Designing for Mathematical Play

Mathematical play can center student voices, invite agency, and provide opportunities to investigate novel and challenging ideas. Studies of mathematical play suggest positive benefits for motivation, enjoyment, and learning, but the bulk of this work has occurred in the early grades, with few studies examining the potential affordances of mathematical play for adolescents and undergraduates. My team and I have designed and implemented playful mathematics tasks in the topics of function and covariation, calculus, and abstract algebra, examining the task and implementation features that supported students’ productive development and use of mathematics when playing. Drawing on four data sets, we have identified five design principles for developing playful mathematics tasks: (1) enable free exploration within constraints; (2) engender anticipation within the task; (3) provide a method of intrinsic feedback; (4) offer meaningful challenge while still being feasible; and (5) allow the student to act as both designer and player. I will share findings from three playful math tasks – Guess my Shape (exploring function families and covariation), Tropical Algebra Hangers (exploring identity and inverse in abstract algebra), and Major Tom (exploring the relationships between position, velocity, and acceleration) – along with a discussion of the task aspects that can foster students’ development of key mathematical ideas during play.