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The Importance Of Surprise In Mathematical Beauty, V. Rani Satyam
The Importance Of Surprise In Mathematical Beauty, V. Rani Satyam
Journal of Humanistic Mathematics
Mathematicians, mathematics education researchers, and philosophers have written about mathematical beauty and many of the qualities commonly associated with it, such as simplicity, brevity, enlightenment, etc. One key theme that underlies many of these qualities is surprise or the unexpected. In this article, I discuss the integral role surprise plays in mathematical beauty. Through examples, I argue that simplicity alone is oftentimes not enough for a piece of mathematics to be considered beautiful, but rather it is unexpected simplicity that we seek. I propose, moreover, that surprise is necessary for enlightenment. The paper also reports results from an activity designed …
Surprise And The Aesthetic Experience Of University Students: A Design Experiment, Ofer Marmur, Boris Koichu
Surprise And The Aesthetic Experience Of University Students: A Design Experiment, Ofer Marmur, Boris Koichu
Journal of Humanistic Mathematics
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 …