How do we encourage students to study for an at-home, open-book test?

I recently gave my first at-home Calculus exam. My students had 24 hours to complete their exam, and were allowed to use all class resources (books, notes, my lecture videos, etc.). I am realistic and know some of them probably worked together or used other online resources as well. My worry was that students would not study in advance, thinking there was no need. I wanted to incentivize them to look over the material and work practice problems before the actual test began, so that they would internalize more of what we’re studying.

So I asked my students to create videos of themselves solving practice problems and talking through the steps/reasoning. I provided a list of problems spanning all of this exam’s concepts. Each student who chose to participate (for extra credit on the exam) claimed a problem, recorded themselves solving it, and posted it to our Canvas discussion board. I viewed the videos for correctness (though many students checked their work with me before making their videos) and commented on any small errors they contained. 31 of my 39 students partook in this opportunity.

Since I had already curated this list of problems to choose from, I also encouraged all students to use the list as a study guide, pointing out that they could check their work by looking over the videos posted by their classmates. In class the day after the exam, I polled my students asking if they had viewed their classmates’ videos, and whether that was helpful. Over 60% of the students who answered the poll said they had viewed a classmate’s video, and of those, all of them said viewing it was helpful. They also all said that creating the videos was helpful for their studying.

I expected the video-creation to cause more issues than it did, but the students all seemed to figure out which technology worked best for them, and I did not put any stipulations on how they created/shared the video. I showed them how to make a video in Zoom (just by recording a meeting with no one else in it and using the Whiteboard) and how to share the video link. Some students used other apps on their computers or tablets to record themselves working. Some students even solved the problem on paper and recorded their work with their phone camera. For students without access to video technology, I allowed them just to solve their problem on paper and to share a picture of their work. All of my students have reported having access to a camera at least, so this solution seemed to work for everyone.

I would use this extra credit assignment again. I think it was a great way to get students engaged with a problem and helping each other. It also created a trove of study material for other students; now instead of 40 students emailing me to check their work on a review problem, I could just point them toward the videos made by their classmates. Ideally students would comment on each other’s videos with questions or suggestions, but this didn’t happen, despite my urging them to. I think in a class that started off online (and not a class that was forced online in March) with a clearer initial expectation of commenting, this could be changed.

I’d love to hear how other math instructors have encouraged students engagement online!