Dissertation
The Evolution of Proof Image
Washington State University
Doctor of Philosophy (PhD), Washington State University
01/2022
DOI:
https://doi.org/10.7273/000004428
Handle:
https://hdl.handle.net/2376/118946
Abstract
Proof image is a mechanism for constructing proofs that has come about within the last 10 years. In this study, I investigated what the evolution of proof image looks like as a prover goes through the process of convincing themself of the truth of multiple claims, and how they use this process in producing a formal proof for each claim. This evolution is compared across experience, through undergraduate mathematics majors and professors, and across content areas, with one claim from each of the areas of discrete mathematics, linear algebra, and introduction to real analysis. One notable result is that proof image is not binary, but can be viewed as being at one of four levels: basic, emerging, proficient, or complete. Additionally, this study showed that it is possible to have a complete proof image, with a formal proof that is not sanctioned by a small group of experts, and it is also possible to have a proof image that is not complete, yet sanctioned as a formal proof by a small group of experts. In both cases, being able to form an entity of understanding of why a claim is true seemed to be an important piece of the proof image that aided in the formalization process.
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Details
- Title
- The Evolution of Proof Image
- Creators
- Kaleinani Boardman
- Contributors
- Kristin Lesseig (Advisor)William Hall (Committee Member)Molly Kelton (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Teaching and Learning, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 340
- Identifiers
- 99900883240101842
- Language
- English
- Resource Type
- Dissertation