Independent Learners vs Educational Principles

A conversation after the lecture today has led me to think once again about something I’ve been wondering about for a few years. At University, students should develop to become Independent Learners, responsible for their own learning, being active learners rather than passive receptors of knowledge.

Now, if we think students should become Independent Learners, we should treat them as such, surely? Currently I am trying to work out where I stand between these two extreme points:

  • We should not give students lecture notes because it means they won’t come to lectures and it is bad for them.
  • We should trust students to be mature enough to use lecture notes and any other material to their best benefit, and if they don’t, then it is their problem and not ours.

I am currently sort of leaning towards the first position, but definitely not at the extreme point (otherwise I wouldn’t be writing blog posts, I guess). But one argument today is starting to veer more towards the second position. Not putting up lecture notes might “benefit” those students who haven’t yet realised that going to maths lectures is an extremely good way to learn (for most people). But not putting up lecture notes also disadvantages those people who put a lot of effort into understanding a course and might be helped by this extra resource.

Now we could ask: which group needs more help? Which group is actually larger? I would hope that in Cambridge the second group is larger, those people who do put a lot of effort into learning because they have chosen to study maths because it interests them.

We are often accused in Cambridge that we only cater to the top 10% or top n% (the n varies in different people’s perspectives) of students, and don’t look after the people who don’t find themselves at the top of the tripos (but are still amongst the best mathematicians in Britain). My blog is meant to cater for both those groups: to give more help to understand lectures, by summarising the important points and suggesting ways of working at understanding it, as well as leading those who want to a little more deeply into connections with other subjects (often only studied later on).

I have a colleague at UCL who said that when he (for the first time) didn’t give out lecture notes, the attendance and participation at his lectures went through the roof. I’d like to hear more on that before I entirely make up my mind. But I am starting to consider whether I might make my lecture notes available to students after the lecture course has finished. Though… that means they will be in circulation and next year’s students will get them before the course… So I have to decide whether I think that is a bad thing or not.


6 thoughts on “Independent Learners vs Educational Principles

  1. I had a great teacher back home who took a rather unconventional approach to the “Calculus 1” course. She’d give out lecture notes, and your homework was to read them before the lectures. Then, during the actual lectures, she’d only answer questions people had about the material they (should have…) read. At the end of the class, or if no one had any questions, she’d give out a mini test, to be completed in 10 to 15 minutes, to see if you really had understood everything. The purpose of her method was to teach students to “learn how to learn on their own”, since you’ll only have lecturers digesting knowledge for you for 3 or 4 years. This was my favorite lecture ever.

    (I’ll discuss what was the outcome of this method when I come back from London. 😉 )


    • I agree with some of your points but not all. If a student can only manage to copy out what is written on the blackboard/overhead/whatever without listening to any explanations, then yes, they would get it from handed out lecture notes just the same, possibly better. However, if you can keep up (and I think most people can learn this, though possibly some more easily than others), then you get a lot of extra explanation. Also you see an argument developed before you, with “we do this because” or “let’s try this next step” or “we want to get to there” or “this is a bit like that proof we had for …” You will also get some “this is how I think about it” or “that used to confuse me but this is how I now understand it”.

      Ok, so if I were to hand out lecture notes *after* the lecture, then students could listen in the safe assurance that they will get a copy of the notes afterwards. But personally I would then worry about “what is that bit isn’t written down in the notes?” I suppose I could remedy that by writing exactly what is in the notes, and so people know only to write what I don’t write. That gets confusing though: your notes are all disjointed and mixed up.

      If I handed out the notes *before* the lecture, then students could (if they are interested enough/disciplined enough/organised enough…) read ahead and so they know what is in the notes and then can listen to (and if they want, write down) the extra explanations. But when I was in this situation myself, I rarely managed to read ahead sufficiently (and look, I’ve turned out to be one of the people going on to maths PhD so I can’t have been that bad!). Then I got very confused about whether I needed to write this down or not, spent the time in lectures skimming the lecture notes and getting lost and not listening after all. You can say that was my fault… But then so is not managing to keep up and listening to the verbal explanations “the student’s fault”. The crucial fact of the matter is that different people learn in different ways and it is very hard (perhaps even impossible) to satisfy everyone’s learning style.

      I am thinking about this a lot and may try to come up with a compromised solution which might be flexible enough to suit several different learning styles. The question I haven’t quite resolved for myself though is this: do first year undergraduates already know their learning style? They have never had lectures (well, most of them haven’t), and they are encountering abstract maths for the first time (again, most of them). Yes, some of them will know their learning style. And for some of them it won’t matter anyway because they will understand the material anyway. But I think for the vast majority it will be very difficult to find out what is actually the best way for them.


  2. Further thoughts that have come out of subsequent discussions: There are always, and have been for a long while, students who type up lecture notes and make them available on the web. Regardless of any one lecturer’s opinion on whether that is good or bad, it is reality. So given this reality, it is perhaps better to proved the lecturer’s notes rather than a student’s copy from lectures, which adds one more possibility of typos? I’m not saying lecturers’ notes are typo-free… but copying in lectures might introduce more. I’m still not entirely convinced of what my position is on this, so further input is welcome.


  3. I write notes for my own benefit whilst/before giving courses. In the past I have made these available to students, mostly because of a lack of confidence in my own lecturing (thinking that if the notes are available then they will be able to work out what’s going on even if they don’t understand me). This year I have not given out notes and I think it has forced me to improve my lecturing: to go at a more reasonable pace and to have confidence in myself. It has also encouraged noticeably higher levels of attendance and engagement, with people asking for clarification more readily (knowing that if they don’t understand it in their own notes, there’s no other source).


    • That is really interesting. I also make notes for my own benefit, in fact I could not lecture without them “off by heart” as some people are able to do. (Who knows, once I’ve been doing it for… 20 years or so, maybe I can then.) You’re saying that not giving out notes made you put more effort into lecturing well, and made students more ready to ask questions.
      When I gave out notes in Category Theory Part III last year, in fact I think it made me lecture better, because people kept expecting a different explanation in lectures to that which was in my notes. (When I say people, I think it was mostly one person who was very persuasive.)
      Cultivating an atmosphere were students actually dare to ask questions (really questions rather than pointing out typos) is also quite hard, I think. I have had some questions in Part III which really put me off my stride, and which I couldn’t answer immediately. You do tend to think more clearly when you’re not standing in front of a whole lecture theatre. So my first years’ tendency to ask difficult questions after the lecture rather than in the lecture is more comfortable for me. But how does one encourage actual comprehension questions in lectures? I’ve had a few, and I have tried to respond to them, but often I think people are embarrassed to ask because they think it will make them look stupid. My answer to that would be that if you don’t understand it, the likelyhood that there are several other people who also don’t understand it is quite high (perhaps unless you’ve missed the last three lectures or so). There will always be some people who have understood it (or think they have) and who might (intentionally or unintentionally) sneer at question-askers, but we shouldn’t let that put us off. (Not that I asked questions in my first year here though… I only learnt it later.)


  4. In my first year of undergrad I had to take all my Maths classes with Physics and Engineering undergrads. This was because my university bundled us all together in the beginning. The mathematicians and physicists loved the method of reading the material beforehand and just asking questions during the lectures, but the the vast majority of the engineering students hated it. This was because most of them still clung to an algorithmic approach to maths, and so they just wanted to know the bare minimum to be able to solve whatever equations they might encounter (in exams…), and the best way to do this is to observe someone else solving a specific problem in front of you. I guess their point of view doesn’t really apply here.

    In any case, the method we had kind of resembles a bit of what happens in Cambridge: in the lectures many people just take notes, then they read and try to make sense of them at home, then they try the example sheets, and finally they have supervisions where they can ask questions and engage in a dialogue regarding the material. And when you look at it, it seems that the lectures are actually the most useless part of it all, since the students aren’t really understanding everything, they’re just copying what’s on the board. Sure, there are students who can (or at least claim to) understand everything in real time*, and may have questions as well. But couldn’t such students also understand the material if it were given in a handout? What I’m getting at is the main flaw of lectures, its pre printing press format: the lecturer writes her notes, copies them on the board, then the students copy them to their notebooks. It seems like everybody’s time is being wasted. Yet one might argue that some students only understand the material if they take their own notes during the lecture, but should we really maintain an outdated method just because some students can only learn this way? Shouldn’t we maybe teach them to adapt to a more efficient modus operandi while there is time?

    * The likelihood of this happening after week 5 in Part III turns to zero if you square it…


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