Expanding Competence: Creating Space for Students to Engage with Each Other’s Mathematical Ideas

Nicholas Johnson

Recent efforts to investigate opportunities to learn in mathematics classrooms highlight varied conceptions of what it means to know and do mathematics, and in turn what it means to be mathematically competent (e.g., Boaler & Staples, 2008; Nasir, Hand, & Taylor, 2008). This work draws from sociocultural perspectives on learning and presents a dynamic conceptualization of competence—what counts as competent mathematical activity is negotiated and constructed within learning environments, and therefore varies across and within classrooms (Gresalfi, Martin, Hand, & Greeno, 2009). As dominant views of mathematical competence can overlook students’ varied ways know knowing and participating (Martin, 2009), unpacking competence and how it shapes and is constructed in interaction provides an approach to examine opportunities to learn as they play out in classrooms and schools. But while research on classroom teaching has begun to explore the ways in which engaging students with each other’s ideas can support learning while also positioning students to see themselves and others as competent contributors to classroom mathematical activity (Franke et al., 2015; Turner et al., 2013), little research has examined the specific ways that classroom interactions serve to construct what count as competent ways of participating, or relations between collective understandings of competence and other indicators of students’ learning.This dissertation presents a comparative case study of two third-grade classrooms where teachers supported students to engage with each other’s mathematical ideas. Offering a preliminary synthesis of sociocultural characterizations of competence, and drawing from a variety of data sources including classroom video, student work and assessments, and teacher interviews, this study investigates how competence is assigned, the forms of participation that are assigned competence, and how these particular constructions of competence shape the mathematics that students learn and the kinds of agency they exercise. Broadly, this dissertation seeks to contribute to the field’s understanding of how current reform efforts may be enacted in classrooms in ways that move beyond general descriptions of good teaching, through exploring the nuances of how specific supports, lesson structures, and interactions open or constrain opportunities for students to “take up their space” (Hand, 2012) in mathematics classrooms.

About Nicholas Johnson

Nick Johnson is a doctoral candidate in Urban Schooling at UCLA. He studies teaching and learning through the lens of children’s mathematical thinking. Prior to entering graduate school, Nick worked as a classroom teacher, instructional coach, and professional development coordinator and facilitator, supporting teachers to make use of research-based information about the development of children’s mathematical thinking. Nick’s work strives to build connections between research, policy, and classroom practice, and to better understand issues of equity as related to teacher learning and children’s schooling experiences.