This study examines how undergraduate students use hand gestures to offload cognitive demands on their working memory (WM) when they are engaged in three major proving activities: reading, presenting, and constructing proofs of mathematical conjectures. Existing research literature on the role of gesturing in cognitive offloading has been limited to the context of elementary mathematics but has shown promise for extension to the college level.
My framework weaves together theoretical constructs from mathematics education and cognitive psychology: gestures, WM, and mathematical proofs. Piagetian and embodied perspectives allow for the integration of these constructs through positioning bodily activity at the core of human cognition. This framework is operationalized through the methodology for measuring cognitive demands of proofs, which is used to identify the set of mental schemes that are activated simultaneously, as well as the places of potential cognitive overload.
The data examined in this dissertation includes individual clinical interviews with six undergraduate students enrolled in different sections of the Introduction to Proofs course in Fall 2021 and Spring 2022. Each student participated in seven interviews: two WM assessments, three proofs-based interviews, a stimulated recall interview (SRI), and post-interview assessments. In total, 42 interviews were conducted. The participants' hand gesturing and mathematical reasoning were qualitatively analyzed. Ultimately, students' reflections during SRIs helped me triangulate the initial data findings.
The findings suggest that, in absence of other forms of offloading, hand gesturing may become a convenient, powerful, although not an exclusive offloading mechanism: several participants employed alternative mental strategies in overcoming the cognitive overload they experienced. To better understand what constitutes the essence of cognitive offloading via hand gesturing, I propose a typology of offloading gestures. This typology differs from the existing classification schemes by capturing the cognitive nuances of hand gestures rather than reflecting their mechanical characteristics or the underlying mathematical content. Employing the emerged typology, I then show that cognitive offloading takes different forms when students read or construct proofs, and when they present proofs to the interviewer.
Finally, I report on some WM-related issues in presenting and constructing proofs that can be attributed to the potential side effects of mathematical chunking. The dissertation concludes with a discussion of the limitations and practical implications of this project, as well as foreshadowing the avenues for future research. / Doctor of Philosophy / In this study, I examined how undergraduate students can rely on their hand gesturing to reduce the cognitive complexity of mathematical proofs. Specifically, I studied gestures produced by students when they are engaged in various kinds of proving activities: reading for comprehension, reading for validation, presenting, and constructing proofs of mathematical conjectures. During the experiments, the participants were not given pencils/paper, calculators, or any other and other figurative materials. Therefore, they had to rely on their imagination, working memory, and hand gestures to make progress on the tasks.
Results suggest that students' hand gestures have a beneficial effect in navigating cognitive challenges associated with mathematical proofs. Moreover, I show that this effect takes different forms depending on the proving activity in which the student engages. Finally, I report on some memory-related issues in presenting and constructing proofs. The dissertation concludes with a discussion of the limitations and practical implications of this project, as well as foreshadowing the avenues for future research.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/113662 |
| Date | 03 February 2023 |
| Creators | Kokushkin, Vladislav |
| Contributors | Mathematics, Norton, Anderson Hassell, Elgart, Alexander, Doolittle, Peter E., Alibali, Martha, Arnold, Rachel Florence, Johnson, Estrella |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf, application/vnd.openxmlformats-officedocument.wordprocessingml.document |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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