Mathematics and its metaphors

In Foundations of Embodied Learning, Nathan argues that learning relying on the body and sensory methods (embodied learning) is a natural human activity that is too often left behind in education, especially with higher grades (Nathan, 2022). As mentioned in the introduction, the duality between the mind and body is a concept still valued in our society, which brings many to believe that the more abstract mathematics is, the purer it becomes (Gerofsky, 2026). Although, mathematics ideas and learning mathematics are grounded on metaphors of embodiments and space (Nathan, 2022), which is an idea shared by Antonsen (2016) when he mentions that mathematics are metaphors (like the equality symbol) express with a specific language. Thus, connecting mathematics back with the body allows students to approach concepts under a different perspective, which could help them truly understand concepts and developing those metaphors rather than learning description of concepts by heart.

 

First Stop:

“A child might look like they are underperforming, but that performance is often mediated by learned descriptions of the world rather than working the world (Nathan, 2022, p.6)”

 

I had to read this sentence a couple of times before it became clear to me. In other words, Nathan (2022) argues that when a student look like they are struggling with mathematics concepts or problems, it is often due to the evaluation context. If we encouraged students to use resources they know well (objects, body movements, sensory methods) when evaluated rather than only fact retrieval and disembodied direct application of concepts, they might show much more understanding of the concepts. Thus, other than facilitating learning, evaluating mathematics in an embodied way can reflect more truly the competencies of a student. For example, this week we investigated to the effect of parameters in function using a graph calculator. Having read this article, I encouraged my students to show me how the curve moved with their body. By doing so, it was much easier for me to know if they were able to find the different patterns because moving like the graph is much easier for them to do than using words to describe the movements of the graphs.

Also, I noticed that moving first helped them connect the patterns to descriptive words (like compression, vertically, negative section, x-axis).

 

Second Stop:

“What makes mathematics difficult for many people is not their inability to understand the ideas, but to learn the meaning of the formal notation and how it describes these basic ideas and their variants (Nathan, 2022, p.147).”

 

This quote struck me because of the connections I was able to make with a previous course, my practice, and this week activity. In a previous course, we learned that mathematics is a form of discourse and students need to learn its norms, language, and symbolic tools (Sfard, 2001). I needed this quote by Nathan (2021) to fully understand this idea. In other words, the norms and language of mathematics expressed in symbols are charged in meanings and metaphors. If one struggle to grasp the metaphor of a symbol, instead of being able to manipulate the idea, they will be doomed to learn its particularity by heart, which is an impossible task. For example, when I first started teaching, I noticed that my students were rarely using measurements in the metric system while describing routes or objects to me. I started wondering how strong their understanding of measurements, area, volume, and similar solids could be if metric measurements were not part of their daily life. Indeed, I felt like many of my students were learning volume formula by heart rather than constructing them in depending on the solids they were looking at. Thus, I started using body measurements (like this week activity) when we are looking at geometry concept. I wonder if I could push this metaphor further and make them be the area and volume of a solid by making them cover or fit into different solids.

 

In brief, by bringing different approaches to concepts, especially embodied approaches, it helps students to develop their narrative of mathematics concepts. What metaphors do you recall relying on to learn mathematics concepts? Which ones do you use when you teach? Are there concepts that you think would benefit from using different perspectives to be better understood? For example, I feel like the meaning of the equality symbol is a concept I still have students struggling to understand truly.

 

References

Antonsen, R. (2016, December 13). Math is the hidden secret to understanding the world. [TED talk]. Youtube. https://youtu.be/ZQElzjCsl9o

Nathan. M. (2022). Foundations of embodied learning. Taylor & Francis. DOI: 10.4324/9780429329098

Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational studies in mathematics, 46(1), 13-57