Reading: Angelika Stylianodou & Elena Nardi (2019), Tactile construction of mathematical meaning: Benefits for visually impaired and sighted pupils
Summary:
The authors of this article argue that tactile perception is an important and valuable way of engaging with mathematics for all learners – not just visually impaired ones. Rather than treating touch as a special accommodation, they frame it as a shared classroom practice that can support inclusion and challenge ableist assumptions about how mathematical understanding should be developed. Their study aims to show that when tactile approaches are implemented universally, they can benefit both visually impaired and sighted students by further expanding how mathematical ideas are explored and discussed.
The study draws on classroom data from students in Years 1, 3, and 5, aged 6-10, and focuses on a task involving a shape that resembles a circle, but missing a circular segment (as in, the shape contains a short straight segment in place of being continuously round). One sighted student was able to clearly feel the straight-line segment in the shape by observing it only through touch, but struggled to notice it visually – likely because the shape appears so similar to a circle at first glance. This highlights how visual perception can encourage a quick, whole-shape assumption, while tactile exploration encourages a slower, part-to-whole understanding. A visually impaired student also contributed meaningful observations through touch when comparing the new shape to a circle, showing that tactile engagement supported meaningful mathematical thinking across the entire class. By including this activity as a universal design, the mathematics lesson became more inclusive and encouraged students to develop non-ableist perspectives on mathematical learning capacities.
Stops:
1) "A conjecture that our study explores is whether, and if so how, universally designed mathematical practices lead not only to better inclusion of [visually impaired] pupils but also bring benefits to all pupils" (p. 1).
This quotation truly spoke volumes to me. Over the last few years as a science educator, I have been working to make my courses more accessible to all learners, not only those with learning plans that outline specific accommodations. Inclusion in schools is often framed as catering only to students with identified exceptionalities, but to me, inclusion means designing classroom experiences where all students benefit from purposeful supports. This approach benefits students as well as teachers, as it shifts accommodations away from being seen as something only certain students “need” or as extra work to be added on, and instead positions them as opportunities to enrich and improve instruction overall. Unfortunately, I have encountered many teachers who struggle to implement inclusive practices (often due to limited training, resources, and capacity related to workload). I believe that universal approaches offer a practical way to support the needs of as many students as possible within a shared classroom environment.
2) "In any case, we have argued that inviting the entire class to explore mathematics through touch could possibly lead to broadening everyone’s perspectives on what constitute valid mathematical practices" (p.4).
This quotation prompted me to reflect on what is meant by “valid mathematical practices” and challenged the assumption that mathematics is primarily visual or symbolic. Traditionally, mathematical practices are often defined through diagrams on paper, visual representations, or written explanations. While I try to switch up my teaching strategies and incorporate different activities to support student learning, this paper helped me see how embodied mathematics through touch can allow students to move beyond their initial assumptions and attend more carefully to parts of an object rather than viewing it only as a whole. In my own experience, activities like these are often considered “extra”, less serious, or even invalid, yet the findings in this study challenge that perspective. They demonstrate the value of non-traditional practices and invite reflection on whose ways of knowing are privileged in classrooms and whose are dismissed.
Questions:
1) What do you think counts as “valid” mathematical practice in classrooms? Who or what tends to define this, and how does that influence which students may be seen as “successful”?
2) Is there a clear line between what is considered an accommodation and what is simply good teaching practice? If universal design is implemented, in what contexts might individual accommodations still be needed, if at all?
3) If some students learn mathematics most effectively through visual or symbolic representations, should tactile approaches be expected of them in the name of inclusion? Where might choice or flexibility fit into this tension?
Hi Sarah,
ReplyDeleteI want to thank you for the interesting questions you have raised, and these are my thoughts. In today’s educational landscape, the distinction between accommodation and effective teaching practice is increasingly blurred. Traditionally, valid mathematical practice has often been defined by speed, correct answers, and proficiency with symbolic or written representations—standards largely shaped by curricula, assessment systems, and teacher training. These norms tend to privilege students who learn quickly and perform well in conventional formats, while marginalizing those who demonstrate understanding in alternative ways.
An inclusive approach challenges this narrow definition of success by recognizing that students engage with mathematics through diverse sensory and cognitive pathways. Many learners are naturally drawn to lessons that appeal to their senses—whether through visual representations, hands-on activities, discussion, or movement. Embracing this diversity allows educators to design learning experiences that honour multiple ways of making mathematical meaning, rather than positioning one mode of learning as the standard.
From this perspective, strategies such as visual aids, interactive tasks, collaborative discussion, and tactile or embodied activities should not be seen solely as accommodations, but as good teaching practices that benefit all learners. In EPSE 511, I was taught that Universal Design for Learning (UDL) supports this shift by encouraging teachers to plan flexibly from the outset. That said, even in universally designed classrooms, some students may still require individual accommodations—such as assistive technologies or alternative formats—to ensure equitable access to learning.
Importantly, inclusion should not mean replacing one dominant mode of learning with another. While tactile approaches can be powerful, they should not be expected of all students in the name of inclusion. Instead, learners should be given choice and flexibility to engage with mathematics in ways that suit them best. The ultimate goal is not to enforce a particular method, but to ensure that every student has meaningful opportunities to learn, express understanding, and be recognized as mathematically capable.
Hi Sarah,
ReplyDeleteThank you so much for these thoughtful questions and for reminding me of how we can consider what makes “real” math in the classroom, as the idea of valid mathematical practice is often connected with the use of the written word, signs, and the right answers on a test. This, of course, comes with the particular demands of the lessons, tests, and teacher training, so a child may appear unsuccessful if the concept is explained through touch, words, or motion.
I also believe that the distinction between accommodations and good teaching is not clear-cut. Universal design is a good approach in this regard because it makes support beneficial for the whole class rather than only for the kids who need it. However, some kids may require accommodations according to their needs, such as sensory needs.
Finally, inclusion should offer choices. Although rich tactile activities can deepen understanding and challenge the notion that math is a visual entity, students should not be required to learn in a single modality. Allowing students to select among visual, tactile, and symbolic approaches honors differences in learning strengths while valuing touch as a legitimate way of learning mathematics.
Thanks for this very interesting discussion about choice, accommodation and universal design for learning. I am drawn to Clementina's comment that we should not just be substituting one dominant mode for another. Great discussion about what might be considered mathematically valid (and why)!
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