Workshop - Understanding Mathematical Explanation: Uniting Philosophical and Educational Perspectives; Spring 2020; New Brunswick, NJ

This award supports a workshop to develop new insights about the nature of mathematical explanation by bringing together philosophers of mathematics, epistemologists, psychologists, and mathematics educators to discuss how developments in their own fields could meaningfully contribute to the development of an account of mathematical explanation that unites these multiple perspectives. Invited speakers and attendees will be given several opportunities during the workshop (in panels, working groups, and informal settings) to engage in significant work on cross-cutting themes. The workshop organizers also plan to use targeted advertisement in local schools of education and school districts to attract interest among pre- and in-service teachers to attend the conference. As a broader impact, workshop organizers expect that these results will have a significant impact on educational work on mathematical explanation, and that this will in turn lead to new understandings and teaching methods that will ultimately impact teachers and students of mathematics at all educational levels.

The notion of explanation is central to both philosophy and education. These disciplines have made significant developments concerning the role and character of explanations in scientific inquiry and in the classroom. However, the notion of explanation in the field of mathematics has proved to be particularly challenging; both philosophers and educators are unclear about what is needed in a mathematical explanation so that it goes beyond merely demonstrating that some mathematical phenomenon is so to explaining why it is so. Since here has been little influence of philosophical accounts of mathematical explanation in educational research, and vice versa, the workshop organizers expect that bringing together experts in these fields and some related fields in a workshop setting has potential to advance our knowledge and understanding of the notion of mathematical explanation in the both fields. They plan to enhance that potential by inviting speakers who are not only experts in the study of explanation and understanding from their own disciplinary perspective, but also open to crossing traditional disciplinary boundaries and to using different theoretical and methodological traditions in their own work.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.