Many students ask for printed notes, preferably before the lecture. In many disciplines I know this is standard practice and you wouldn’t get away with not providing them.
There is an argument that having to take notes rather than concentrating on listening and following means the material is not really entering the brain. A recent discussion with a group of people revealed to me though that it might be different for “prose” and maths. Many mathematicians read research papers with a pen and paper next to them, so they can write down calculations, follow the proofs, etc. I myself found as a student that if I wasn’t taking notes, I didn’t understand and couldn’t concentrate on the lectures. I got terribly confused in those lectures that did have notes, because I didn’t know whether what was being said would be in the notes, or was extra so I should write it down, or what… Then I would be reading in the notes to see if it was there, which stopped me listening, so I got very lost. And I know I’m not the only person to have experienced that, though I also know that different people learn in different ways, so I’m sure notes are very helpful for some other people.
In my Part III lectures last year I came to quite a good compromise (or so I thought). I had latexed notes available on my website, which students could use to read ahead or use generally if they didn’t like taking notes and listening at the same time. But if they, like me, could understand better by taking notes, they could take down what I wrote on the blackboard, which would give them a complete set of notes by itself. In Part III, for most people the fourth year of their studies, students should know how they learn best and can decide for themselves which method is better for them. Then I found that people were complaining because I was “just reading out my notes”! Which I wasn’t, I was giving my lecture (using my notes), and of course that resulted in my lecture notes, which is why they were my lecture notes! I have been in some talks and lectures where people actually literally read out what they have written in front of them. If they have “spoken onto the page” that can work, but if they are reading out long sentences which one would normally find in written language, then it is, for me, impossible to follow. And personally I don’t think that works well for maths in any case.
But there are some other considerations which are not to be neglected. If there are notes, some people don’t come to the lectures. Ok, one could say that is fine, that is their problem (or not, if they learn better by themselves). For first years, especially in first term, it is very hard to take notes and keep up with the lecturer so they can hear the explanations as well as write down what is written on the blackboard/overhead/… Surely that means we should make it easier for them and give them notes, so they have a correct set at least? The problem is, how is anyone supposed to learn how to take notes if they never have to? The reality is that most maths lectures (certainly in Cambridge, but the ones I had in Germany as well) are given at a blackboard or equivalent, and some lecturers actually don’t have any notes as such. So at some point in their undergraduate degree, students will have to cope with this. Or photocopy notes from a friend who does it better :-).
I hope that my new experiment of a blog (thanks to Vicky Neale and Richard Weber for the inspiration) addresses some part of that: students can read a summary of the lecture, so they should at least have the correct statements of results. Then there are books available to supplement the notes for the people who find it easier to learn that way. And there is always the chance to ask me questions through the blog (or in fact after a lecture in person).