Learning Calculus through Video Production
Andrea Heyman, a Ph.D. student in the Department of Mathematics, developed an innovative assignment for students in her Calculus I class—making short explanatory videos to demonstrate their understanding of calculus principles.
Heyman taught her course during Columbia’s 2014 Summer Term to students from Columbia and those visiting from other institutions, all of whom had varying levels of familiarity with calculus. She conceived the video project as an assignment that would not only ensure that her students had mastered the subject matter, but also help them to cultivate communication skills.
“A lot of these students, they’re not in it for the calculus; they’re in it for some requirement,” Heyman remarks. “The calculus material is not going to be what sticks with them going into their future careers …. The skill that I really wanted my students to have coming out of the course was not just the calculus material, but the ability to think in a rigorous manner and, more importantly, communicate that thought process to someone else—to be able to explain something technical so clearly that somebody who was not familiar with the subject would be able to understand what they were saying.”
“The skill that I really wanted my students to have coming out of the course was not just the calculus material, but the ability to think in a rigorous manner and, more importantly, communicate that thought process to someone else.”
Heyman had this learning objective in mind while planning her course, but didn’t hit upon the idea of using video until attending the 2014 Teagle Summer Institute, an intensive, multiday series of workshops, discussions, and written reflections centered on the use of emerging tools to support effective teaching. The Institute features an array of presenters, including, among others, instructors from various disciplines, library personnel, educational technologists, and representatives from offices and resources supporting teaching on campus.
“It was through seeing some of the people who came into the program giving talks on their use of video and talking with my tablemates that I came up with the idea,” she says.
Her tablemates, and the Teagle Summer Institute presenters, were drawn largely from the humanities and social sciences, and in fact the assignment can be seen as a creative synthesis of pedagogical innovations being used in those fields and the rigorous explanations found in mathematical proofs in more advanced mathematics courses—one that, as Mark Phillipson, Director of the GSAS Teaching Center notes, reaches beyond the “snapshot of the end result” that an exam or problem set can offer to provide a richer portrait of a student’s learning.
Implementing the Assignment
Heyman introduced the assignment in the first week of the six week course to allow students time to consider their topics and to review existing explanatory videos as models. Students were allowed to choose their own topics, though Heyman ensured that the salient topics of the course were all addressed, since the videos would be released to the course as a whole as study aids for the final exam.
Heyman partnered with Barnard’s Instructional Media and Technology Services, which provided guidance to students on making the videos. The few student concerns brought to Heyman, however, were not technological but conceptual: which topic to choose, the best method for explaining it, etc.
Carefully reviewing and evaluating one five-minute video for each of 30 students was very time-consuming, but Heyman was pleased with the end result.
“Overall, I was very impressed,” she says. “They chose topics that were very reasonable to do in the time limit, and they were able to thoroughly explain or work through the problem. I think they did it very well.”
“They were able to hone the skills that I was hoping they would come away with, and I think that they enjoyed doing so—especially some of these which were just above and beyond with the creativity component. I think that gave them an outlet for expressing their more creative side in a class where that’s not usually encouraged or paid attention to in any way.”
For their part, the students responded positively to the assignment, with some even opting to make their videos publicly available on YouTube.
“I had more than one student who said ‘I thought I was going to hate this assignment, and it turned out that I didn’t, that I actually enjoyed it,’” Heyman notes.
Heyman is exploring ways to improve the project for a future course, including building more collaboration among students into the assignment. But the experience of incorporating video into the course, from the initial spark of the idea at the Teagle Summer Institute to its culmination in the final videos and student feedback, has given her a new perspective on what can be achieved in an introductory calculus course.
“Before the summer program, it didn’t even occur to me that video was something I would be able to use in my class. And even after seeing some of these presentations, they were all from people in fields very different from mine … The one huge takeaway I got was that these tools can be applied to math, and that’s something I hadn’t really thought of before. With a little bit of creativity, you can adapt a lot of these tools to your specific learning goals as an instructor.
“I was really pleased to see what the students came up with. It taught me that asking them to do this sort of thing was not unreasonable. They were able to hone the skills that I was hoping they would come away with, and I think that they enjoyed doing so—especially some of these which were just above and beyond with the creativity component. I think that gave them an outlet for expressing their more creative side in a class where that’s not usually encouraged or paid attention to in any way.”