentation among students, we argue that teachers’ and students’ classroom interactions can be enriched by explicit support from a discussion intervention. We introduce an established discussion approach, Quality Talk, which has been shown to foster students’ critical-analytic thinking across subject areas and contexts (Murphy et al., Sci Educ 102(6):1239–1164, 2018a, Quality talk: Developing students’ discourse to promote critical-analytic thinking, epistemic cognition, and high-level comprehension (Tech. Rep. No. 5). The Pennsylvania State University, 2018b, Am Educ Res J 55(5):1113–1160, 2018c). We draw attention to key Quality Talk discourse elements and scaffolding talk moves used by teachers and students during small-group discussions. Through two exemplar transcript segments from discussions involving prospective teachers and elementary students, we highlight the roles of such discourse elements in advancing the co-construction of mathematical arguments related to solving complex mathematical tasks. This chapter offers novel insights into mathematics teaching and learning by illustrating how discourse elements provide valuable tools for students’ engagement in, and teachers’ facilitation of, discussion-based mathematical argumentation. Such insights have potential to inform the work of teachers, teacher educators, and others engaged in elementary classroom contexts. Additionally, the dual lenses of mathematical argumentation and classroom discourse can further researchers’ and practitioners’ efforts to gain in-depth understandings of students’ mathematical thinking and growth.