The issue of whether to record lectures or post slides or more generally how much material to give to the students is a new question (the last 20 years?) but I do have an anecdote from 1978.
I was taking an applied math course on Mathematical Modelling from James C Frauenthal (He would sometimes write his initials \(\binom{J}{F}\)) and he passed out his notes ahead of time. I think I was the only student who read them ahead of time. One time I had read the following passage ahead of time:
We have been somewhat cavalier in our assumptions.
During class he said
What is wrong with this mathematical model?
I replied
We have been somewhat cavalier in our assumptions.
He was somewhat surprised, but pleased that someone was reading his notes.
FAST FORWARD TO MODERN DAY.
How much material should we make available for our students? I post slides and recordings.
PRO: If a student misses class they can catch up. Especially good if missing class is rare.
PRO: If a student is in class then they can go back to some point they were confused on.
PRO for slides: When asking a student when they began getting lost we can find the exact slide. This is much better than the word salad that students sometimes emit when describing where they are lost.
BILL: So you understood the definition of P. So you were lost when I defined NP?
STUDENT: No, I got lost when you described some kind of really exciting algorithm.
BILL: Exciting algorithm? What did it do?
STUDENT: You said it was a paradox.
BILL: This is a class in algorithms. We have not discussed any paradoxes.
STUDENT: Did so!
BILL: We can figure out what ails thee. What did the algorithm do?
STUDENT: Something about the whole being greater than the sum of its parts.
BILL: Parts! I think you mean that we solve sub parts and then put them together. This is the Dynamic Programming paradigm. OH- I think you confused paradigm and paradox.
STUDENT: That's exactly what I said. Dynamic means exciting! And paradox is just another name for paradigm.
Often it was hard to see where they got lost.
CON: Students may skip class and not go over the slides or recordings!
CON: The technology sometimes does not work.
BILL: You missed class and expect me to redo the lecture in my office. Did you watch the recording?
STUDENT: No. The recording did not work and it's your fault!
BILL: The first day of class I said you should come to class for the following reasons
1) You can ask questions. The paradox is that's hard to do in a large class, but with so many student cutting class, it's a small class!
2) Taking notes is a good way to solidify knowledge.
3) Going to class forces you to keep up.
4) The technology might not work. Last semester this happened four times. Twice it was my fault, and twice is was not my fault. But that does not matter- it will happen.
5) If you show up in my office hours and want me to explain what I lectured on I will be annoyed.
STUDENT: Uh,... I missed the first day.
CON: In the long term students get in the habit of not going to class. I can't tell if this is worse than it used to be.
CON for Slides: Its hard to be spontaneous. Some of the classrooms don't even have whiteboards to go off-script with. The following happened in the pre-slide days (apologies- I've told this story before on this blog) on April 25, 2003 in my Automata Theory class. I had already done decidability and was going to do r.e. sets.
STUDENT: Do you know whose 100th birthday it is today?
BILL: Will there be cake? If so will they let me eat cake?
STUDENT: Today is Kolmogorov's 100th birthday.
BILL: AH! I was going to do r.e. sets but instead I will do Kolmogorov Complexity!
STUDENT: Great! Uh. Maybe. Is it hard?
BILL: Its fun!
I then gave a lecture on Kolmogorov complexity on the fly, on the whiteboard. I made it part of the course and on the final I asked them to show that if w is a K-random string of length n then any context free grammar for {w} in Chomsky Normal Form requires at least \( n^{0.99} \) rules (this is not the strongest result possible).
This is impossible with slides. No more on-the-fly lectures.
CON for slides: Some proofs are impossible to do on slides. The Poly VDW theorem and the Kruskal Tree Theorem are two of them. Fortunately those are both in Ramsey Theory that has 30 students and a whiteboard, so for those lectures I use a white board.
PRO for slides: My handwriting isn't that good, so slides helps a great deal.
CAVEAT: I used to read a proof, write it out by hand, type it up in LaTeX, and then make slides. Now I go straight from reading it to slides. This is sometimes not a good idea as I am worrying about fonts and formatting before I really understand the proof. I recently went BACK to the handwritten notes THEN LaTeX THEN slides. That increased my understanding since (1) when doing the handwritten notes I was not distracted by fonts or formatting, and (2) at every iteration I picked up some subtle point I had missed.
CAVEAT: When teaching a large class you really can't use the whiteboard since the people in the back row can't see. I don't know if that's an argument FOR slides or AGAINST large classes.
SO- what do you do: record, not record, slides, no slides.And why? And does it work?
I record and use a visualiser to record what I write on paper and capture my voice, then I post everything up (including a scan of what I wrote). Before the lecture I have the notes available which for my current courses are in the form of Google Colab notebooks, as I am teaching a course with some computational content (quantum computing) and it's nice to be able to have interactive code snippets embedded in the notes
ReplyDeleteDoes all of this work? Do students come to class? Those that don't come to class- do they use your materials (perhaps you don't know)?
DeleteIn graduate school, my advisor would give us lecture notes in advance. This let us follow along without having to do a lot of writing during class. So, I could spend class time thinking to understand the material. Sometimes, I'd make some additional notes to add to what he had written. Of course, if you have a textbook and you are following the text, then you don't need to hand out lecture notes.
ReplyDeleteWhen I taught recitation sections, most of the students would spend the class time writing down everything I wrote on the blackboard. I think they spent lecture time doing the same. This seemed to me to be a very ineffiicent use of their time. When did they spend time thinking?
Interesting discussion. I use slides. Two additional points about slides.
ReplyDeletePro: they are a prompt. I often put up the statement of a result or an example and then work through on the board. But if I have been prompted then I am much less likely to get 3/4 of a way through a proof and have to say "Oh, I forgot, I need the X Lemma, so let me do that as an aside."
Con: If I post my slides in advance then many students (I teach only undergrads) put them on their laptop, open three other windows, and start not paying attention.
I TELL my students to bring their laptops so they can go a bit back or a bit forward if they need to check something. But YES- they may well be on FACEBOOK or whatever the cool kids use nowadays. OR working on their projects for another course.
DeleteThis all feels like a scam, you’re going to require laptops in class then some terrorist with a “gamer laptop” the size of a medium pizza box that glows colours will start typing at 144 wpm into LaTeX as the keys injure everyone’s eardrums and makes the chalk shake off of the chalkboard, destroying everyone else’s laptops.
ReplyDeleteAnd if that’s bad enough, half of these “textbook learning websites” you force us to purchase, are just over complicated interactive sites that again, just reward students who have more expensive computers than others.
I'm a big critic of slides; I think lectures with slides usually have terrible pacing. I also like to encourage student note-taking--there is evidence that it improves retention. So I hand-write a big fraction of my lectures. Maybe slides excel for teaching art history, but I don't believe the highest level of math teaching is possible with slides. For that purpose, slides are inherently flawed and no teacher is brilliant enough to make them great.
ReplyDeleteI do my lecturing with an iPad, a stylus, and whiteboard-simulation software named Explain Everything. This has all the advantages of a real whiteboard (of infinite size) plus a lot of other advantages. I can pull up illustrations and videos and write all over them. When answering questions I can write all over my notes to emphasize things I wrote and draw connections between them, then I can hit "undo" to get back to nice clean writing. I can quickly go back and revisit things I wrote early in the lecture, or even in a previous lecture. I can have some stuff pre-written on the whiteboard (from the comfort of my home) if I don't want to write it all during the lecture. I can face my audience while writing. I don't need to worry about which classrooms have physical whiteboards.
Used creatively, it gives me a huge advantage over slides or physical whiteboards. I'll never go back to physical whiteboards, and I'll definitely never degrade myself to teaching math primarily with slides (though I think slides are sometimes good for research talks).
If anyone wants to see how that looks, check out my lecture on Gaussian discriminant analysis at https://drive.google.com/file/d/1IOk_FWjIL0uBOXoQvTkjiL3ipiRzwqOZ
I’m just starting lecturing, so your opinion is highly valuable, of course. I see all your “pros” for slides, and I agree with them. However, there is one “con” for me that is missing: Courses with slides tend to be taught too fast.
ReplyDeleteWriting on a board does help slow the pace down to a reasonable speed.
DeleteWhat happened with R. Lipton's blog?
ReplyDelete