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Open Access Publications from the University of California

Expanding Competence: Supporting Students to Engage with Each Other’s Mathematical Ideas

  • Author(s): Johnson, Nicholas Charles
  • Advisor(s): Franke, Megan L
  • et al.

This case study examined competence in two third-grade classrooms where teachers centered children’s mathematical thinking in instructional decision-making. Offering a 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 investigated how competence was assigned, the forms of participation assigned competence, and how these particular constructions of competence shaped the mathematics that students learned and the kinds of agency they exercised.

Analyses revealed two predominant ways of participating shared across both classrooms—providing explanation and engaging with others’ mathematical ideas. Constructing competence around and in relation to students’ explanations and engagement with each other’s ideas created space for students to participate and be positioned competently for making a wide variety of contributions, including ways of contributing available when their understanding of the mathematics was still emerging. The two classrooms surfaced and built upon students’ partial understandings in different ways, leveraging students’ explanations and engagement with each other’s ideas to support individuals to take up their space in class discussions while also advancing instructional goals. Analyses of an end-of-year problem solving assessment demonstrated that students developed a strong understanding of multiplication and division, both in relation to their own prior achievement as well as to that of their peers across the state. Thus, both classrooms expanded collective notions of competence, and were successful in supporting students to demonstrate their mathematical learning. The findings of this study 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 their mathematical thinking, and the contexts in which particular instructional practices are effective.

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