Flipping conclusion

[2018-11-29 Thu]

As I posted before (here and here), I tried flipping my lecture course Topology and Groups this year (2018). This meant converting my lecture notes into a sequence of online videos with accompanying notes (each lasting approximately 15-20 minutes) and converting my problem sheets into worksheets we would work through in class. Each week, the students have been required to watch about 90 minutes of videos and then in class we have worked through the worksheets, focusing on examples, group-work and discussion, which is supposed to support the learning from the videos.


Some notes:


The main difficulty I had with designing this course was figuring out what exactly to do in the lecture sessions. If you're thinking of doing lecture-flipping, you'll hit this problem too. If it helps, you can see the worksheets we used on the course website, which is what I settled on in the end. Some of this was group discussion centred around questions I'd ask the whole class (some were Mazur-style multiple choice questions we'd vote on). Some of it was the class working in groups on problems I thought they'd be able to crack in under ten minutes.

The verdict

On the whole this experiment has worked quite well, though there are things I would do differently if I taught a flipped course in future.

The good

Here are the things I liked:

The bad

Here are the things I didn't like:

The students' verdict

At the end of the lecture on Monday of week 5 (nearly halfway through the course), I gave out a questionnaire (questions mostly copied from Mazur's book Peer Instruction) to monitor what the students thought of lecture-flipping. Here is what they said:

  1. What do you like about this class?
    • The course content.
    • The detailed lecture videos, in-class questions and answers.
    • It helps me understand stuff and write proofs properly.
    • I like that we go through questions because I find it much easier to understand the material if I know how to apply it to questions and problems.
    • Lecture videos useful (can rewind!). Examples are illustration of ideas.
    • The geometric examples, group work, working out solutions together, small class size.
  2. What do you dislike about this class?
    • Thursday's lecture is at 9am
    • Only 3 hours a week, which is too short!
    • Lack of problem sets: not clear what the exam will look like.
    • I would've liked a project that was less about computation and more about theory [This refers to the first assessed project, which was indeed heavily computational; after reading this comment, I made sure the second assessed project was more theoretical.]
  3. If you were teaching this class, what would you do?
    • Do a bit more theory.
    • Full details of examples presented.
    • Maybe have some nicely presented answers to a couple of the class questions.
    • More detailed explanations in class.
    • Nothing different.
  4. If you could change one thing about this class, what would it be?
    • Collect all the notes into one PDF so it is easier to revise from during exams. More also more questions to work on at home (not graded as I wouldn't have enough time).
    • Upload solutions of classworks.
    • Some kind of problem sheet (maybe shorter than usual, given lecture videos) to direct towards the exam.
    • It's great fun! [I assume this was meant to say "I wouldn't change anything, as it's great fun" rather than "I would change the fact that it's great fun"...]
  5. So far, has the amount of video you needed to watch each week been reasonable?
    • Yes, less than I thought.
    • Yep!
    • Yes (written by most students).
    • Yes very reasonable, especially with notes underneath to supplement the video.
    • I wouldn't mind watching more videos.
  6. Any other comments?
    • Enjoying this style a lot.
    • Maybe explain some details of some complicated proofs.
    • Really enjoying the lecture flipping.
    • Please use a finer pen in the videos. I'm really enjoying the videos though!

What worksheets worked/didn't work

I was particularly happy with the class we did following the video on the homotopy extension property (Week 5, Monday). This is something I didn't cover last time I taught the course because I didn't have the time and I thought it was a bit heavy and technical. This time, I did the heavy-lifting in a couple of videos and then in class we worked through a sequence of six questions to which the answers were mostly of the form "By the homotopy extension property...". These questions gave some nice applications (homotopy type of a CW complex depends only on the homotopy type of the attaching maps; \(X/A\simeq X\cup CA\); a connected CW complex is homotopy equivalent to one with a single 0-cell) so the students could see the value of the technical stuff they'd learned, and could see easily how to apply it. The trick was for them to figure out how exactly to use the homotopy extension property in each case.

I thought the first session on covering spaces (Week 7, Monday) worked quite well as it was heavily example-focused. One tweak which might make it even better was the following: I had asked them to list all the 3-fold covers of the figure 8 and many of them didn't know where to start; if I had said instead "Can you write down a 3-fold cover of the figure 8 whose monodromy is (something)?" it would have been a bit easier and more directed. Then I could have asked them to try to do the same for other monodromies and exhaust all the possibilities. It's really important that the students know where to get started with these in-class questions, because otherwise they can take ten minutes of valuable class time figuring out where to begin.

I was less happy with the class on braids (Week 6, Monday): the computation of the Artin action worked quite well as a class exercise, but the material on Dehn surgery was a bit too unstructured and went over most people's heads.

The future

In response to the questionnaire:

Next time:

Comments, corrections and contributions are very welcome; please drop me an email at j.d.evans at lancaster.ac.uk if you have something to share.

CC-BY-SA 4.0 Jonny Evans.