With Edward B. Burger (who earned a Ph.D. from the university), Starbird has written a prize-winning textbook, The Heart of Mathematics: An invitation to effective thinking, and the recently published general-audience book Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas. Starbird has also produced three courses for The Teaching Company: Change and Motion: Calculus Made Clear, Meaning From Data: Statistics Made Clear and (with E. Burger) The Joy of Thinking: The Beauty and Power of Classical Mathematical Ideas.
Insight recently had the opportunity to meet with Starbird and learn about his interest in making math more accessible, his approach to teaching and his new book.
Insight: What is the Saturday Morning Math Group and how are you involved with the program?
Starbird: The Saturday Morning Math Group is the Department of Mathematics effort to reach out to local junior high and high school students. Chair Goodman-Strauss started SMMG when he was a mathematics graduate student. SMMG has been supported by a member of the faculty, Karen Uhlenbeck, for many years. Once a month, on a Saturday morning, about 100 students, plus some parents and teachers, come to campus to hear a professor give a one-hour lecture. Then there’s a break for refreshments and in the second hour graduate students lead students in hands-on activities. I’ve basically given a talk every year for many years—sharing intriguing ideas about infinity, topology, statistics and other topics with students.
SMMG has been a terrific success because it opens the eyes of students to the excitement of mathematics, particularly in areas that they wouldn’t see in a high school curriculum. It also demonstrates the college’s commitment to K-12 education in the community. The response we’ve received from everyone involved has been excellent.
Insight: Much of your work has involved helping the college develop courses for non-majors. How did you become interested in making math accessible to non-majors?
Starbird: Making deep mathematical concepts accessible and enjoyable for intellectually curious people is a part of my life that’s blossomed in the last 15 years. As a teacher, I’ve learned that the great challenge in education is to get students to think for themselves. My goal is not so much to teach specific mathematical techniques, but to help my students become better thinkers—are my students grappling with ideas, are they developing the habits of thinking clearly and are they expressing those habits in class?
Insight: How do you go about confronting this challenge and achieving these goals?
Starbird: When students take courses in their general education—whether in music, literature or history—they study the greatest music of all-time, they read the literature that English departments consider to be the best of all-time and they study the greatest advances in human history. Shouldn’t mathematics courses compete on that same playing field? Shouldn’t we offer students the really big ideas, the ideas that are so important that every educated person would do well to appreciate them? Well, mathematics has those kinds of ideas. Insights in mathematics have allowed people to reason about things that had been previously incomprehensible. We can make the big ideas of mathematics the core content of our courses.
Then, in thinking about the take-home lessons of the course, we need to ask, “What is it that students will keep for life?” Students are going to forget the technical details of mathematics, but will remember strategies of thinking—the very precise and clear-minded thinking that mathematics demands. Inquiry-based learning is one technique that lets students absorb the strategies of analysis they see in their mathematics courses and make those methods of thought applicable to any walk of life. So, instead of just becoming better in the classroom, students can become better artists, better businesspeople and better citizens, too.
Insight: Did this approach lead to your new book, “Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas,” which you co-wrote with Edward Burger? Are you planning similar projects in the future?
Starbird: Actually, the textbook The Heart of Mathematics: An invitation to effective thinking, which I also co-wrote with Burger, was the first book we wrote. It embraced the philosophy of making significant ideas in mathematics the core mathematical content of a course for non-technically oriented students. (In 2001, the book won the Robert W. Hamilton Book Award.) It’s been very successful and is commonly used by mathematics students and professors around the country. Our newest book was inspired by the same philosophy, but written for a general audience, rather than college students.
Now I’m working on a book about creativity, which looks into whether strategies associated with mathematical research and investigation can create new ideas in realms outside of mathematics. My scholarly work focuses on how to make difficult and complex ideas accessible.
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