On the different ways that mathematicians use diagrams in proof construction |
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Authors: | Aron Samkoff Yvonne Lai Keith Weber |
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Affiliation: | 1. Rutgers University , USA samkoff@gmail.com;3. University of Michigan , USA;4. Rutgers University , USA |
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Abstract: | The processes by which individuals can construct proofs based on visual arguments are poorly understood. We investigated this issue by presenting eight mathematicians with a task that invited the construction of a diagram, and examined how they used this diagram to produce a formal proof. The main findings were that participants varied in the extent of their diagram usage, it was not trivial for participants to translate an intuitive argument into a formal proof, and participants’ reasons for using diagrams included noticing mathematical properties, verifying logical deductions, representing ideas or assertions, and suggesting proof approaches. |
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Keywords: | mathematicians diagrams proof construction |
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