Math seeks to improve teaching

Photo by Diana Li.

The Mathematics Department is taking steps to improve what some undergraduates have called subpar teaching in its introductory calculus courses.

The department launched new problem-solving sessions this fall for students in Math 112, 115 and 120 — single and multivariable calculus courses — and provided peer tutors for students in Math 120. Extra efforts were also made last spring to coach new graduate student math teachers, mathematics professor Michael Frame said, and the department is looking to hire a new faculty member who will focus on mathematics instruction.

“I don’t think the efforts to improve are in response to anything, but rather reflect the correct view that we can always do better,” Frame wrote in a Tuesday email.

Frame said he has helped to coordinate the calculus sequence at Yale for the last decade and that changes to those classes are driven by his “institutional memory of what works and what doesn’t.” Several sections of Math 112, 115 and 120 are offered each semester, and are primarily taught by graduate teaching fellows in the department.

Graduate students interviewed said Frame has spearheaded efforts to improve teaching in the department for many years. But Frame, who was diagnosed with cancer in 2009, said his health may prevent him from continuing this work, and the Mathematics Department is currently seeking to hire a new person to oversee the calculus courses as well as develop new courses and train teachers.

The optional problem sessions were introduced this semester to give calculus students an extra opportunity to practice skills learned in class, said Rishi Raj GRD ’12, who leads one of two sessions for Math 120 that each meet three times a week. He added that when he taught Math 120 and other calculus courses in previous semesters, he felt there was not enough class time to work through multiple examples.

While the new problem-solving sessions are taught separately for each calculus course, the Mathematics Department used to offer evening tutoring that combined students from all three introductory calculus classes. Raj said the old tutoring model “did not go well at all” because students often found it unhelpful to listen to questions from courses other than their own. Now, the Math 112, 115 and 120 problem sessions each meet for two hours on three different days of the week.

Andrew Casson, director of undergraduate studies in the Mathematics Department, said the problem sessions are “ongoing experiments” and may be configured differently in the future. Attendance at the optional sessions has been lower than expected, he said, particularly among Math 120 students.

Raj said only five or six students typically come to his Math 120 sessions. By contrast, around 15 or more students attend the sessions for Math 115, said Miriam Logan GRD ’12, who teaches the 115 sessions.

Two students interviewed who have attended Math 115 sessions said they were useful for improving their understanding of concepts taught in class.

“The TAs sometimes have trouble being direct in their points [in class],” said Eric Conway ’15, a student in Math 115. “We feel that at least the problem sessions do a better job of explaining points in the class.”

Rachel Tobin ’15, another Math 115 student, said she liked the problem sessions because they allowed her to ask “one-on-one” questions and receive individual help. She added that other students at the session had often struggled with the same concepts, and they all benefited from practicing problems together.

But two Math 112 students interviewed said problem sessions for their course were less helpful, as the TA spent more time explaining proofs of calculus concepts than going over sample problems.

Along with the problem sessions, the Math Department introduced peer tutors — students who have previously taken the course and performed well in it — for Math 120 this semester, Frame said. Peer tutors have previously been used in other math classes and have received positive reviews by students, he added.

The department also took additional steps last spring to ready second-year graduate students for their first teaching experiences this fall.

The graduate students gave 30-minute guest lectures to a group of undergraduates that had previously taken calculus at Yale, and then were given feedback and presented a second lecture to the same audience a few weeks later. Frame said the graduate students found the critiques of their lectures helpful and that the department plans to continue the program with second-year graduate students in spring 2012.

Though five of six students interviewed said they were not impressed with the teaching in their calculus courses, Logan said she thinks the Mathematics Department is “very attentive” to the quality of math teaching.

“The extra initiatives that are being undertaken this year indicate the department’s continued devotion to maintaining a high standard of teaching,” she wrote in a Tuesday email.

Two graduate students and former Math 120 teachers, Raj and Joseph Lauer GRD ’12, were awarded Prize Teaching Fellowships earlier this year, which are given to graduate student teachers who are nominated by their students for good teaching.


  • ldffly

    Bring back Serge Lange.

  • JohnnyE

    Easy to find a math researcher. Hard to find a math teacher.