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Collaborative Creativity in Undergraduate Mathematics: Exploring Student Experiences of In-Class Collaborative Proving

Authors :
Amanda Lake Heath
Source :
ProQuest LLC. 2024Ph.D. Dissertation, Middle Tennessee State University.
Publication Year :
2024

Abstract

Creativity and collaboration are key components of a mathematician's work, and thus in the preparation of future mathematicians, undergraduate mathematics courses should aim to develop students who can effectively work collaboratively and creatively with one another. Despite this need, research on mathematical creativity has primarily investigated creativity as an individual, rather than collaborative, construct. At the undergraduate level, there is even less research on collaborative creativity and how students experience it in mathematics. Undergraduate introduction-to-proof courses provide a context in which students transition from computational-based mathematics to abstract, proof-oriented mathematics and are potentially challenged with becoming practitioners of their own mathematical ideas for the first time. This course provides a context ripe for exploration of experiences in collaborative creativity in mathematics. Throughout this dissertation, I respond to the overarching research question: How do students experience creativity in collaborative proving? This research is presented in the form of three research studies and corresponding manuscripts, each investigating student experiences of collaborative creativity in proving from a different perspective. Each of the three studies presented in this dissertation were conducted in the same context of an undergraduate introduction-to-proof course. This course was instructed through collaborative, inquiry-oriented methods, including regular engagement in small-group collaborative proving activities and whole-class discussions. Data in the form of in-class video recordings, student written reflections, and focus-group stimulated-recall interviews were collected over the course of a semester-long introduction-to-proof course. Beginning in Manuscript 1: "Critical Moments in Creative Collaborative Proving," I examined the creative processes a group of three students engaged in during three different collaborative proving episodes. In this first study, I examined collaborative creativity in proving through a lens of intersubjectivity, viewing the group of students as both a whole unit as well as each student as a component part. The second manuscript, "In-the-Moment Experiences of Creativity in Collaborative Proving," focused upon only the individual experience of creativity through collaborative proving and examined student reflections of how they felt, or did not feel, creative in their in-class collaborative proving activities. The third and final manuscript, "Student Experiences of Creativity in a Collaborative, Inquiry-Oriented Introduction-to-Proof Course," de-emphasized the daily collaborative proving course activities, and rather "zoomed out" to examine what contexts students recalled throughout their course as having fostered their creativity and what within each of those contexts allowed them to feel creative. Many of the findings presented throughout these manuscripts illustrate how collaborative creativity in proving is similar to individual creativity in proving, but others highlighted how a collaborative context may introduce unique experiences and complexities to be considered in conceptualizing creativity in proving. Specifically, it was observed that students recognize themselves as creative in collaborative contexts, and unique features of a collaborative setting, like social risk taking (i.e., making mistakes, seeking/receiving help, diverging from a teammate's idea), a shared sense of responsibility and ownership over creative ideas, and exposure to a variety of mathematical proving approaches from multiple peers. These results distinguish collaborative creativity in proving from extant findings regarding individual mathematical creativity. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Details

Language :
English
ISBN :
979-83-8363-013-6
ISBNs :
979-83-8363-013-6
Database :
ERIC
Journal :
ProQuest LLC
Publication Type :
Dissertation/ Thesis
Accession number :
ED659781
Document Type :
Dissertations/Theses - Doctoral Dissertations