Self efficacy and mathematical proof: are undergraduate students good at assessing their own proof production ability?

The aim of this research in progress is to investigate how university students assess their own proficiency in producing mathematical proofs and how this compares to their actual performance in proof tasks. Following the educational psychology literature it emerges that self-efficacy is an accurate predictor of academic achievement and the aim of this small study is to investigate self-efficacy in specifically in the context of undergraduate students’ proof production. The particular focus on proof is of relevance for its implications for our understanding of undergraduate students’ perception of what constitutes an acceptable proof. The study so far consists of a two-part questionnaire administered to 76 undergraduates in one university in the UK. We report the findings from this questionnaire and discuss the implications of the result on students’ understanding of mathematical proof. Background There is strong evidence in the educational psychology literature (Bandura and Schunk, 1981; Pajares and Graham, 1999; Zimmerman, 2000) that self-efficacy (Bandura, 1977) is an accurate predictor for academic achievement. For example Pajares and Kranzler (1995) found that self-efficacy influences Proceedings of the 13th Annual Conference on Research in Undergraduate Mathematics Education mathematics performance to a degree similar to general mental ability. We define self efficacy here, following Bandura (1977), as the judgement students make of their own capability of performing a given task (in our study the task is proof production). It is acknowledged in the mathematics education literature that students find proof one of the most difficult ideas to negotiate when starting mathematics studies at university (Moore, 1994; Weber, 2001). In this study in progress we aim to investigate whether there is a disparity between students’ perceptions of their ability in producing proof and their actual proof production skills. We have concentrated on self-efficacy (following Hackett and Betz, 1989) as this is distinguished from other measures of attitudes (e.g. confidence in learning mathematics) and it can be used as an assessment closely linked to the performance in one specific task and not a general assessment of performance of the whole filed, in this case mathematics (Fennema and Sherman, 1976). We decided to concentrate on proof production because proof is much studied in mathematics education but very seldom in terms of students’ self perceptions as provers. Insights into how students’ assess their performance at proof production, and comparison with their actual performance might also contribute to the debate about whether students have an accurate idea of what constitutes an acceptable proof. The study Participants were 76 first year undergraduates studying mathematics (or a joint degree with a substantial mathematics component) at a highly ranked UK university. Data collection took place towards the middle of the first semester, so participants had, at the time the study happened, completed 8 weeks of degree level mathematics study.