Week 2 Readings Multimodality and Mathematical Meaning-Making
Multimodality and Mathematical Meaning-Making: Blind Students’ Interactions with Symmetry
Solange Hassan Ahmad Ali Fernandes & Lulu Healy
Summary
In Multimodality and Mathematical Meaning-Making: Blind Students’ Interactions with Symmetry, Fernandes and Healy explore how blind students construct mathematical meaning through coordinated bodily, tactile, and imaginative activity. Focusing on geometry, a domain typically treated as inherently visual, the authors examine how two blind students engaged with concepts of symmetry and reflection using tactile tools, hand movements, folding actions, and mental simulation. Drawing on embodied cognition and phenomenology, particularly the work of Merleau-Ponty, the paper argues that mathematical cognition is not confined to the brain or to vision, but is distributed across the lived body and its interactions with the world.
Through detailed task-based interviews, the authors show that symmetry was not merely recognized as a visual property but felt through touch and enacted through movement. The students developed mathematical understanding by coordinating tactile exploration, memory, gesture, and imagination. Importantly, Fernandes and Healy demonstrate that blind learners do not simply follow the same learning trajectories as sighted learners using different sensory channels; instead, they often develop distinct but equally rigorous ways of reasoning mathematically. The paper ultimately challenges vision-dominant assumptions in mathematics education and reframes abstraction as something that emerges from embodied experience rather than from detachment from the body
Stop 1: Mathematics does not have to be visual to be abstract
One moment that made me pause was the authors’ assertion that knowing symmetry does not transcend feeling it. This stood out to me because symmetry is so often taught as something to be seen on paper, identified by visual alignment or mirror images. In this study, however, symmetry emerged through folding actions, tracing shapes with the hands, and simulating movement across an imagined axis. The students’ understanding was not weaker because it was non-visual; in many ways, it appeared more intentional and precise.
This stop made me reflect on how deeply visual assumptions are embedded in how mathematics is taught and assessed. Fernandes and Healy show that abstraction does not require stripping away sensory experience. Instead, abstraction is built through sensory experience, particularly through touch and movement. This resonates strongly with embodied views of learning and challenges the idea that visual representations are the most “advanced” or “pure” form of mathematical thinking.
Stop 2: Connecting this reading to Susan’s questions on multisensory mathematics
What I especially appreciated this week were Susan’s questions (in her description of this week's reading) about multisensory mathematics, particularly her suggestion that students might learn the same mathematical function through sound, colour, tactile objects, or kinesthetic movement. I found this framing really compelling because it treats multisensory learning not as an accommodation, but as a legitimate way of generating new mathematical insight.
This reading felt like a direct response to that idea. Fernandes and Healy do not ask how blind students can be helped to “access” visual mathematics; instead, they ask what mathematics becomes when vision is no longer central. Their work suggests that multisensory mathematical experiences do not merely replicate visual ones, but can produce different, and sometimes richer, ways of grasping structure, invariance, and transformation.
Susan’s second prompt, about designing mathematics for people who “don’t see with their eyes” or “don’t hear with their ears,” also stayed with me. The paper makes it clear that designing for sensory difference requires more than translation; it requires rethinking what counts as mathematical activity in the first place. This reinforced for me that inclusive design in mathematics is inseparable from theoretical questions about cognition, perception, and meaning-making.
While thinking about Susan’s question, I found myself exploring examples of sonic and auditory mathematics online. I came across several projects that translate mathematical structures into sound, such as sonified graphs where changes in pitch represent variation, or musical patterns that embody symmetry through repetition and inversion. What struck me was how clearly structure could be heard rather than seen.
Although Fernandes and Healy focus primarily on tactile and kinesthetic modalities, their argument that mathematical cognition is fundamentally multimodal helped me make sense of these auditory approaches. If mathematical understanding is grounded in coordinated sensory-motor experience, then sound becomes another valid medium through which pattern, symmetry, and transformation can be explored.
While thinking about multisensory mathematics and what Susan asked about learning through sound or movement, I explored an example of sonic mathematics/sonification created by NASA.
Solange Hassan Ahmad Ali Fernandes & Lulu Healy
Summary
In Multimodality and Mathematical Meaning-Making: Blind Students’ Interactions with Symmetry, Fernandes and Healy explore how blind students construct mathematical meaning through coordinated bodily, tactile, and imaginative activity. Focusing on geometry, a domain typically treated as inherently visual, the authors examine how two blind students engaged with concepts of symmetry and reflection using tactile tools, hand movements, folding actions, and mental simulation. Drawing on embodied cognition and phenomenology, particularly the work of Merleau-Ponty, the paper argues that mathematical cognition is not confined to the brain or to vision, but is distributed across the lived body and its interactions with the world.
Through detailed task-based interviews, the authors show that symmetry was not merely recognized as a visual property but felt through touch and enacted through movement. The students developed mathematical understanding by coordinating tactile exploration, memory, gesture, and imagination. Importantly, Fernandes and Healy demonstrate that blind learners do not simply follow the same learning trajectories as sighted learners using different sensory channels; instead, they often develop distinct but equally rigorous ways of reasoning mathematically. The paper ultimately challenges vision-dominant assumptions in mathematics education and reframes abstraction as something that emerges from embodied experience rather than from detachment from the body
Stop 1: Mathematics does not have to be visual to be abstract
One moment that made me pause was the authors’ assertion that knowing symmetry does not transcend feeling it. This stood out to me because symmetry is so often taught as something to be seen on paper, identified by visual alignment or mirror images. In this study, however, symmetry emerged through folding actions, tracing shapes with the hands, and simulating movement across an imagined axis. The students’ understanding was not weaker because it was non-visual; in many ways, it appeared more intentional and precise.
This stop made me reflect on how deeply visual assumptions are embedded in how mathematics is taught and assessed. Fernandes and Healy show that abstraction does not require stripping away sensory experience. Instead, abstraction is built through sensory experience, particularly through touch and movement. This resonates strongly with embodied views of learning and challenges the idea that visual representations are the most “advanced” or “pure” form of mathematical thinking.
Stop 2: Connecting this reading to Susan’s questions on multisensory mathematics
What I especially appreciated this week were Susan’s questions (in her description of this week's reading) about multisensory mathematics, particularly her suggestion that students might learn the same mathematical function through sound, colour, tactile objects, or kinesthetic movement. I found this framing really compelling because it treats multisensory learning not as an accommodation, but as a legitimate way of generating new mathematical insight.
This reading felt like a direct response to that idea. Fernandes and Healy do not ask how blind students can be helped to “access” visual mathematics; instead, they ask what mathematics becomes when vision is no longer central. Their work suggests that multisensory mathematical experiences do not merely replicate visual ones, but can produce different, and sometimes richer, ways of grasping structure, invariance, and transformation.
Susan’s second prompt, about designing mathematics for people who “don’t see with their eyes” or “don’t hear with their ears,” also stayed with me. The paper makes it clear that designing for sensory difference requires more than translation; it requires rethinking what counts as mathematical activity in the first place. This reinforced for me that inclusive design in mathematics is inseparable from theoretical questions about cognition, perception, and meaning-making.
While thinking about Susan’s question, I found myself exploring examples of sonic and auditory mathematics online. I came across several projects that translate mathematical structures into sound, such as sonified graphs where changes in pitch represent variation, or musical patterns that embody symmetry through repetition and inversion. What struck me was how clearly structure could be heard rather than seen.
Although Fernandes and Healy focus primarily on tactile and kinesthetic modalities, their argument that mathematical cognition is fundamentally multimodal helped me make sense of these auditory approaches. If mathematical understanding is grounded in coordinated sensory-motor experience, then sound becomes another valid medium through which pattern, symmetry, and transformation can be explored.
While thinking about multisensory mathematics and what Susan asked about learning through sound or movement, I explored an example of sonic mathematics/sonification created by NASA.
On the Chandra X-ray Observatory educational site, there’s a project called A Universe of Sound, where actual astronomical data from telescopes like Chandra, Hubble, Webb, and Spitzer are translated into sound and even composed into a symphony that can be played by musicians. In this work, values such as brightness and wavelength are mapped to musical elements like pitch, timbre, and volume, allowing listeners to hear patterns and structures that would otherwise be seen in images alone. This sonification project was developed not just as an artistic experiment but as a way to make complex data accessible to people who are blind or low-vision, and to invite new ways of perceiving scientific information through sound rather than sight . I found this example while exploring online, and it really made me think about how mathematical relationships and patterns can reveal themselves through auditory experiences — a concrete instance of what Susan was suggesting about engaging learners through multisensory pathways.
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