We build on mathematicians’ descriptions of their work and conceptualize mathematics as an aesthetic endeavor. Invoking the anthropological meaning of practice, we claim that mathematical aesthetic practices shape meanings of and appreciation (or distaste) for particular manifestations of mathematics. To see learners’ spontaneous mathematical aesthetic practices, we situate our study in an informal context featuring design-centered play with mathematical objects. Drawing from video data that support inferences about children’s perspectives, we use interaction analysis to examine one child’s mathematical aesthetic practices, highlighting the emergence of aesthetic problems whose resolution required engagement in mathematics sense making. As mathematics educators seek to broaden access, our empirical findings challenge commonsense understandings about what and where mathematics is, opening possibilities for designs for learning.
This material is based on work supported by the National Science Foundation (NSF) under Grant No. DRL-1643313. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF. We are deeply indebted to the NSF’s late Karen King, whose advocacy for this project made this research possible; Christopher Danielson, for his design of and invitation to Math On-A-Stick; Melissa Gresalfi (project co-PI), for her feedback and encouragement; Nathalie Sinclair and Leona Schauble, for multiple rounds of conceptual and analytic feedback; Rogers Hall, for methodological guidance; the early members of the Playful Mathematics Learning Team (Panchompoo [Fai] Wisittanawat, Kate Chapman, and Amanda Bell), for research design and data collection; and our reviewers and JRME editor Patricio Herbst, whose expertise helped us clarify the manuscript’s contribution.
Lara Jasien, CPM Educational Program, 9498 Little Rapids Way, Elk Grove, CA 95758; larajasien@cpm.org