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.
Highlights
Proof is a central part of mathematics: being able to accept the values that this activity conveys is considered to be one of the characteristics of successfulInternational Journal of Research in Undergraduate Mathematics Education undergraduate mathematics students and an important step on the way to enculturation in the practices of mathematics (Dawkins & Weber, 2017)
This paper reports on an exploratory study investigating the proof production and proof writing outcomes of first-year undergraduate students who voluntarily chose to engage with an automated theorem prover
When we asked whether the two groups performed significantly differently in the first test we found that the mean performance of the No Lean (NL) group was 7.1 and the Lean (L) group was 7.8
Summary
Proof is a central part of mathematics: being able to accept the values that this activity conveys is considered to be one of the characteristics of successfulInternational Journal of Research in Undergraduate Mathematics Education undergraduate mathematics students and an important step on the way to enculturation in the practices of mathematics (Dawkins & Weber, 2017). The overwhelming evidence from such research is that students struggle with many aspects connected to this activity (Harel & Sowder, 1998; 2007; Dreyfus, 1999; Weber & Alcock, 2004; Selden, 2011), often despite the good will and well thought through pedagogic intentions of their teachers (Weber, 2004). For this reason, several teaching interventions have been trialled to assist students with mathematics learning such as flipped classrooms (Talbert, 2015; Lo et al, 2017) and the introduction of enquiry-based courses in mathematics (Rasmussen & Kwon, 2007). This paper reports on an exploratory study investigating the proof production and proof writing outcomes of first-year undergraduate students who voluntarily chose to engage with an automated theorem prover
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