Fostering Student Agency Through Playful Math

Speaker: Amy Ellis (University of Georgia) Abstract: Playful math describes the activities and features of an instructional environment that can facilitate mathematical play. This can include task features, instructional moves, interactions, and engagement with tools and artifacts. A key aspect of playful math is an emphasis on students’ agency to explore self-selected goals and to author novel problems. When crafting playful math environments, we shift the design role to the student, enabling students to construct and explore challenges for one another. We present findings from a project investigating the enactment of playful math activities, exploring students’ problem posing, learning, and engagement in the topics of function and graph translations, calculus, and abstract algebra. Drawing on three data sets with undergraduate secondary pre-service mathematics teachers and secondary students, we will describe examples of student authoring that introduced new mathematical directions and opened novel opportunities for exploration. We will share findings from three playful math tasks – Mystery Transformation (exploring transformations of the plane), Curve Tracing (exploring derivatives as scaling factors between two velocities), and Tropical Algebra Hangers (exploring identity and inverse in abstract algebra) – along with a consideration of the task features, instructional moves, and aspects of student interaction that supported their emerging agency through problem posing. Talk at the AMS Special Session on "Compassion as a Mathematical Practice" at the 2026 Joint Mathematics Meetings in Washington, DC. Browse the rest of the videos from this session in the following playlist:    • AMS Special Session on "Compassion as a Ma...