What is it about?

What might be a connection between learning to move physically and learning mathematical concepts? According to emerging theories from the cognitive sciences – 4E (embodied, enactive, embedded, extended) -- this curious connection is not only plausible but imperative! Our lab designs interactive technologies that invite mathematics students to move their body in a way they have never tried before, such as raising their hands at different speeds. They solve these movement challenges by perceiving the situation in a new way, for example noticing how the distance between their hands increases as their hands go up. In turn, this new perception is the cognitive basis of the new mathematical concept, here, proportionality. The students then formalize their new perceptions using standard mathematical forms and symbols. This design architecture has been implemented internationally in a variety of HCI platforms and with intersectionally diverse students from elementary through graduate school.

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Why is it important?

The Mathematics Imagery Trainer is important both as an educational technology that enables students to ground school content in their naturalistic inclinations and as an empirical context for cognitive scientists to investigate cutting-edge theories claiming that mental activity is inherently embodied and enactive. Philosophers often debate over our human capacity to experience the meaning of ideas. What does it mean to experience meaning? These ancient, fundamental philosophical questions about knowing and the experience of meaning bear critical implications for educational practitioners seeking to foster students’ understanding of new ideas. Where will the meaning of these ideas come from? How would students understand these ideas? Specifically for mathematics, a timeless complaint has been that students learn meaningless procedures that they forget the next day. Based on cognitive developmental psychology research on the emergence of meaning from sensorimotor activity, we believe that our Trainer interactive devices create opportunities for students to ground the meaning of mathematical concepts in new ways of attending to the world -- new perceptual structures that we call "attentional anchors." As students coordinate their hands in a new way, they understand new concepts.

Perspectives

The Embodied Design Research Laboratory at the University of California Berkeley has been participating in global efforts to harness the potentials of new human–computer interaction platforms to create radically new learning experiences for all students. Our perspectives adhere boldly to the embodied paradigm shift in the cognitive sciences. Technology has now arrived full historical circle to a point where it not only emulates but can also extend naturalistic interactions with non-digital substantive materials. We are excited by the convergence of formative tributaries from theory, technology, and methodology that frame our design-based research investigations into the futures of mathematics education.

Dor Abrahamson
University of California Berkeley

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This page is a summary of: The mathematical imagery trainer, May 2011, ACM (Association for Computing Machinery),
DOI: 10.1145/1978942.1979230.
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