Investigating secondary school students' epistemologies through a class activity concerning infinity

In this paper, we report findings from a pilot study investigating school students’ epistemologies of mathematics by using novel mathematics definitions. Students aged 17 and 18-year-old in Italy and the UK were asked to complete a worksheet that used a numerical approach to determine the sizes of infinite sets and were, then, invited to attend focus group interviews about their experience with the material. Thematic analysis of the interviews reveals that this approach is useful to distinguish between naive and advanced epistemologies and using unseen mathematical definitions can help enrich our understanding of epistemologies held by students of school age.