Students' beliefs on empirical arguments and mathematical proof in an introduction to proof class

Abstract

We report findings from a longitudinal study of students’ beliefs about empirical arguments and mathematical proof. We consider the influence of an ‘Introduction to Proof (ITP)’ course and the consequences of the observed changes in behaviour. Consistent with recent literature, our findings suggest that a majority of the thirty-eight undergraduate students in this study do not find empirical arguments convincing, even at the beginning of their ITP course. We use Sankey diagrams to show that, while many were unconvinced by these arguments at the start and end of the course, others began the course endorsing empirical arguments as similar to their own, shifting toward deductive-symbolic arguments by the end. Finally, we consider the value of Sankey diagrams for understanding changes in population behaviours, and the consequences of our work for future research on the role of empirical arguments in the classroom.

KEYWORDS:

• introduction-to-proof
• mathematical proof
• proof transitions
• empirical and deductive arguments
• and Sankey diagrams

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 While the original authors refer to this instrument as a ‘test’, we prefer the term ‘survey’ to distance ourselves from the implicit claim that the instrument’s items feature objectively correct (and incorrect) responses.

2 We note the nuances of statement b and recognize this may be problematic but we take the phrasing that Stylianou et al. use in their paper.

3 We understand that statements (a) through (d) are not mutually exclusive, nor do they need to be. The participants are asked to choose between statements (a) through (d) that best fits their thinking.