Making mathematical play visible through personal aesthetics in a digitized upper elementary mathematics classroom

This dissertation explores the nature of mathematical play in a technology-equipped upper elementary classroom, where play is rarely considered a legitimate form of mathematical engagement. Focusing on a Dynamic Geometry Environment (DGE) as an aesthetic space, I investigate how play merges through student interaction with mathematical objects and how personal aesthetics can help make it visible. Drawing on theoretical insights from Vygotsky and Huizinga about play, and informed by Sinclair's roles of personal aesthetics, this research treats aesthetics not merely as a lens for interpretation, but also as integral to the phenomenon of play itself. In playful mathematical engagement, students' personal aesthetics are activated: their intuitive decision-making, discovery and insight, surprise, sense of fit guide exploration among other qualities. As such, aesthetic experience both defines and reveals mathematical play. Classroom-based analysis of open-ended tasks in Sketchpad reveals how students' aesthetic responses illuminate episodes of play, and how play, in turn, activates personal aesthetics. I argue that when task design and digital environments are aligned to support open-ended exploration, mathematical play and aesthetic engagement form a mutually reinforcing loop. This dynamic enables students to make mathematical discoveries that are personally meaningful. The study follows a group of upper elementary school students as they engage with a sequence of tasks in Web Sketchpad. These tasks, ranging from structured polygon constructions to open-ended design challenges, were analysed using a framework of aesthetic indicators to reveal moments when engagement was playful. Data include classroom observations, screen recordings, student conversations, and design artefacts. Findings show that mathematical play flourished most in tasks that afforded aesthetic decision-making and interpretive freedom, and within environments that support play. When students experience mathematics as aesthetically meaningful, they begin to see it as a space to explore, imagine, and make personally resonant decisions. Supporting such engagement may be key to rethinking mathematics education for older students.