What's the Best Way to Teach Calculus?

By Keith Devlin @KeithDevlin@fediscience.org

Short post this week, to give you time to read an important (and how!) research paper on university-level calculus instruction, published recently in SCIENCE, Vol 381, Issue 6661 (31 August 2023), pp. 995-998.

Yes, it’s yet another study comparing active student engagement with traditional, lecture-based instruction. But wait. The paper’s title is Establishing a new standard of care for calculus using trials with randomized student allocation. As that indicates, this one is different. It’s a large scale, pragmatic study, with randomized student allocation to the treatment and control groups. So it’s not to be ignored.

Conducted at Florida International University in Miami, with funding from the NSF, the researchers studied a sample of 811 students across 32 sections taught by 19 instructors over three semesters. (FIU is a large, Hispanic-serving institution.)

Led by Physics Education Professor Laird Kramer and Mathematics Professor Edgar Fuller, the research team found that, across demographic groups, the treatment (active student engagement) was more effective than the control (traditional, instruction-based calculus), with engagement fostering not only deeper understanding of calculus and improved grades, but also promoting the inclusion of under-represented students.

That latter factor addresses a huge issue in contemporary US education. Calculus is a gateway course for STEM degrees. Yet of all students who initially pursue STEM degrees, over half graduate without one, often after struggling through their coursework. A key finding of the study is that defaulting to traditional lecture-based instruction exacerbates disparities in failure rates, and disproportionately affects women, Hispanic, and Black students.

But that’s enough from me for this month. You can access the paper online on the SCIENCE website.