Reconfiguring mathematical settings and activity through multi-party, whole-body collaboration- Molly L. Kelton • Jasmine Y. Ma
This article examined how
multi-party whole-body collaboration can reshape mathematics learning by
reconfiguring the body/spaces/mathematics relationships. Based on theories of
embodied cognition and the social production of learning spaces, the authors
contended that mathematics learning is not only cognitive and symbolic but also
physical, social, and spatial.
Through two case studies of
students’ mathematical experiences, a walking scale number line activity at a gym
and a Whole and Half ratio and proportion activity at a classroom, the study
illustrates the role of students’ bodies during the production of mathematical
objects. The role of students’ bodily movements, their interactions with peers,
and their positioning incorporate mathematical meaning, as disruptions to these
movements highlight the impossibility of separating the social and the mathematical.
The results indicate that intentionally
using designs that engage the whole body and collaborative movement hold promise
for expanding our notions of mathematical activity. Whole body collaborations
that generate productive friction within traditional spaces of school
mathematics can lead to new possibilities for "sense-making,"
"creativity," and "engagement."
Stop1: When bodies became
mathematical objects
I stopped, particularly when the
authors talked about situations when “the students' own bodies became
mathematical objects, for example, by standing on a number line or forming
whole and half intervals with their hands.” What struck me, however, was that
these concepts of movement, space, and coordination were not just informing or
supporting mathematical concepts; they were actually the mathematics itself.
That is, when the students bumped into each other or had to stop and wait for a
partner before they could proceed, mathematics was disrupted. This stop helped
me see mathematics as something that emerges through interaction, not just
through symbols on paper.
Stop 2: When classroom space was
“edited” for learning
I stopped when, in the Whole and
Half activity, students started using unexpected parts of the classroom-the
floor, Smart Board, and open spaces between desks-to build and extend
mathematical intervals. This was a striking moment because it shows how learning
spaces are not fixed entities; they are mobilized by how students move and act
within them. I stopped here because this made me think of how often classroom
routines restrict movement and reduce creativity. In this activity, students
reimagined the classroom and used their bodies to investigate increasingly
complex ideas. At this stop, I wondered how many mathematical opportunities are
lost each day when classrooms are built to keep bodies still rather than
allowing movement to support thinking.
Question:
I wonder what new possibilities for
inclusion and sense-making might emerge if students are encouraged to edit
spaces on the floor, on the walls, and in open areas as part of their
mathematical activity, and what supports teachers might need to make this
workable.
Thank you, Rosmy. This article helped me think more deeply about how space, movement, and wholebody collaboration can transform mathematical sensemaking. What struck me most is the authors’ argument that bodily action does not simply support mathematical thinking—it actually constitutes the mathematics. When students positioned their bodies on a walking number line or formed “whole” and “half” intervals with their hands, their spatial coordination, timing, and interactions became central to the mathematical ideas being produced. Disruptions—like bumping into each other or pausing for a partner—were not distractions; they revealed how mathematics unfolds through interaction.
ReplyDeleteI was also captivated by how students “edited” the classroom in the ratio and proportion activity. By using the floor, the Smart Board, and the open spaces between desks, they reimagined what counts as a mathematical workspace. Their creativity only emerged once the physical environment became flexible. This made me reflect on how traditional classroom routines often silence movement and, with it, many opportunities for sensemaking.
This raises an important question: What new forms of inclusion and engagement might appear if students are routinely encouraged to use the floor, walls, and open areas as tools for mathematical reasoning? For many learners—especially those who think spatially, physically, or socially—embodied spaces could offer entry points that paperandpencil tasks cannot.
To make this workable, teachers may need structural support, professional learning, and permission to embrace the productive unpredictability that comes with movement. But as the article shows, when students are free to innovate with space, entirely new mathematical possibilities emerge.
Rosmy, thank you for this. The way you describe the tasks makes the article easy to picture, and your writing has that nice balance of clarity and curiosity.
ReplyDeleteYour first stop is especially strong. The line you draw, that movement and coordination weren’t just supporting the math but were the math, is such a sharp insight, and you explain it in a way that makes the argument feel obvious once you see it. I also loved your second stop, because “edited space” is the perfect phrase. It captures how students weren’t simply moving around, they were actively redesigning the environment as part of the mathematical work, and you make that feel both exciting and a little unsettling in the best way, like: how much thinking do we accidentally shrink when we ask bodies to stay still all day?
One thing your post made me keep thinking about is what counts as learning when the mathematical object is being made through bodies and shared coordination. If the meaning is happening in timing, spacing, waiting, repairing, and negotiating, then translating it back into a neat written answer can sometimes flatten what students actually figured out together. And because your question is already beautifully oriented toward inclusion, I’m also wondering how “editing space” might open doors for some students while quietly making it harder for others, depending on comfort with movement, proximity, or being watched. I really appreciate that your question doesn’t just celebrate the idea, it invites us to imagine what teachers would need to make it workable and fair in real classrooms.