| This thesis begins by examining the roles of aesthetics in the activity of research mathematicians and develops a model that structures the diversity of aesthetic responses offered by mathematicians in the literature. The model is applied to the descriptions of mathematical experiences and beliefs provided by two groups of professional mathematicians in order to both further refine the categories of the model and gather illustrative evidence. Through subsequent theoretical analysis, the model gains explanatory and predictive power with respect to the ways in which aesthetic responses contribute fundamentally to the production and appreciation of mathematical knowledge, particularly during the process of inquiry. An introspective analysis of my mathematical experience enables the transition to the second part of the thesis, which focuses on educational concerns. This second part begins with arguments that support the desirability and possibility of aesthetic engagement on the part of the student mathematics learner. The model developed for research mathematicians is then applied to examples of student mathematical activity in order to determine first, its relevance in those learning contexts; and second, whether students can have similar aesthetic responses and if so, whether those responses contribute to inquiry and cognitive growth. Finally, a small set of curriculum recommendations are made which, based on the evidence gathered throughout the thesis, might contribute to stimulating and developing aesthetic engagement in the mathematics classroom. |
