1. Embodied Measurement:
This week began with
calibrating my own body as a measurement system.
I recorded my handspan, cubit, fathom, pace, and other body-based units, and
noticed how these “ancient” measures immediately made mathematics relational
and personal. Rather than starting with centimetres and metres, I began with myself as
the unit, a reminder that measurement is not neutral, but deeply human and
cultural.
Measuring the World: My Garden Beds Dreaming about Summar!
I then used my full embodied measurement system to measure the garden beds I built from old railway ties. Each bed is approximately 3 fathoms long, ¾ of a fathom wide, and just under a cubit high a space I can feel, walk, and reach. What used to be “16 × 4 × 2 feet” is now something I know with my arms, steps, and body. I wasn’t just measuring the space; I was inhabiting it. This helped me see how abstraction grows out of experience, rather than replacing it.
Reading Summary:
Gerofsky (2011), Chapter 18
Seeing the Graph
and Being the Graph
In Chapter 18, Gerofsky (2011) explores how students come to understand graphs not only by seeing them, but by being them. She shows how gesture and movement help learners connect the changing horizontal values (x) with the changing vertical values (y), long before they can articulate this relationship formally. Gesture becomes a bridge to abstraction. Students trace, sweep, point, and move to express variation, slope, and change turning the body into a living coordinate plane. Rather than gesture being a “crutch,” Gerofsky shows it as a powerful generator of mathematical meaning.
Video Reflections:
Roger Antonsen – Math is the Hidden Secret to Understanding the World
My “Stops”
Stop 1 – Patterns
and Representation
Antonsen’s central idea that “math is about patterns and connections” stopped me immediately. I loved how he showed that mathematics is not about formulas first, but about noticing relationships, and then representing them in multiple ways. This is written into our curriculum but rarely understood to this depth. The space to ask questions, to wonder, to play with patterns, and to engage in dialogue is often missing. When Antonsen said this is where we get to do “the cool stuff,” I felt that deeply, because that is exactly where students begin to see themselves as mathematicians.
Stop 2 – Embodiment
and Meaning
What struck me most is
how naturally Antonsen connected mathematics to the human experience. His talk affirmed that abstraction is not the goal, meaning is.
Abstraction is simply one way of expressing that meaning once it has been
lived, felt, and explored.
Connections to My Practice:
Being the Graph
Gerofsky’s work immediately connected to a project I did with Grade 7 and 8 students where we built a life-size Cartesian plane using a tarp and tape. Students represented their yard sites on this giant coordinate grid, with the school as (0,0). In Grade 7 they created two-dimensional drawings, and in Grade 8 three-dimensional nets, then plotted themselves across the four quadrants. Reading about gesture helped me see why this worked: students were not just reading a graph; they were living inside it.
Another powerful stop was Gerofsky’s idea of using the body itself as the graph, with the navel as (0,0). I had never considered the body as a coordinate plane, and yet it makes perfect sense. The younger students in her study used finger movements and gestures to represent complex relationships that would otherwise be inaccessible. Their bodies carried the mathematics before the symbols ever could.
Final Reflection:
Why This Matters
This week reminded me that embodied mathematics is not “extra.” It is foundational. When students move, gesture, build, and measure, they are not avoiding abstraction, they are building it. Gerofsky and Antonsen helped me see that mathematics becomes powerful when we create space for experience, dialogue, and pattern-seeking, and when we trust the body as a legitimate mathematical tool.
Tracy, first of all - I am intrigued that you went out into the garden this week :) I too am dreaming about my summer garden despite the fact that it is absolutely freezing outside this morning! I love how you described inhabiting the space! That is a wonderful way to think about embodied learning.
ReplyDeleteGraphing with the body initially feels intimidating to me. But then I paused and thought about how often I act out a graph or relation or use my body to guide students in thinking about end behaviour of graphs. It also made me think about this math dance I have seen before https://www.youtube.com/shorts/OFzqDatEvCo. I like how you explicitly said gesture isn't a crutch but an important component of mathematical learning, which I think was an important through-line for all the articles this week.
I have not actually gone out to my garden beds and the image was when I first built them years ago. It is just wishful thinking because it is so miserable weather here today. I love the dancing graph I am going to share this with my high school teachers. https://youtube.com/shorts/OFzqDatEvCo?feature=shared
DeleteAmazing idea!!!
There is something thought-provoking and quite elegant about thinking of oneself as a unit. I didn't really frame the measuring activity in that way, but it makes quite a lot of sense. Even in our bodies, we may find smaller, more specific units on our limbs and extremities.
ReplyDeleteThe notion of inhabiting space reminded me of a quote from Gaston Bachelard's The Poetics of Space (1957): "It is better to live in a state of impermanence than in one of finality." Are our bodies themselves a place in which our consciousness lives? If someone prescribes to that philosophical contextualization of our bodies, then we must also understand that as we grow, age, and transform (whether intentionally or not), the unit of our bodies is deeply personal and dynamic. We can see this in Gerofsky's Being the Graph--to connect the Cartesian plane with one's own body shows that not only is mathematics personal and based on experience, it is unique to every single person's lived-in physical nature.
Raymond, I really liked how you framed the body as both a unit and a place where consciousness lives. That idea connects so strongly with Gerofsky’s “being the graph” for me. When students use their bodies to gesture, trace, and inhabit mathematical space, they aren’t just representing mathematics , they are becoming the representation. If our bodies are always changing, then our mathematical units are not fixed either, they grow, stretch, and adapt with us. That feels like such a powerful counter-story to the idea that mathematics is rigid, static, and detached from lived experience. It also reinforces for me why embodied experiences are not “extra” or “slow.” When I measured my garden beds with my body, or when my Grade 7 and 8 students lived inside a life-size Cartesian plane, abstraction didn’t disappear, it emerged. The symbols made sense because they were grounded in something we had felt, walked, and reached.
DeleteYou might enjoy this video of the history of the imperial measurement system: https://www.youtube.com/watch?v=6uaBJq-gd_o
ReplyDeleteSo many great insights in this discussion! Tracy, I love the idea that you are starting from your body, rather than from a cm or a metre, as the basic units for measurement. (And I'd love to see how your garden looks nowadays, once things start to melt a little!) Also wonderful, from Antonsen: that abstraction is not the goal...meaning is. How often we, as math teachers, feel that we are heading towards abstraction as the ultimate level of mathematical sophistication! But that seems to me like a musician heading towards printed sheet music, rather than to a more holistic, embodied and felt understanding of the music, which might benefit from dancing and moving to it rather than focusing on the abstract memory aid of sheet music!
ReplyDelete