In winter 2015, I was given the opportunity to design and teach my department's first fully online course, in calculus. Some design challenges emerged in the process, not least of which was the question of assessing homework. In a face-to-face class, students either turn in handwritten solutions to online problems or present them orally in class. But how can you have students presenting work to each other when they don't even meet? My solution—the only solution that could really work—was to have students present work via recorded video and then put those videos in an accessible place for the rest of the class. The process worked as follows:

1. Students would go to an online homework set whose due date had past and select one problem from it.
2. Then, within three days of claiming a problem, students would make a video of themselves working out a complete solution to that problem. The audience for this video was their classmates (not me).
3. The video had to satisfy the following requirements: (1) it had to be less than 6 minutes long; (2) it had to be complete and mathematically correct; (3) it had to be clearly communicated; and (4) the presentation had to have the student's voice, face, and handwriting in the frame at all times.
4. Once the video was done, it was uploaded to a special YouTube channel created for the course; the channel's visibility is set to “Unlisted” to prevent it from being visible to external search engines.

Students were given flexibility in how they presented their solutions, but were required to have their face, voice, and handwriting in the video at all times. The default method, which most students used most of the time, was to find (or purchase) a whiteboard and simply write out their solutions like a teacher would write out an example while using a video camera (often the webcam on their laptops or phones) to record the action. Although the course was online, many students lived on or near campus and went to the library or an empty classroom to make their videos. Other students bought inexpensive whiteboards and filmed themselves in their houses or apartments. Variations on this basic theme soon emerged. One student, for example, couldn't afford a whiteboard, so she taped a grid of blank sheets of paper to her wall and used a magic marker. Another student used software on his tablet that captured his handwriting while simultaneously capturing a video of him writing.

The requirement of having one's face, voice, and handwriting in the frame addressed two issues. One was academic integrity; without all three elements present, the video could be faked. The other, more important reason was to give a human face and voice to the students in the class who otherwise would only know each other as names on a discussion board. As the course unfolded and the videos rolled in, we got to know each other through verbal styles, organizational tendencies, the decor of one person's living room, or the shape of another person's handwriting. The class began to be a learning community rather than a list of names. The video assignments in the course were an effective play on the structure around which the course was built. We used a flipped learning model in which students watched videos before class activities, and with these video assignments, students also contributed their own video material to the class, becoming producers rather than just consumers. This repository of video examples was available at any time, including during exams, so there was a social and academic incentive to make the video quality as high as possible. This assignment was so successful that it has been also implemented in some of our face-to-face classes. My colleague Shelly Smith has been using video assignments in her Calculus 2 classes with similarly positive effects. As we have continued to use video homework, we have surveyed students on their experiences with this assignment, and we've learned some surprising things:

• Students engage in significantly more detailed preparation for making a video than they would for writing up a homework set.
• Students also monitor and reflect on their work to a much greater extent than they do for written homework.
• In general, students seem to engage in self-regulated learning to a degree that we don't usually see in written work. This could be simply because video presentations are public demonstrations of learning, whereas written work isn't generally made available to other students.

Whatever the reasons, we see much more advancement in self-regulated learning behaviors in a handful of video assignments than we do in reams and reams of written assignments.

The concept of a video homework assignment like this is nothing new to many disciplines, such as languages and the fine arts. And there's no reason to believe that this form of assessment, in which the vital human relationship between student and their professors and students with each other is center stage, can't be successful in any discipline. It's an idea well worth pursuing.

Robert Talbert is an associate professor of mathematics at Grand Valley State University.