What do university mathematics students value in advanced mathematics courses?

Abstract

In this paper, we present a qualitative study on what values students perceive in their abstract algebra course. We interviewed six undergraduates early in their abstract algebra course and then again after their course was completed about what motivated them to learn abstract algebra and what value they saw in the subject. The key finding from the analysis was that participants found intrinsic value (i.e., their enjoyment of the subject) to be essential to learning abstract algebra. While participants desired utility value in the form of mathematical applications, they ultimately did not find this necessary to learn abstract algebra. Finally, some participants had different motivations for learning abstract algebra than for learning other branches of advanced mathematics, such as real analysis, suggesting that motivation research in mathematics education should not treat mathematics as a unitary construct. We offer analysis about how the nature of advanced theoretical proof-oriented mathematics may have contributed to these findings.