This post is about the language of mathematics. I find it quite funny when 1 says: “Often mistaken for I, preserving everyone’s identity when used to multiply (Petsinis, 2026).” But would my partner find it funny too? Would he ‘get the joke’? During this conference, there were many instances where two people were talking to each other and understanding each other, but I had no clue of what was happening.
Sfard (2007) mentions that mathematics is a type of discourse and that it is hard to learn new concepts (names) without anchoring them in something familiar. Thus, teaching mathematics should aim to connect the new knowledge to something familiar (Sfard, 2007) in a way that students develop an operational understanding of concepts (Sfard, 1991). I believe that art could be the link between making mathematics visible in a way that reaches more students in the classroom. Afterall, Aylieann MacDonald (2026) mentioned that mathematics can be seen under different perspectives with a beautiful image. Today, when Dave Whyte was showing his animation of points, I could not help but see how these points could become a function represented on a graph for my students. How asking a point to obey a ‘rule’ to follow a path that would end up satisfying them with the shape they desire could be what they are missing to develop an operational understanding of the different representations of functions. Because I spend most of my time teaching function and I understand the language of function, but what if my students do not have a familiar idea to connect function to? A visualisation created by a deep and engaging creative process can definitely help them anchor it to a more familiar concept than the Cartesian plane.
References
MacDonald, A. (2026, August 5th). It’s about time [Conference presentation]. Bridges 2026, Galway, Ireland.
Petsinis, T. (2026). Euler’s vision. Proceedings of Bridges 2026: Mathematics and the Arts. https://archive.bridgesmathart.org/2026/bridges2026_Supplement_111.pdf
Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational studies in mathematics, 22(1), 1-36
Sfard, A. (2007). When the rules of discourse change, but nobody tells you: Making sense of mathematics learning from a commognitive standpoint. The Journal of the Learning Sciences, 16(4), 565-613
Noemi, your post really made me think about what it means to describe mathematics as a language. I was especially struck by your observation that there were times at Bridges when two people were having a mathematical conversation and you had no idea what they were talking about. I had many of those moments too! It made me think about how important a shared mathematical language is for creating access to mathematics. At my school, we are talking about making a more intentional effort this year to develop a common mathematical language across our classrooms, and your post made me see this goal in a slightly different way.
ReplyDeleteThis feels particularly important in my school because we have such a large population of English language learners. Mathematical vocabulary can become another layer of challenge when students are already developing English. If we want students to participate in mathematical conversations, then we need to make sure they have access to the language of those conversations. Sfard (2007) describes mathematics as a discourse, and I think this idea connects strongly to the work of creating a common mathematical language in our classrooms. If students do not yet have the language to participate, they can be left outside the mathematical conversation even when they may have mathematical ideas to contribute.
At the same time, your post made me think about whether a common mathematical language necessarily has to mean one common way of communicating mathematics. I really liked the connection you made between Dave Whyte’s animation and functions. I honestly would not have immediately made that connection myself. As I watched his points moving, I was thinking more about the animation itself than about how those points might become a function. Your description made me realize another way of seeing the mathematics.
That has me thinking about my own interest in art as an access point to mathematics. Perhaps students do not always need to begin with the formal language of mathematics. They might first encounter an idea through an image, movement, making, or another visual representation and then develop the mathematical language around something they can already see or experience. In that sense, the art is not replacing the mathematical language; it is providing an entry point into it.
I also appreciated that you began your post with the experience of reading the mathematical play, even though you said the post was not really about that. I think it actually does connect. I loved experiencing how quickly our group moved from being strangers to becoming a community through the play. There was something about sharing the story, the humour, and the performance that gave us a common language, even before we knew one another. That feels connected to what I have experienced throughout Bridges. Mathematics can sometimes feel like a language that separates us when we do not understand it, but it can also be a language that brings people together.
Maybe that is what I am taking from your post: creating a common mathematical language is important because it can help ensure that students are not left outside the conversation. But perhaps our role as teachers is also to provide multiple ways for students to enter that conversation. Your example of seeing functions in Dave Whyte’s moving points made me wonder what mathematical ideas my students might already be able to see, make, move, or represent—even before they have the formal words to describe them.
References
Sfard, A. (2007). When the rules of discourse change, but nobody tells you: Making sense of mathematics learning from a commognitive standpoint. The Journal of the Learning Sciences, 16(4), 565-613
@Noemie,
ReplyDeleteThe term discourse brings me back to our Early Years course with Dr. Matthews in which we also have a discourse with ourselves. I find it intriguing that I've claimed to understanding abstract ideas floating around non-linearly in my brain but have become extremely challenged to verbalize in a narration out loud to myself or others: If we cannot explain it to ourselves in a way that makes sense, then do we really know it at all? This extends to language in general and how we experience the world. I agree with Ludwig Wittgenstein (1921) wrote, "the limits of my language mean the limits of my world". I've taken a walk along the same streets, but one day I learned about a new flower, and now I see that flower everywhere along those streets. It's not like they weren't there before, but instead I filtered them out of my experience because I didn't have the awareness or attention to perceive them as significant.
Like Sfard said about anchoring understanding in prior familiar experiences first, the shared vocabulary of any arts in tandem with the vocabulary of mathematics greatly expands the set of words used to be able to communicate a concept and have someone else understand it. I agree with you that arts (any of them as a means of self-expression we've been practicing since childhood) could indeed be used to enhance our understanding of mathematics (and conversely, have mathematics enhance our understanding of the arts)!
I wonder how many patterns are being filtered out of perception by my students because they are unaware of their existence or they don't have the vocabulary to discriminate between them.