Abstract
A premise of this article is that the current methods used in mathematics education research may be preventing researchers from adequately addressing the body and, in particular, the alignment of acting and knowing. Pursuing a non-dualistic and non-hierarchical approach to learning and knowing, I experiment with new methods that aim to increase situated and embodied validity. I do so through a short video clip of a four-year-old child interacting with TouchCounts, which is a multi-touch application designed to support early number sense. I work through the many arm, hand and finger actions made by the child, both manually on the screen and digitally in the air, focusing on the translations of these actions across contexts, which I understand as learning through remembering. I then discuss some consequences of these methods, which involve narrative and re-enactment, on knowledge production, both for learners and for researchers, specifically when digital technologies are involved.
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Notes
Lather is interested in transgressing traditional forms of scientific validity that constitute representational and postpositivist assumptions. She proposes four forms of validity that are in better alignment with poststructural research paradigms. I note that the embodied one was deployed long before mathematics educators began focusing on theories of embodiment.
Like many people, I find transcripts hard to ‘read’. I get lost in the symbols used to indicate non-linguistic aspects of the event and often find the descriptions of gestures and actions hard to imagine. A few years ago, in an article written for a special issue on language and mathematics for a French language journal, my co-author and I (Forte and Sinclair, 2019) decided to provide a more narrative description of a classroom video. Jérôme Proulx contacted me to tell me how much that narrative description was engaging and convincing, a comment that surprised me at the time, but it has remained with me ever since, no doubt contributing to the present writing.
Given the positioning of the video camera, my own movements are harder to see. A better re-enactment would involve (at least) two people, which would bring in eye contact, timing of movement and speech and positioning. I think all this is potentially quite relevant, but for this first attempt at image re-enactment, I restrict the focus to Ruby.
The word remembering is etymologically associated with the mind, as retaining in the mind, from the Latin memor (mindful). Given Ruby’s specific form of remembering, I prefer to associate the word ‘member’ to the meaning of body part or limb rather than just to the mind. Remembering thus becomes a fully integrated mind–body process.
There are some connections with the notion of concept image, but significant differences as well: for Barsalou, the experience is full (including social, emotional) and not just cognitive or strictly mathematical; also, while concept image is often assumed to be some coherent set of ideas that make up one’s understanding, Barsalou is explicit about the layers of experience, which may have overlaps, but are not parsed into categories such as pictures, properties and associated problems.
There is a large body of research around the ideas of quantum cognition (see Wendt, 2015), though Barsalou’s connects specifically to theories of embodiment. See also de Freitas and Sinclair (2017) for an interpretation of the quantum perspective in the context of mathematics education. See also Forde (2021) for a quantum-informed theorising of mathematics education.
Here, the apparatus of quantum mechanics becomes the situation, and that situation produces the concept (of addition, in this case) in the same way that the two-slit apparatus is a measurement that produces the concept (of particle) (Barad, 2007).
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Acknowledgements
Deep appreciation to Ricardo Nemirovsky, Sean Chorney, Sheena Tan and Anna Baccaglini-Frank for their perceptive comments, which led to many improvements, and to David Pimm for always being a dependable and generous first reader and inveterate editor.
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This research was funded by the Social Sciences and Humanities Research Council of Canada. Grant number: 435–2018-0433.
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Sinclair, N. Knowing as Remembering: Methodological Experiments in Embodied Experiences of Number. Digit Exp Math Educ 10, 29–46 (2024). https://doi.org/10.1007/s40751-023-00132-7
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DOI: https://doi.org/10.1007/s40751-023-00132-7