Undergraduate students’ perception of mathematical proof

Abstract Mathematical proof plays a key role in studying mathematics at the university level. In this exploratory study, we investigate mathematics students’ perception of the role of proofs during their degree at a UK university. Nineteen semi-structured interviews were conducted with students in Years 2–4 of their degree. We found that students recognized proofs as an important part of their degree. However, they perceived them as difficult, especially when encountering them initially. Further, students’ enjoyment in working with proofs was linked to their understanding. In the transition to working with proofs, the second year of study was identified as an important period by more than half of participants while the first year’s importance was also recognized. Seeing examples in class, continuous practise and self-study were frequently mentioned aspects of study that aided the transition. Key modules mentioned in this context were Real Analysis (Years 1–2) and a second-year module on Algebra and Number Theory. We observed evidence that suggests proofs are initially difficult when first encountered and propose further investigation on whether proof constitutes a threshold concept in mathematics.