Lynn McAlpine and Cynthia Weston - How six outstanding math professors use reflection to improve their teaching

An increased value is being placed on quality teaching in higher education. An important step in developing approaches to better instruction is understanding how those who are successful at teaching go about improving their own teaching. Although reflection has frequently been referred to as a mechanism for accomplishing this improvement process (in both literatures on university and public school teaching), there had been no research which documented it as a cognitive process. So, a number of years ago, we undertook a program of research in which the concept of ``reflection'' provided the frame of reference. We wanted to see if and how it improved practice.

We chose to look at outstanding professors since the literature suggests that experts tend to reflect more. And, we chose mathematics as the subject area since there appears to be a general public concern about the quality of students' learning in this area. We investigated in detail the reflective processes of six professors each teaching an undergraduate course in mathematics or mathematics education. We tracked their day-to-day planning, instructing and evaluating of learners. We documented what these professors were monitoring during and after teaching, what changes they made as a result, and what knowledge they drew upon in making decisions. Of particular interest was their attention to feedback from students in making decisions about how to adjust their teaching.

What we will do in the presentation is describe how these professors used reflection to improve their teaching, and present the model of reflection that resulted from the analysis. We have found that this model provides a language for describing reflection and therefore a way to be intentional in using reflection.