Fixing the Crooked Heart: How Aesthetic Practices Support Sense Making in Mathematical Play

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.

Children’s Games and Games for Children

This article examines the mathematical activity of five-year-old Liam to explore the difference between the mathematics games designed for children and the children's games that emerge through playful activity. We propose that this distinction is a salient one for teachers observing mathematical play for evidence of mathematical sense making.

“The Play’s the Thing”: Mathematization as Dramatization

Mobilizing prevalent themes in the fields of mathematics education, literary criticism, and philosophy, this paper contextualizes ‘the mathematical’, ‘mathematical thinking’, and ‘mathematical pedagogy’ with respect to ancient Greek concept of mathesis, modern notions of mathematical agency, the Keatsian concept of negative capability, and the analogy of ‘staging’ a dramatic/mathematical ‘play’. Its central claim is that mathematization is dramatization—that learning mathematics (indeed, learning to learn, which is what the Greek mathesis actually means) is an activity of setting things up and (in this ‘set’ or ‘setting’) allowing things to play out (e-ducere). Beginning with Paul Ernest’s identification of the difference between absolutism and fallibilism in the philosophy of math education, and incorporating concepts from Pythagoras, Hippasus, Heraclitus (the ‘ancients’), Descartes, Kant, Keats (the ‘moderns’), as well as Freud, Heidegger, and Badiou (‘nos prochains’, to quote Klossowski ), we argue that ‘mathematical knowledge’ cannot be understood simply within the framework of logicism, formalism, or even simply as an epistemological articulation. Rather, we endeavour to show that the process of ‘learning mathematically’ allows us to gain insight into the foundations of ‘being’ itself (i.e. ontology). Learning to learn (mathesis) proceeds, as such, by way of staging and playing-out the half-known or unknown (the ill-seen and ill-said) in the hopes of uncovering the mystery (Greek myesis) at the heart of things.

Investigate, because of the golden rectangle

“Investigate, because of the golden rectangle” offers mathematics students and enthusiasts inspiration for mathematical play by way of a guided construction of the golden rectangle. The discussion is illustrated with numerous hand-drawn sketches. A golden rectangle is a rectangle whose side lengths are in the golden ratio, which is, where the Greek letter (pronounced “phi”) is approximately equal to. Readers learn that an indirect, even haphazard, approach in mathematical play may lead to unanticipated discoveries. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.

Designing for mathematical play: failure and feedback

Purpose The purpose of this paper is to explore three different types of digital environments for mathematics learning that may support mathematical play and the failure and feedback mechanics present in each. Design/methodology/approach Interaction analysis and the lenses of failure, feedback and mathematical play are used to analyze the mathematical interactions afforded by three different digital environments. Findings Each digital environment supports or restrains the potential for mathematical play through mathematical representations, failure and feedback. Originality/value The primary contribution of this paper is to highlight different ways in which digital failure and feedback designs can influence the emergent experience of mathematical play.