Tongue Gestures & Social Risk In Math Class
In this realm, mathematics has always happened in bodies. We count on fingers, trace curves, “hold” an angle open with our hands, and talk our way through an idea using rhythm, emphasis, and pauses. What Susan Gerofsky's paper "Mathematical learning and gesture: Character viewpoint and observer viewpoint in students’ gestured graphs of functions", adds to the conversation is that gestures can be diagnostic of how a learner is relating to a piece of mathematics. In her work on graphing, students’ bodies sometimes stay “outside” the representation (as if observing the graph), and sometimes move “from within” it (as if riding the graph). Those are not just performance styles; they can mark different forms of engagements and imaginations.
Wittgenstein helps us name what’s at stake: mathematics education is a set of language games, rule-governed ways of using words, symbols, diagrams, and bodies in particular settings. Meaning is not a ghost behind the sign; it is what a community counts as a correct move within a shared form of life. Gestures, then, are not “extra” but part of the game being played. The danger is that schools often stick to a narrower gesture game than many students find natural: quiet, restrained, desk-bound symbol talk as the only legitimate one.
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What are her gestures to animate math, I wonder? This matters for equity because gestures are culturally patterned and culturally judged. Lately, I’ve been thinking about tongue gestures: playful pointing with eyes wide open, or tongue held gently by the teeth with closed or softened eyes. the tongue rarely encodes “the slope is negative,” but it can encode how the learner is navigating uncertainty, effort, and social risk—which is part of mathematical practice. In some communities these signal specific stances: teasing, uncertainty, confidence, contentment. In others, they can be read as disrespect or distracted. The same mathematical thinking can be misrecognized because the body is being assessed, and the body is that of an outsider.
Is Kuhnian incommensurability relevant here? Yes, but locally: different gesture traditions can function like partially non-overlapping language games, where cues don’t translate cleanly and “competence” is assumed or gets misread. The practical aim isn’t to declare worlds sealed off; it’s to build translations across math gesture games by looking for constants at the level of function—pointing to anchor reference, tracing to show form, balancing to show equivalence—while widening what counts as doing mathematics.
Follow-on work from Gerofsky's article may be to replicate her gesture-based lens in more culturally diverse classrooms; add teacher “gesture-interpretation” interviews to study recognition and misrecognition; and test whether instruction that legitimizes multiple embodied channels changes who is seen as mathematically competent, not just who gets the right answer.
I quickly read Seeing the graph and being the graph, and my first thought was to imagine my students in the research situation: moving the graphs. I must admit it made me smile. My students and my Naskapi colleagues are extremely quiet. They often say: “it is easy to differentiate us from the Innu, Innu are loud and their language sounds like singing”. My students are very discreet; I had never struggled with students speaking over me in class. I cannot imagine my students using their whole body to represent features of a graph. Obviously, this does not apply to all of them, there are always few exceptions.
ReplyDeleteAlthough, I do believe using gestures to describe salient features of a graph can help them build metaphors necessary to truly understand characteristics of graphs. My student’s way of seeing the world is through verbs and actions. By using movements to describe curves on a graph, which is a concept very foreign to them, it gives them a different analogy to build their understanding on. In my experience, without this analogy, I would have fewer students with a good understanding of graphs and Cartesian plane. Like you said, when I teach, I try to find constants in between my gestures and my students’ gesture to build math translations.
You got me thinking. What if teachers mirrored the relevant student gestures ... What can we expect from that?
DeleteIt is really interesting to work on gesture (particularly mathematical gesture) across particular cultures, age groups, gender identifications, etc. The urban BC classes I worked with were highly multicultural, within the social framework of Greater Vancouver. I expect there might be differing norms and comfort levels with body movement in other configurations!
ReplyDeleteJust a note that you are currently in a reading group of 4 people (which I'll reshuffle this week...) Thanks to Noemi and later Taylor for responding to Jean-Jacques -- Colleen N., are you reading Jean-Jacques' writing? And Jean-Jacques, are you reading and responding to your other group members? I will soon be re-shuffling the groups, and I will make sure that the four of you get into 3-person groups for the next part of the course!
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