Spring 2014 was the first time I had video lectures from 6.851 that students could view, which was suggestive of doing inverted lectures. I had used inverted lectures in 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra in Fall 2012. This was my second attempt at inverted lectures, so I implemented some improvements I had from my previous experience, such as focusing more on problem-solving and trying my hardest not to add more material. Though it is simply my natural tendency to dive into more content, I tried not to turn the in-class sessions into more lectures. As a result, I thought 6.851 was a lot more successful, interactive, and fun.
In Spring 2014, we met once a week, though perhaps it should have been twice a week. First I answered students’ questions or maybe reviewed the lecture material in a different way, usually presenting it backwards or something just to make it a different delivery in order to make sure the material was understood by the students. We then focused primarily on solving problems. I gave one or two problems to which I knew the solutions and then one or two unsolved problems. The students had the option of working on either or both. A lot of the time, the solved problems were a warm-up to trying to solve the unsolved problems. The students who were less interested in research would solve the solved problems, and they would be happy. The ones who wanted to go further would work on the unsolved problems, and there were a lot of students who did both.
For the most part, every student worked in a group. The group size varied from two–perhaps just a friend in the class–to six or seven. The students self-clustered in groups, which tended to remain unchanged from week to week. This was definitely the largest format that I have ever done for a problem-solving session. There were between 60 and 80 students, which was much bigger than what I was used to from the optional open-problem sessions. In terms of working with the individual groups, if students were working on a solved problem, I might give them a small hint in the right direction. If students were working on an unsolved problem, I brainstormed with them for a few minutes before moving onto the next group.
The size was definitely a challenge in that I would only get to speak with each group maybe twice in a 2.5-hour session. It was hard for me to keep in touch with everyone all the time. I and the two TAs went around and did a sort of message passing. If someone had an idea, and someone else from another group was working on the same thing, then we would mention it to that particular group.
We logistically could not adhere to an oral broadcasting system of every idea. Instead, students entered their ideas into a message board online. At the end of the 2.5-hour session, when everyone was still working in their group, they might have had a moment of looking at the message board and think, “Oh, too bad, we had the same idea.” But for the most part, the sessions resulted in several different ideas that, when put together, gave a pretty complete picture and exploration of the problem. Another advantage to logging progress with the message board was that the ideas were captured in a more permanent form.
The idea was that even if not all the students were working on the unsolved problems, there was still exposure to people who were working on them. Everyone in the course was able to see that progress happens. We ended up solving a lot of the unsolved problems and wrote papers out of those results. I think this process gave a very tangible sense of excitement that students would not necessarily have seen if there had just been the optional open-problem sessions. For me, it was a lot of fun to incorporate this aspect of research into the main line of the class. Everyone was able to observe that the field was advancing and that it was, in fact, really exciting.