UC Irvine

Problem-posing practices are considered important for nurturing students’ inquiry, learning, and agency in mathematics. In this dissertation study, drawing on socially situated frameworks of learning, I designed and investigated a math curricular unit, centered on problem-posing (as against just problem-solving), in low-tracked eighth-grade classes in a school serving predominantly working-class Latinx neighborhoods. I partnered with a mathematics teacher to co-design and implement problem-posing-based lessons with the goals to (1) understand how students gain entry to the practice of problem-posing, (2) investigate how learning processes unfold over time in interaction with peers, materials, and the teacher, and (3) shed light on the ways in which students negotiate their agency and social risks of posing a math problem. Research data include video-based observations, student written-work, reflections, and classroom artifacts collected in two different settings of task-based paired interviews and a classroom-based teaching experiment.

The study findings reach beyond the past focus on the cognitive aspects of problem-posing and its linkages with individual creativity and ability. Instead, they offer dimensions of mathematical doubts as a novel characterization to support expansive and agentic forms of student problem-posing (Chapter 1), an understanding of the sociocultural processes of productive posing (Chapter 2), and conceptualization of collective agency and risk-taking in problem-posing (Chapter 3). Together, the study findings elaborate on our understanding of how students become engaged problem-posers and the central role that student doubts and collective action play in supporting productive forms of posing. I also discuss how problem-posing practice is uniquely positioned to amplify capabilities, identities, and epistemic agency of students of color who get disproportionately sorted in remedial courses. The findings provide preliminary ideas of problem-posing pedagogy’s potential to challenge the deeply-rooted deficit discourse of race, poverty, and ability in education. The findings have implications for the design and analysis of inquiry-oriented learning environments in both formal and informal settings.