In this week's article, Stylianidou and Nardi argue that tactile tools designed for visually impaired students can benefit all learners, as part of a broader study challenging "ableism" in mathematics education. The authors make an important distinction between two approaches to inclusion: "reasonable accommodation," which involves modifications that enable people with disabilities to participate equally with their abled peers, and "universal design," which creates environments and tools that can be used by everyone from the outset, without requiring additional accommodations. They examine what happens when sighted students and a visually impaired student named Luke explore the difference between two shapes through the sense of touch. One shape ("Shape X") is made with Wikki Stix (a flexible wax-and-yarn teaching material) and depicts a circle with a circular segment removed, creating a subtle flat edge. The other is a regular circular disk (the yellow circle). When students closed their eyes and used only touch, they easily detected the straight edge on Shape X. However, when viewing Shape X visually, the straight segment was much harder to notice because it occupied such a small portion of the otherwise circular shape. This is an example of how universal design benefits all: sighted students noticed details they would have otherwise missed, while Luke participated as a full member of the mathematical community rather than being singled out for special accommodations. Additionally, Luke's tactile-based insights—describing how a circle "feels like it's gonna roll more" while Shape X would "bob up and down"—enriched the mathematical discussion for everyone, challenging assumptions about what constitutes valid mathematical thinking.
The thing that struck me the most while reading this article was the difference between "reasonable accommodation" and "universal design." Though I have given some thought to these ideas in the past, they really gave me pause as I read this article. I am wrestling with understanding and wanting to ground myself in the idea of universal design. However, we live in a world that is deeply ableist. I see it in systems where students who are supposed to be included in the classroom spend their days wandering the halls or playing in the resource room. I see it in our classrooms as we emphasize reading over listening to books. It is everywhere, and I have been complicit. I tried to strike up a conversation with my husband about this idea—he spent 22 years working with blind students—and was surprised at his response. He immediately began explaining that not only were mainstream teachers resistant to learning how to accommodate, but VI teachers themselves were very protective and rigid about their established methods. Those working with visually impaired students one-on-one, classroom teachers, and even parents all seem to default to accommodation rather than embracing universal design. In other words, ableism is so ubiquitous that even those dedicated to supporting disabled students may unknowingly perpetuate it. The design and delivery of mathematical materials provides a clear illustration of this problem.
Mathematical thinking is typically constructed through textbooks designed for sighted students. Most of us visually imagine a circle based on our experiences of seeing circles everywhere. However, as Stylianidou and Nardi note, accommodations that simply translate visual materials into tactile ones—like Braille math textbooks—often have significant limitations. I've seen how the Braillist is frequently behind schedule, and how Braille doesn't translate directly from visual mathematics. The Braillist must deeply understand the math to translate it accurately, yet misinterpretations are common. This illustrates why the authors argue that reasonable accommodation, while well-intentioned, is insufficient. Universal design—where all students engage with the same tactile or multimodal materials from the start—eliminates these translation problems and the delays that leave VI students waiting for access while their sighted peers move ahead.
What makes this study significant is its focus on a modality typically associated only with visually impaired students, with the premise that it would benefit all learners. It offers an important change in perspective, which Roger Antonsen argues we need to truly understand something. The study’s approach also aligns with Sfard’s commognitive framework (Sfard, 2007), which defines thinking as individualized communication with oneself that emerges through social interaction. This tactile modality opens new pathways for students to engage in mathematical discourse together. When students describe shapes without using sight, they must articulate spatial relationships differently, leading to fresh mathematical insights. As Luke demonstrated, describing a circle as something that "feels like it's gonna roll" offers a perspective that enriches everyone's understanding. This raises important questions: What new mathematical understandings can we arrive at when we deliberately shift our sensory perspective? How might universal design not only include more students, but actually deepen mathematical thinking for all?
Finally, I have one last burning question for us to ponder. In what ways have you seen ableism manifest in your own teaching or learning experiences, even when intentions were good?
References:
Antonsen, R. (2016). Math is the hidden secret to understanding the world [Video]. TED Conferences. https://www.ted.com/talks/roger_antonsen_math_is_the_hidden_secret_to_understanding_the_world
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. http://www.jstor.org/stable/27736715
Stylianidou, A., & Nardi, E. (2019). Tactile construction of mathematical meaning: Benefits for visually impaired and sighted pupils. In M. Graven, H. Venkat, A. Essien, & P. Vale (Eds.), Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 343–350). PME.
I’ve also spent time thinking about the difference between universal design and reasonable accommodation. While the term “reasonable accommodation” feels new to me in the context of your article, I realize that it’s often the approach I would naturally fall back on. In my actual teaching, I haven’t had to implement much universal design since I haven’t had students who required extensive accommodations. Still, I can see that, systemically, schools tend to rely more on reasonable accommodation than on proactively designing for all learners from the outset.
ReplyDeleteI was also surprised to read that even those working one-on-one with students, or in fields supporting learners who might benefit from universal design, often default to reasonable accommodation. It was eye-opening to learn that resources intended to support visually impaired students—like Braille math materials—are often limited. Translations can miss important mathematical nuances, and misinterpretations are common, which can leave students without full access while their peers move ahead.
One part of your discussion that really stood out was the activity where students described a circle. My first thought was that students would likely use language, gestures, or hand motions to describe a circle—but they would mostly fall back on visual cues. When students are blindfolded and have to explore the shape tactilely, however, they are forced to use different kinds of language and perspectives. I find that idea exciting because it shows how tactile experiences can expand students’ mathematical vocabulary and deepen their understanding. It suggests that by engaging students in multiple sensory ways, we not only make math more accessible, but also help all students articulate and conceptualize ideas in richer, more precise ways.
The image of students missing a straight edge with their eyes but instantly detecting it with their hands feels like such a powerful metaphor for schooling in general. How often do we assume we have “seen” understanding, when another sensory pathway would reveal something completely different?
ReplyDeleteYour unpacking of accommodation versus universal design is important. Ableism being so embedded that even people deeply committed to supporting disabled students can reproduce it.. I caught myself thinking about how often I design a lesson visually first, then later ask, “Okay, how could I adapt this?” instead of asking from the beginning, “What would this look like if touch, sound, and movement were just as central as sight?”
Luke’s description of the circle as something that “feels like it’s gonna roll” absolutely delighted me. It seems to grounded in physical intuition about curvature and continuity. It makes me wonder how many mathematically sophisticated ideas our students have that do not sound “academic,” so they are overlooked.
It seems like this thinking is moving away from only adding supports and more about redesigning norms of participation. If tactile noticing can surface details sight misses, then it may have to be replanned! Valuing this form of knowing is vital too.
Reading this also brought me back to moments using vertical whiteboards with my students. When they stand, gesture, trace shapes in the air, or use their arms to show rotation, their explanations become fuller. I used to see that as just engagement. Now I am wondering if that is actually a small step toward decentering vision and legitimizing other ways of sensing math. I wonder how might my assessment change in a universally designed math classroom, especially if students are demonstrating understanding through gesture, manipulation, or sensory language instead of primarily through written or visual representations?