Calculus practitioner series: Meeting the changing needs of our students and client disciplines

Awardees: Robin Gottlieb (FAS), Juliana Belding (FAS), Peter Garfield (FAS), Jameel Al-Aidroos (FAS), Janet Chen (FAS), Oliver Knill (FAS), John Hall (FAS), Meghan Anderson (FAS)

Summary: Awardees plan to design and record a multimedia series on the  interdisciplinary nature of calculus with speakers from Harvard faculty from the STEM and quantitative social science fields.

Bridging disciplines, mathematically

Awardees created curriculum modules that highlight connections between single-variable calculus and the disciplines using calculus: STEM fields and quantitative social science fields. The online, multi-media modules feature short video clips of practitioners in other fields and departments discussing problems in which calculus is relevant, interspersed with quizzes to allow students to try related problems and check their understanding. “The goal of the whole series was to help students make that connection between their math course and how practitioners in various fields use both the tools and concepts of calculus,” explained Robin Gottlieb.

Modules created feature statisticians discussing probability and survival analysis, an economist discussing the interplay of math and economics, a mathematical biologist discussing population dynamics, a physicist talking about Einstein’s Mass-Energy Equation, and an applied mathematician discussing medical imaging. One module titled “What Makes a Good Question? Analyzing Item Response Curves and Their Parameters” features practitioner Brian Lukoff, co-founder of Learning Catalytics and former Harvard postdoctoral student. In this module, Lukoff introduces the item response model widely used for questions on standardized tests. Students analyze the parameters of this model, using dynamic graphing tools and calculus computations, and determine their role in creating good questions. In another module, bio-mathematician Wes Cain discusses the concept of a bifurcation, a sudden change in the expected behavior of a system in response to a small change in a parameter. He gives some examples relevant to climate dynamics, population dynamics and his own research in cardiac rhythms.

One of the greatest challenges Gottlieb, Belding and their team encountered was finding the resources they would need to accomplish their goals, especially after they realized just how great the time commitment would be. In fact, Juliana Belding shifted to a part-time position completely dedicated to the project; without that, the project would have never been completed. Belding taught herself how to edit video, which was time-consuming, particularly since she was not a dedicated film editor. She found that it was more difficult to explain their vision for portraying the pedagogy to a video-editing expert. They found that it took nearly a year to begin to take advantage of the resources available to them on campus via the Bok Center, the Media Production Center, the Academic Technology Group, among others. Realistically, Gottlieb mentioned, “there’s no time to do this on top of everything else.”

Once production was underway, they gained additional insight into the video production and editing process. At the suggestion of Marlon Kuzmick of the Bok Center, Gottlieb and Belding decided to use a student host in most of their modules, hoping this would put the practitioner on camera at ease and provide a bridge to the student audience. They were surprised to find that some of these students had technical expertise that could assist their project, as well as some on camera experience that added to the quality of their modules.

They began consistently using their students in focus groups, and established a “Student Advisory Board” to view rough cuts of their video footage. Belding quickly learned that there was lots to be gained by showing the footage to the students before she was completely happy with it, because she learned so much from their immediate feedback: “it’s never going to be pitch perfect before you bring it in front of the students for feedback, but it can be better targeted for the larger student audience by getting early student feedback.” They made the footage available to their Student Advisory Board online, but also held viewing parties in small groups. In both scenarios, the students provided their feedback via online forms, but Gottlieb and Belding found that the in-person viewings typically yielded more thoughtful responses.

The biggest takeaway from student feedback was that students all preferred short, two to five minute clips that they were more likely to sit through, and that they enjoyed having tasks to complete in between clips to keep them engaged. Gottlieb believes that this kind of interactivity and frequent checking in is especially important to ensure that the consumer of the video is actually learning something. “This is not like watching TV,” she remarked, noting that modules produced in a highly polished form without student interaction may primarily serve the viewer as entertainment, rather than as a learning tool.

Five of the eight modules have been used as supplementary extra-credit curriculum in multiple semesters of the single-variable calculus courses, with high levels of participation and overall positive student feedback. Assessment of the modules is still ongoing. With support from Jenny Bergeron in Assessment, Belding developed a pre-course and post-course survey to measure impact of modules on student beliefs of calculus relevance to other fields. This has been administered to roughly 500 students, but the fact that different instructors use the modules in different ways makes it challenging to compare the data. Within courses however, we have been able to do some analysis. In Fall 2014 Math 1b, there was no change in overall beliefs for those who did modules versus those who did not. However, in the domain of life sciences, there was a statistically significantly difference (in the positive) on the beliefs of relevance of calculus to life sciences for students who completed two modules in those fields (N = 92). Furthermore, the survey has become a broader tool to consider student beliefs of relevance of calculus, how these change over a course and their relation to course performance and persistence in mathematics courses.

In order to complete the remaining modules, Gottlieb and Belding used funding from the math department. Their ultimate goal is to make the modules and assessment surveys available to anyone working with STEM and quantitative social science majors in introductory calculus courses.

Toward this end, Belding and another collaborator Peter Garfield, are creating an MOOC course “Calculus Applied! How Biologists, Economists, Physicists, Statisticians and Others Use Calculus in their Work” built around the modules. This is through HarvardX and has a launch date of Spring 2017. As Belding is now at Boston College and Garfield is heading to U C Santa Barbara, we are bringing in Wes Cain, a biomathematician, to join as lead faculty on the MOOC. Cain was one of the practitioners we filmed in the series. At the time he was a visitor at Harvard on sabbatical, but now Cain is a senior lecturer in the department. All three will see the MOOC through.