- The class was very small (8 people).
- The room was a standard lecture room with a blackboard at the front and rows of seats.
- There were two assessed projects for the students to do during the
term (counting for 10 percent of the final grade). One of these was
an extended computation using Van Kampen's theorem (Poincaré
dodecahedral space) and the other was about the Riemann-Hurwitz
formula and branched covers.
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.
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.
Here are the things I liked:
- The students came to class knowing something, so you could build on what they knew and help them to consolidate their understanding. You can easily figure out if they got confused by something and fix it (instead of waiting for their homework solutions a week or so after they stopped thinking about it).
- The standard lecture is all about the lecturer talking for 1-2 hours. These sessions were more focused on the students doing things and you can break it up into much shorter segments which helps maintain student focus.
- There is no need to rush to cover material: everything operates on a schedule, and if you don't finish the worksheet in class then the students have more stuff to think about at home. As a result, you can spend longer on things they find confusing and the pressure you usually feel towards the end of a course is much-reduced.
- Usually, you need to finish lecturing the material before the
students can start thinking about it and doing problems. In this
model, the students are working on problems whilst covering
the material in videos.
Here are the things I didn't like:
- It is difficult to get students working together. This is partly a
cultural thing (many students like to sit and think before opening
their mouths) and partly an artefact of the layout of the standard
lecture room (I should in retrospect have moved the tables so that
they were sitting in a more informal way). Here are some things I
would try next time:
- Teach in a room with more boards so that the students can stand up and write on the boards. This is bound to be more interactive for them than sitting taking notes.
- Give out fewer copies of the worksheet in class so that the students are forced to share (thanks to Jeff Hicks for this ingenious suggestion!). Of course, you can still put the worksheets online for the students to download so they have an individual copy.
- There is the problem that some students finish the questions faster than others, so you either let them sit and get bored (or set them extra things to do) or you curtail the students work on that particular problem and get them to present their solutions. In the interests of making /some/ progress in class, you have to do a combination of these things, but it always feels like a fudge.
- Because I didn't want to overload the students, and because they were already watching lots of videos, I didn't set mandatory homework; instead I said that they should finish off the worksheets outside of class and hand in their work every few weeks and I would give them formative feedback. This didn't work well: they mostly just handed in what they'd done in class and left the rest of the worksheet undone. I will of course tell them that everything is examinable, so they can use these extra questions to help them when they revise the material. But I would introduce a mandatory homework component on top of the videos next time.
- Students tended to forget things after each class session because
they didn't do any further work to consolidate what they had
learned. In other words, while the class sessions were great at
helping them understand the videos, they were not long enough to
truly consolidate the material.
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:
- 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.
- 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.]
- 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.
- 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"...]
- So far, has the amount of video you needed to watch each week been
- Yes, less than I thought.
- Yes (written by most students).
- Yes very reasonable, especially with notes underneath to supplement the video.
- I wouldn't mind watching more videos.
- 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
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.
In response to the questionnaire:
- I made sure that the second assessed project was less computational and more theoretical than the first.
- I wrote up full solutions to all the class worksheets. I used the
classes as an opportunity to help students develop their intuition,
so a lot of the proofs we figured out were quite hand-wavy or
pictorial. This was sometimes difficult for them as they're used to
a much more rigorous approach (hence the comments like "Full details
of examples presented", "Maybe have some nicely presented answers to
a couple of the class questions.", "More detailed explanations in
class"). Reading the solutions for the worksheets will hopefully
help them figure out how to convert what we talked about in class
into rigorous proofs.
- The main thing I would do differently in future would be to add a "homework" section to each worksheet: this seems to be the main thing that both the students and I wanted.
- I would reorganise the physical layout of the classroom and use other strategies to try and encourage the students to talk to one another more.
- I will revisit each worksheet, evaluate whether it really helped the students achieve their learning objectives for the session, and them modify accordingly.