From mathematical play to playful math

Abstract

Mathematical play can support student agency and engagement, offer learning benefits, and foster productive mathematical dispositions. However, the bulk of research on mathematical play investigates the mathematics that emerges in young children's natural play or in students’ play in informal spaces such as video games. We introduce the term “playful math” to describe the activities and features of an instructional environment that can facilitate mathematical play, and we investigate the efficacy of incorporating playful task design elements into algebra activities. Drawing on two small-group teaching experiments with middle-school students, the first with two participants and the second with three participants, we identified 13 phenomena characterizing students’ mathematical play activity: Competitive Fun, Feeling Proud, Enjoyment, Wonderment, Taking on Authority, Perturbation, Investment, Immersion, Agency, Perseverance, Creative/Unusual, Harder Math, and Laughter. We found that all phenomena except Wonderment and Perturbation occurred more during playful math tasks. We describe two vignettes exemplifying the mathematical play phenomena and discuss implications for task design and instruction.