Learning about Proof with the Theorem Prover LEAN: the Abundant Numbers Task

Thoma, Athina and Iannone, Paola (2021) Learning about Proof with the Theorem Prover LEAN: the Abundant Numbers Task. International Journal of Research in Undergraduate Mathematics Education. ISSN 2198-9745

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Abstract

This exploratory study reports on characteristics of proof production and proof writing observed in the work of first-year university students who took part in workshops on the theorem prover LEAN (https://leanprover.github.io). These workshops were voluntary and offered alongside a transition to proof module in a UK university. Through qualitative analysis of 36 student produced proofs of an unfamiliar statement we highlight characteristics of proofs produced by students who did engaged and who did not engage with LEAN. The analysis shows two characteristics of proofs written by students who engaged with the programming language. The first concerns proof writing and includes the accurate and correct use of mathematics language and symbols, together with the use of complete sentences and punctuations in proofs. The second concerns proof structure and includes the overt break down of proofs in goals and sub-goals. We conclude by hypothesising a link between the characteristics observed and the experience of engaging with the theorem prover and we reflect on the potential that engagement with this theorem prover may have in mathematics instruction at university level.

Item Type: Article
Uncontrolled Keywords: automated theorem prover,proof,undergraduate mathematics,education,mathematics (miscellaneous) ,/dk/atira/pure/subjectarea/asjc/3300/3304
Faculty \ School: Faculty of Social Sciences > School of Education and Lifelong Learning
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Depositing User: LivePure Connector
Date Deposited: 12 Aug 2021 00:14
Last Modified: 06 Sep 2021 00:09
URI: https://ueaeprints.uea.ac.uk/id/eprint/81058
DOI: 10.1007/s40753-021-00140-1

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