부산대학교 도서관

Sociocultural perspectives on learning highlight varied conceptions of what it means to know and do mathematics, and in turn what it means to be mathematically competent. This work 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. This paper brings together research on children's mathematical thinking, classroom practice, and the ways in which competence is constructed in interaction through a focus on the ways in which one third-grade teacher negotiated a common tension in reform classrooms--centering children's ideas while engaging them in focused, substantive mathematics. Qualitative video analyses of classroom interactions revealed that the teacher created varied and multiple ways for students to participate by both supporting them to engage with the details of each other's ideas and by broadening what was recognized as competence. Constructing competence around and in relation to students' explanations and engagement with each other's ideas created space for students to participate in a range of ways that were recognized as competent while also advancing the mathematics under discussion. These findings illustrate the relational nature of competence, and suggest that examining competence in relation to children's thinking can provide a potential way to bring together learning about who children are and how they participate, the details of the mathematics, and the contexts in which particular instructional practices are effective.