UC San Diego

This dissertation challenges the dominant view of mathematical problem-solving as disembodied and abstract by examining how disabled rock climbers problem-solve across the domains of rock climbing and mathematics. Drawing on enactivism, ecological psychology, and critical disability scholarship, this qualitative study centers six disabled climbers’ experiences in constraint navigation as an epistemic resource for reimagining mathematics education. Through focus groups, semi-structured individual interviews, rock climbing observations, and task-based mathematical interviews, this study addresses three research questions: 1) What are the affordances and constraints designed into the context of the problem space for rock climbing?; 2) What are individuals' perceived similarities and differences concerning problem-solving across the domains of (a) rock climbing; (b) mathematics; and (c) their daily lives?; and 3) What are the observed similarities and differences with regard to the problem-solving strategies amongst the domains of rock climbing and mathematics?Findings show that while participants initially characterized mathematics as decontextualized and disembodied, their enacted problem-solving in mathematics demonstrated cross-domain coherences when climbing expertise was explicitly positioned as relevant. Through grounded theory analysis, I created a holistic problem-solving framework with six interconnected dimensions -- Disposition, Affect, Efficiency, Environment, Expertise, and Strategies— revealing that attributes transfer in varied patterns while also flexibly responding to domain affordances and constraints. Exploring how disabled individuals navigate constrained environments can provide a magnifying glass into how learning can emerge from constraints. Ultimately, mathematics education would benefit all students by honoring the embodied intelligence they bring from rich lived experience.