David Cox, “Reflections on Teaching”

On Thursday, February 28th 2019, Professor David Cox shared with the audience about the ways in which his teaching, and the College, have changed since his arrival on the faculty in 1978, as well as some lessons learned. David began his teaching career at Haverford while finishing his dissertation, then spent four years at Rutgers before coming to Amherst for the next 40 years of his career. When he arrived he realized that Introductory Calculus (MATH 11, now named MATH 111) was a barrier for many students. The department had previously attempted to address the issue through the creation of a special section of Introductory calculus which met more frequently in order to provide students with additional instruction in pre-calculus. This approach was not fully successful, however, as it included too much content in the one-semester course for many students.

The Development of MATH 5 and MATH 6

In 1982, David proposed MATH 5 and MATH 6, a two semester course that would provide students with a full year to cover the content currently in MATH 11. And, as 5 + 6 = 11, that was quite pleasing to David! The department was in support of this work, although there were some individuals on campus who worried that this approach reflected a lowering of academic standards. In Fall of 1982, 47 students enrolled in MATH 5. The course met four days a week, with one day allocated each week to in-class homework problems/worksheets or exams. 

The lessons that David learned from this course were:

  1. The benefits of just-in-time teaching. In the previously offered special section of Calculus, the students did not thrive because they needed the pre-calculus content to be immediately relevant. With MATH 5, he was able to teach the pre-calculus concepts as they arose and were needed.
  2. It’s very helpful to observe students in their learning process. By observing how students approached the homework worksheets in real time, David was able to support their learning and develop future worksheets that would bring out and clarify their confusion. As David stated, “Active learning benefits students and faculty because I could make better pedagogical choices.”
  3. Beware of “Homework Mode.” When students were merely working through their homework assignments during the fourth hour of the week, many of them wanted to complete the homework as quickly as possible and get out of class. In response, David found that he needed to develop different, more complex problems and restructure this time.

The Formation of the Q Center

In December of 1994, the Forum on Academic Concerns of Black Students at Amherst meet at the Drew House. This forum raised three issues: 1) the lack of faculty of color, 2) the fact that diverse students didn’t see themselves in the curriculum, and 3) that students wanted more academic support. In response, Amherst created the Ad hoc Committee on Academic Support in 1995, whose work include the “A Promise to Keep” report. A recommendation from this report included the creation of a Quantitative Center, which opened 5 years later.

In David’s view, two consequences of that work were a change in faculty attitudes about academic support and the creation of a lecture TA position, which was the origin of the Math Fellows program. David immediately included a Lecture TA in MATH 5 and 6, and the first lecture TA in the program was Tony Jack. David would have lunch with the TAs in Lewis-Sebring on regular intervals, which allowed him for the first time to see students as developing teachers, even as sophomores. David noted in his talk that this is a potential pipeline for students to become future academics, but “for this to happen, we have to see them as scholars, as teachers, as mathematicians, now.”

The Development of Intensive Sections in MATH 111

In the early 2000s, David read about the work of Uri Treisman, a mathematician who was interested in how students study. To learn more, Dr. Treisman lived in a dorm, and in doing so, found that students who were not doing as well in the class tended to study by themselves, while students who were doing better in the class studied together. In response, Dr. Treisman created a one-credit class where students would work together to solve hard problems. The adoption of this model at Amherst took the form of MATH 111i, which included an additional 80 minute worksheet section each week. At the same time that David was helping spur this initiative, he also learned about the work of Catherine Goode and the concepts of stereotype threat and fixed vs. incremental mindsets. It was clear in David’s presentation that this work has continued to pervade the work of MATH 111i, the Math Fellows program, and his approach to mentoring students throughout their time at Amherst.

A final point in David’s presentation focused on the range of pedagogical approaches he has tried throughout the years, including an inquiry based learning approach to teaching students to write proofs, asking students to complete mini (15 min) worksheets and then debrief their process with the class, and different methods for structuring groups.

Throughout his presentation, David included a number of take-away points and reflections on teaching. These included the following: 

  • Try stuff. Learn from Everything. Keep what works.
  • When changing a course, give it time, and don’t change everything at once.
  • For senior faculty, we need to give our junior colleagues time to try something new and support their efforts.