Surprise and the Aesthetic Experience of University Students: A Design Experiment

Abstract

Little is known about instructional means by which the aesthetic experience of mathematics can be enhanced for undergraduate learners. This paper presents and discusses an iterative lesson design process towards creating an opportunity for students to appreciate the beauty of an unexpected solution to a challenging calculus problem. The lesson design draws on insights from both mathematics education research on aesthetics and research on aesthetic appreciation in music. The data were collected over the course of five lessons with different groups of calculus students in which the intended problem was presented in two different ways. In addition, stimulated-recall interviews were conducted with nine students who took part in the later lessons and exhibited strong emotions regarding the problem. The data suggest that the students' aesthetic response to the problem was essentially conditioned by the extent of their surprise as a result of revealing a clever solution to the problem after being exposed to repeated failed attempts. Implications for practice are drawn.