Reconfiguring mathematical settings and activity through multi-party, whole-body collaboration (Kelton & Ma, 2018)

Kelton and Ma’s (2018) work centres on a theoretical framework grounded in research on physical learning spaces as complex social sites that both produce and are productive of mathematical reasoning. The second pillar of their framework calls for more holistic perspectives on whole-body interaction, moving beyond earlier work in the field that has at times prioritized the hands. The third pillar highlights the entanglement of social space and bodies. In this section, Kelton and Ma (2018) argue that greater attention should be paid to the physical space of the classroom and its cultural-historical dimensions (p. 182).

The paper draws on two cases to enrich conversations about the possibilities and consequences of multi-party, whole-body mathematics. The first case is situated in elementary grades within a gymnasium featuring a walking-scale number line. Students moved alongside one another, encountering questions of safety when they faced the dilemma of needing to position themselves in spaces already occupied by others, resulting in occasional nudges. The second case involved a task called Whole and Half, in which one person creates an interval of space between two hands (or between a hand and the floor) to represent the whole, while a second person places their hand halfway within that interval. Overall, Kelton and Ma’s (2018) work reconceptualizes embodiment in mathematics as the “mutual inextricability of corporeality, intercorporeality, and space” (p. 194).

My first stop was Kelton and Ma’s (2018) observation that, within the walking-scale number line, students’ embodied orientations varied significantly: left and right, as well as negative and positive, depended on how students were facing one another. Because orientation was relational rather than fixed, mathematical meaning became unstable across bodies. To resolve this ambiguity, students turned to the static features of the gymnasium—such as the wall or the stage—as shared reference points for positioning themselves.

I found this moment particularly compelling because it reveals how mathematical understanding is initially rooted in individual, embodied experience rather than in abstract universality. What appears to be a simple number line becomes complex once bodies enter the space, as orientation, direction, and meaning must be negotiated socially. This challenges the common framing of mathematics as a universal language that operates independently of context. Instead, Kelton and Ma’s example suggests that mathematics can falter—or at least require renegotiation—when it is not meaningfully embodied and anchored in shared spatial reference. In this way, the gym itself becomes an active participant in mathematical sense-making, underscoring how space, bodies, and mathematical concepts are co-constitutive rather than separate.

Whose bodily orientations and ways of moving tend to be centered in your math classroom, and whose might be unintentionally marginalized?

My second stop also occurred in the first case, where one of the authors raised a concern for safety. As the paper focuses on multi-party collaboration, the presence of many moving bodies within a shared space introduced moments of physical risk, particularly when students needed to occupy the same positions on the walking-scale number line. However, rather than treating these moments as peripheral or accidental, Kelton and Ma foreground safety as an integral dimension of embodied mathematical activity.

I am still working to understand how the notion of safety is correlated with mathematical consequences, as Kelton and Ma (2018) assert. In the situation highlighted, a student had to physically move nearby peers in order to reposition themselves on the line. From my understanding, the walking-scale number line represents a model in which only one point can occupy a given position at a time. This aligns with common elementary school representations of a number line, where each value is typically associated with a single point or marker.

However, this constraint becomes less mathematically stable when considered alongside other uses of number lines. For example, when representing inequalities or solution sets, multiple points can be drawn above or below one another while still “occupying” the same numerical location. In this sense, the embodied number line may unintentionally impose a one-body–one-number rule that is not inherent to the mathematics itself. This raises questions about whether the safety issues observed are mathematical consequences, as the authors suggest, or instead arise from the physical limitations of the representation being used. 

When physical limitations and potentially unsafe interactions arise in embodied learning activities, how can teachers intentionally intertwine mathematical knowledge with movement in ways that support sense-making while preventing the production or reproduction of mathematical misconceptions? In the walking-scale number line, students had already learned about number lines prior to the activity—would you follow a similar timeline? I have also tried the opposite approach, implementing activities before explicitly teaching the concept (as in open inquiry), and I personally found this idealistic method to be non-productive and difficult for both students and myself to facilitate.