William McCallum

University of Arizona
2005 DTS Award

William McCallum

Jeanne L. Narum, Director, Project Kaleidoscope, interviewing Dr. Ken Ono.

If a visitor were to come into your classroom/lab— the environment in which you work with students— what impression would s/he leave with?

I had an opportunity to observe myself teaching recently, through a videotape of a class I taught to University of Utah math majors planning to become high schooI teachers. The thing that interested me as I looked at these tapes was how much care it takes to get students to pay serious attention to the ideas of mathematics, particularly in algebra. Students are accustomed to thinking of algebra as following correct procedures, not reasoning about numbers. When you do manage to open their eyes to the revelation that the symbolic language of mathematics is actually about something, they can be quite delighted.

What brought you to an interest in "advancing the frontiers of education" and to connectingyour research to that work?

I first got interested in mathematics education through my involvement in calculus reform in the 90s, as an author of the texts produced by the calculus consortium, which was at that time based at Harvard University, where I had been a graduate student. I had always been interested in teaching, but at that time saw myself primarily as a research mathematician. That project, and other later ones, became a large part of my life, so that I have ended up living in two worlds, so to speak.

Were there risks in doing this? What were they? What made you persevere? How have you documented the successes of your educational efforts?

Since I started my work on undergraduate education before receiving tenure, there might well have been risks, but in fact I was fortunate enough to be in a department with a long tradition of serious attention to teaching and scholarship about teaching. The main challenge for me has been to find the time to continue both my research program and my work in education. Perseverance was not a problem, in fact I have always found it refreshing to be able to switch to the other current when one began to run dry. But it's an unsolved problem for me how to get more hours in the day and more days in the week.

What connections have been of most value in pursuing these efforts, within your campus commu nity as well as in the broader professional communities to which you belong?

The most important connections have been with students. Anybody can have six impossible ideas before breakfast about how to teach mathematics; students provide the looking glass that shows the reality of teaching, if one dares to look. My colleagues in the calculus consortium have been wonderful, a reliable source of inspiration. More recently I have enjoyed opportunities to work with the education research community. I have also received encouragement and intellectual nourishment from the research community of number theorists, which I have always found open to the sort of culture change I believe important for the mathematics profession.

What kind of institutional culture needs to be in place to nurture careers of faculty actively seeking to integrate their research and education?

Fundamentally what is needed is a recognition that problems in education merit the attention of the best minds in the profession. This does not mean that everybody has to work in education, any more than in number theory. But work on education should not seem to be a side obsession or hobby.

What can be done at the national level to encourage and support efforts like your and those of many other leading agents of change on campuses across the country?

Awards like this one help. I think we also need something analogous to the Institute for Advanced Study for mathematics education, where mathematicians and educators would collaborate.

Please tell us about the project that you will be undetaking as part of the DTS award. How can others become involvedw with and/or continue to be informed about your work?

There is often a big difference between the mathematical ideas we think we are teaching our students and what is really going on in their heads. This problem is aggravated by a lack of communication between mathematicians, teachers, and mathematics education researchers. I propose to address both problems by a systematic content analysis—conducted jointly by mathematicians, teachers, and researchers—of problems in algebraic thinking drawn from current school curricula, accompanied by sample student solutions. The results of the analysis, an annotated commentary on the problems and the student work, will be disseminated in a form designed to catalyse other collaborations. Furthermore, the work will lead to instructional materials for professional development of teachers, for teacher education classes, and for university courses in TA training.

Mathematicians, teachers, and educators who are interested in participating should contact me at wmc@math.arizona.edu.