Week 5 Post

Reading

Kelton, M. L., & Ma, J. Y. (2018). Reconfiguring mathematical settings and activity through multi-party, whole-body collaboration. Educational Studies in Mathematics, 98(2), 177–196. https://doi.org/10.1007/s10649-018-9805-8

 

Introduction

Kelton and Ma (2018) explore how multi‑party, whole‑body collaboration can transform mathematical learning by reconfiguring both activity and space. Grounded in theories of embodied cognition and the social production of space, the authors argue that mathematics learning is inherently bodily, interactive, and situated. Rather than viewing classrooms as neutral containers or cognition as primarily mental, they conceptualize learning spaces as dynamically produced through collective bodily action.

The study presents a comparative analysis of two instructional cases using micro‑ethnographic and multimodal methods. In the first case, Walking Scale Number Lines (WSNL), students work in a gymnasium where a large taped number line allows them to physically enact numerical positions and operations such as scaling and opposites. Students’ bodies function as mathematical objects, and coordination challenges—such as avoiding collisions while moving simultaneously—become central to mathematical reasoning. The fixed spatial structure of the number line interacts with students’ movement to shape emerging mathematical practices.

The second case, Whole and Half (W + H), takes place in a fifth‑grade classroom and focuses on ratio and part–whole relationships. Students work in pairs to create and respond to bodily intervals using hands, arms, and full‑body positioning. As students move away from desks and incorporate features like floors, walls, and boards, the classroom space is reconfigured. Mathematical objects in this case are highly mobile, shifting as bodies move and enabling creative extensions of the task.

Across both cases, the authors show that interactional breakdowns are simultaneously social and mathematical, revealing the inseparability of coordination, space, and meaning‑making. Kelton and Ma conclude that intentionally designing for whole‑body, collaborative activity can expand participation, reposition learners as active components of mathematical objects, and open new possibilities for collective mathematical sense‑making.

 

Reflection

One idea that particularly stood out to me in Kelton and Ma (2018) is their claim that “the physical spaces of learning should not be treated as static boxes waiting to be filled with human activity, but instead as complex, historically constituted, dynamically experienced, and socially produced settings” (p. 178). I find this perspective compelling because space itself is deeply mathematical. Many areas of mathematics—such as geometry, vectors, transformations, and even advanced calculus—are fundamentally built on spatial concepts. From this standpoint, it feels limiting to treat space merely as a neutral backdrop for learning. Instead, space should be understood as an active component that shapes how students experience, interpret, and engage with mathematics.

I strongly agree that learning spaces can provide students with different sensations, orientations, and perspectives that support mathematical thinking both mentally and physically. Even when students’ movements in space are not directly aligned with specific curricular content, those movements can still support mathematical processing. Walking, repositioning, and orienting oneself spatially can serve as ways of organizing thought, testing ideas, and developing intuition. Learning, therefore, does not only happen when students are seated and focused on formal representations; it also happens through bodily engagement with space.

A second passage that resonated with me states that “participants creatively leveraged new possibilities for—and constraints on—physical movement in relation to the environment in order to make innovations and elaborations on the mathematical task” (p. 192). This idea is clearly illustrated in the classroom activities examined in the study. For example, in the Walking Scale Number Line activity, students’ bodies functioned as points on a number line, and the need to move simultaneously without colliding led them to invent new mathematical strategies, such as rotating their bodies together to represent opposites. What began as a practical problem of physical coordination became a meaningful way to experience multiplication by −1. Similarly, in the Whole and Half activity, students used their bodies to create and respond to intervals, creatively incorporating classroom features like the floor, walls, and Smart Board to extend the task.

These movements were not distractions but central to students’ mathematical reasoning, as they adjusted their actions in response to spatial constraints and opportunities. Together, these examples demonstrate experience‑based learning in action: students adapt to changing physical conditions, negotiate meaning collaboratively, and deepen their understanding by making mathematics tangible through movement and space.

As a future teacher, this reinforces for me the importance of designing conditions rather than tightly controlling outcomes. When teachers intentionally create environments that invite movement, exploration, and collaboration, they can reduce conceptual gaps and misunderstandings. More importantly, such environments empower students to think critically, challenge themselves, and develop deeper, more flexible understandings of mathematics through embodied experience.

 

Question

Have you had experiences in school‑based learning where physical space—such as seating arrangements, classroom layout, or opportunities to move—shaped how you understood or engaged with the lesson? How did those spatial arrangements support or limit your learning?