My Mathematical Journey: Explorations
By: David Bressoud @dbressoud
David Bressoud is DeWitt Wallace Professor Emeritus at Macalester College and former Director of the Conference Board of the Mathematical Sciences
In 1989 I decided that, for the sake of my own well-being, I would stop worrying about getting my next grant and look around for other ways to use my talents. I started saying “yes” to every opportunity that came along. I think of this time as one of pushing on doors. If they resisted, I moved on to the next. If they swung open, I walked through. This ushered in one of the most creative and productive periods of my life.
The first door I encountered was opened by Ed Messersmith, a close friend and the Episcopal chaplain at Penn State. Together we created a course on Science and Religion. This was done under the auspices of Penn State’s program in Science, Technology, and Society that had been started by Rustum Roy, a professor of materials science with a strong interest in interdisciplinary studies. We only ran the course once, but it was an eye-opening window into the religious and spiritual questions with which many science and engineering majors were wrestling.
The following spring, a very unexpected opportunity came my way. This was the early days of graphing calculators. The then head of the math department, Rich Herman, was wondering whether Penn State should start using them in calculus. As it happened, the State College Area High School had a teacher, Annalee Henderson, who had been an early adopter of graphing calculators and was very active at the state level with the Pennsylvania Council of Teachers of Mathematics (PCTM) in promoting their use. Rich asked Annalee whether she would be willing to teach a section of calculus each semester in 1990–91 using graphing calculators. This would be a way of seeing how they might fit in to the university’s curriculum. Annalee replied that she could not afford to do that on top of her teaching at the high school, but if Rich could find a university faculty member willing to take over one of her AP Calculus classes, she would be glad to do an exchange.
I learned about this opportunity and immediately signed up. The local paper did a story on this, the source of the photo of the two of us (back when I still wore a mustache). Annalee was an incredible teacher, full of wonderful insights for engaging students. We spent the summer of 1990 exchanging ideas and preparing for our classes. For the first time in my life, I encountered someone with whom I could talk about teaching and share frustrations and enthusiasms. I realized how much this focus on teaching was missing from the university’s math department. It was the beginning of my recognition that Penn State might not be the right place to pursue my passions.
Annalee took me to the annual PCTM meeting where I met a friend of hers from Pittsburgh, a real fireball exciting everyone about the possibilities of graphing calculators, Diane Briars. Tragically, Annalee died of a heart attack in 1994 while hiking in Rocky Mountain National Park. But my path would cross Diane’s again many years later after she became president of the National Council of Supervisors of Mathematics, then president of the National Council of Teachers of Mathematics, then working with me in the Conference Board of the Mathematical Sciences as its Chair. Annalee and Diane are just two of the many inspiring leaders in secondary mathematics education with whom I have been privileged to work over the years. College and university math departments have so much to learn from them.
The picture of Annalee and myself that ran in the Centre Daily Times on October 22, 1990 with the story about our classroom exchange.
John Brighton became Provost at Penn State in 1991. One of his first acts was to establish a Center for Teaching and Learning. It was tucked away in attic rooms of a building that held obscure administrative departments. I quickly became involved with its work. That is where I learned about such basic ideas as Bloom’s taxonomy. One of the greatest challenges for the new center was simply to create faculty awareness of what it had to offer. Brighton supported it by attending monthly lunches on educational issues for faculty in the College of Science. If anyone else from the math department came to these, I do not remember them.
In the summer of 1992 Jerry Bona, now the department head, encouraged me to attend the conference on Calculus Reform held at Bowdoin College. It was there that I met many of the people who would come to have a profound influence on my thinking about undergraduate mathematics, especially David Smith and Lang Moore. I will have much more to say about Calculus Reform in a future column. An immediate consequence of this conference was that I met Ray Cannon, then Chief Reader for AP Calculus, who was eagerly recruiting college faculty for the AP Reading (the gathering where free response answers are graded). I would attend the Reading in 1993 and continue my involvement with AP, joining the Development Committee in 1999 (the committee that sets the syllabus and writes the exams) and then chairing it from 2002 to 2005.
I also began modifying the syllabi of the courses I was teaching at Penn State. In Fall 1989 I took the honors section of the multivariable calculus class and began shaping it to the vision expressed in Second Year Calculus, the book whose genesis and structure I described in my earlier column, My Mathematical Journey: From F=ma to E=mc2. During that year I worked on this manuscript, then used it for the honors section of multivariable calculus taught in Fall 1990.
I then turned my attention to undergraduate Real Analysis in an effort that would produce A Radical Approach to Real Analysis in 1994. There is much to say about this book, which I will save for a later column.
Finally, I sought to build a course around Newton’s Principia. The honors program at Penn State had been started in the 1970s by Paul Axt, a logician in the math department. In addition to a steep tuition discount and favored access to the smaller honors sections of university courses, its signature innovation was the “cluster course.” This was an interdisciplinary grouping of three courses that was only open to first-year honors students who signed up for all three courses. Talking with a friend in the English department, John Harwood, we decided to build a cluster course around the theme of revolutions. We needed an historian, and John suggested Phil Jenkins.
At the time, Phil was a professor of criminal justice at Penn State, but Phil is really a polymath. In 1993 he switched to Penn State’s department of History and Religious Studies. He is currently a professor of History and co-director of the Program on Historical Studies of Religion at Baylor University.
We chose three periods: the 1680s when I could take the class into the work of Newton and Phil could examine the “Glorious Revolution” that led to the deposition of James II; the 1790s when I would focus on Priestley, Lavoisier, and the chemical revolution and Phil could tackle the French revolution; and the 1920s when I would undertake explorations of quantum mechanics and Phil would lead students into the Russian revolution. Through it all, John would use his class to discuss prominent literature of the time that reflected these upheavals.
It was an incredible experience. We ran it in Spring 1993 with 13 students and again in Spring 1994 with 7 students. The high point of the course came mid-semester when we all focused on Joseph Priestley. A friend of Benjamin Franklin, Priestley had taken up Franklin’s offer to come to America and settle in Pennsylvania. This was after a mob in England had burned down his home because of his unitarian beliefs and support for the French revolution. Priestley settled in Northumberland, Pennsylvania, about 50 miles north of Harrisburg and 60 miles east of State College. Many of Priestley’s papers, including his Last Will and Testament, came to reside in the Penn State library. Each year we made a field trip to his house, now a museum, and examined his papers in the university’s rare books room.
I must give credit to Penn State’s math department for tolerating these non-traditional ventures and counting them toward my teaching assignments. But the fact that I now had more in common with people like John and Phil than other members of the math department was reinforcing my sense that a strictly research-focused department was not my best fit.
Download the list of all past Launchings columns, dating back to 2005, with links to each column.