# Mathematical Field Notes

## Bored now

I just read a BBC article about Jimmy Wales called “Boring university lectures are doomed” and the title and the tone of the article made me angry. As a boring university lecturer, I felt I should speak out.

As an undergraduate, I sat through many boring university lectures. Since September, I have been employed by University College London to deliver boring university lectures and have been doing just that. Just this morning I submitted an application for funding to help us film some of those boring lectures and make them available (to our students and potentially the rest of the world) online. I’m doing these things because I think that lectures are a great way of communicating, even if the lecturer is boring, as long as the audience is good.

Next year I will be teaching a boring course called “Lie groups and Lie algebras”. This is an introduction to the study of abstract symmetry in its most general and useful form: I will explain to my students how to understand rotations in higher dimensional spaces; how this allows you to understand the orbital structure of the hydrogen atom without actually solving Schroedinger’s equation; how the hexagonal weight diagrams of representations of the group SU(3) inspired Gell-Mann and Ne’eman to invent the concept of quarks, one of the fundamental constituents of matter.

All very, very boring. I almost fell asleep typing it.

Though there have been many books and papers written about Lie groups and Lie algebras since their development in the 1880s, there is no book which takes quite the approach I want to take. So I will write a comprehensive set of lecture notes and will stand up for thirty hours and explain the ideas to my students. Not all in one go. That would be boring, even by my standards.

And people will come.

Some people will come because they want to pass the exam. I wish them the best of luck.

Some people may come because they think it will be an easy option. I wish them the best of luck.

Some people will come because they genuinely want to hear what I will say; because it’s nice to hear someone who has thought hard about a subject talking about that subject. And sometimes a lot easier than reading their lecture notes. A lecture course is like a story: a long, complicated story and not the kind you would read your children in bed (I lie; when I have kids I will try this). People who have been to a lecture course will come away with a particular view of the subject, not just details and minutiae which they could find elsewhere. Most importantly, they will get an idea of what details they should worry about and what details are unimportant. That comes about as the result of an extended conversation, a couple of hours every week. I’d have that conversation one-to-one if I could, but I have 168 students and other things to do.

## Structured discussion

In the article I read, Jimmy Wales expressed the view that lectures should be replaced by online videos followed by classes in which the material is discussed. This may work for some courses. But not all. For a start, such discussion must be heavily structured: if you just ask people “what did you not understand from the video?” the responses will vary from “everything” to “nothing” to “I didn’t watch the video”. And if you’re structuring the discussion, why not structure it around the story? Why not tell them the story and ask them to stop you when they don’t understand and ask for clarification? And how does that differ from a lecture?

You could try structuring the discussion around explanatory examples, but to be honest that’s how I try to structure the story. You could try structuring the discussion around problems and questions, but we already have those discussions: they’re called problem classes and are an equally (if not more) important component of the degree course. Maybe we should have more of them? That’s fine as long as the students are prepared to do more questions.

Relying on student-led interactivity is fine, provided the students are interactive. For many reasons, difficult to control, a particular class may not be interactive in a useful way: too many dominant personalities, not enough dominant personalities, intimidating or apathetic individuals who change the whole mood of the class. The format of a lecture gives individuals a safety net: a particularly reticent class will still learn, a particularly enthusiastic class can turn it into more of a structured discussion.

Making videos of lectures available afterwards seems like a more workable idea, reinforcing what they have already seen. Sometimes you need to see something twice or more to get it. Our students are already inundated with difficult ideas and information. I’d rather present them with the opportunity to see it again than provide them with too many different videos to watch. Having said that…

## Videos

…I have seen Khan’s fifteen-minute videos and I think they’re wonderful. I have tried to emulate them, with mixed success: you can see the results on Youtube. Some people like them, some people think my teaching style is flawed. Such feedback is welcome (I’m always ready to learn) but there are lots of teachers out there, so you don’t have to like my teaching style. Judging by the number of views, the most useful videos I’ve produced are the ones where I picked something I explained badly in class and explained it again (either verbatim or through an example). Of course you don’t know which these are until after class when people say “I didn’t understand”.

I think Khan’s style of videos are an effective method of teaching and ultimately I think academics will take it up more and more. But to say that they should replace lectures seems bizarre: I think it’s patronising to assume that our students have fifteen minute attention spans. These videos are at best a supplement to lectures. Lectures are there to give a bigger view on the world, how it all fits together. Some last an hour, some last two hours. Some people get bored.

## Boredom

While I’m at it, I also think it’s patronising to assume that our students are bored and not getting anything out of lectures. They’re at university because they’re enthusiastic and interested in their subject. They want to learn about vector calculus, about representation theory, about studying functions on infinite-dimensional space. They know the material is painful and difficult, many of them relish that fact: it’s why we study our subject, to break open our minds and experience the wonder of comprehending a difficult and beautiful idea. Sure, you can try to jazz it up with technology, but at some point the pain and the effort kick in and there is some extremely hard work to be done.

If you didn’t want to think for yourself, you shouldn’t have signed up for a degree.

## Interruptions

Jimmy Wales says that he thinks lectures should have a pause facility which means they need to be online. I agree that would help when you’re revising or reviewing material and particularly if the lecture is being given in a foreign language. But I’d contend that live lectures have a much more useful pause facility. You put up your hand.

Or if the lecturer’s antisocial and talks into the blackboard, you shout out.

You say “Could you write bigger?” or “Could you explain that again?” or “Could you give us another example? Slower?” or “What does ‘cohomology’ mean?”. Some lecturers might not like it. I do. I would like to think of lectures as structured discussion rather than an exercise in dictation.

My students last year were great at this and my lectures were punctuated with wonderful questions and comments like: “Which of those $y$s have dots on them?”, “We still can’t see the dots from the back” and “Could you just use a different notation?”.

Some students are too shy for that, you might argue. They’re worried about feeling stupid in front of their peers. Their peers who are sitting around, equally perplexed, but silent, who inwardly want to ask the very same questions. They’re going to have to take responsibility for their own learning sooner or later. Part of university is about learning how to learn, how to ask questions and get the information you want. When academics mutter disgruntledly about spoonfed students who have been mollycoddled by the system, this is what they mean. A lecture class will get much more out of their lecturer if they show that they’re engaged, if they actively seek out the answers to the questions inside their heads, if they try to iron out the conflicts in their own understanding. Terry Tao, the Fields Medallist, recommends asking yourself “dumb” questions as a great way of learning, even (/especially) for researchers, because if you can’t work out the answer to a “dumb” question then the question is not dumb (and nor are you).

## Alternatives

Jimmy Wales says that when he was being taught by a boring lecturer he went and found some video tapes about calculus instead. I fully empathise. I have done the same thing many times. Indeed, universities are full of resources for people who want to learn about stuff. One of those resources is lectures. If you know how to use them, you will get a lot out of them, even if you’re bored. As technology moves on, so will the range of resources available: screencasts, online discussion forums, wikis. We should experiment with all of these and see what they have to offer. But that’s no reason to cut out lectures, which form the core of the university mathematics experience.

There are times when they’re deeply inspiring, times when they’re incomprehensible and, yes, times when they’re deadly boring. But if you, as a student, engage with them and actively try to get something from them then you’ll find that lectures are can be as effective a means of communicating as the best-written book or the best-planned video.

Written by Jonny Evans

May 1, 2013 at 6:41 pm

### 4 Responses

1. Hi Jonny,

Thanks for the interesting perspective. I don’t yet really know where I stand on all this. I read the Wales article earlier today, and I sympathise with both his and your viewpoints. Painting lectures as one resource among many is appealing. But then the question is: is it effective use of everybody’s time (both students and lecturer)?

I completely agree that lecturers bring their own perspectives which might not be available in any other materials. It makes sense for universities to pay academics to create these materials. It doesn’t follow that those perspectives should by default (or can only) be put across by traditionally-delivered lectures, though.

As someone who never used to put his hand up in lectures, and rarely understood them, I have to defend myself, so will venture that you’re too quick to blame as “unengaged” the students like myself who keep silent. From my A-levels (especially the maths ones) right through my bachelor’s degree, I accumulated quite a convincing pile of evidence that I learned differently from the majority of my peers. The questions I found myself asking were quite different from the norm, and the insight that generated a “click” moment in me was often very different from what sufficed for the majority of my peers. In my A-level maths, whenever a new topic was introduced I would fall way behind during the lessons, where my peers not only /seemed/ to be picking it up more quickly than I was — they verifiably /were/, because they could answer the teacher’s questions when I couldn’t. Things were similar, though somewhat less pronounced, when I was an undergraduate. Does that mean I was failing to take responsibility for acquiring the learning I needed? I don’t think so. I knew that if I sat down by myself and worked through something in my own peculiar way, often flipping between multiple textbooks and alternative lecture notes, I would get the hang of it. It would be antisocial (as well as frequently embarrassing) for me to subvert the lecture towards my own peculiar needs. (Of course, Cambridge does well here because supervisions can fill this gap.)

So it comes back to different learning styles; I’d probably be the one watching the video tapes, while other students might do better out of the lectures. It’d be interesting to explore along what dimensions these learning styles vary, and how the population is distributed along these dimensions. Long tails would suggest a “many resources” approach is essential, but distributions featuring a few distinct modes would mean universities could concentrate on fewer approaches. That would take some serious educational research though. (That said, for all I know, it’s already been done. As with many debates, we are proceeding amid a regrettable dearth of evidence.)

I don’t think anybody is claiming that lectures need to be got rid of. I certainly didn’t get the impression that Jimmy Wales was saying that. But their position as the most invested-in learning device at [most] universities can reasonably be questioned. I imagine that you’re both a good lecturer and a conscientious one. Most lecturers aren’t, even at the best universities. If you believe in the inevitability of poor lecturing being the norm, as I pessimistically am inclined to do, it becomes harder to be confident that the huge investment in lecture courses is an optimal choice.

Stephen

May 1, 2013 at 8:28 pm

• Hi Stephen,

I absolutely agree that we should aim for a varied approach which allows students to work out what works best with their learning style. This is why I’m applying for this e-learning development grant to film our maths lectures: when backed up with online forums to discuss the content this would be a really powerful supplement for the students to dissect their lectures and work out what they don’t understand.

On the other hand, you need a narrative, you need a body of knowledge and techniques, a thread to guide students through a subject. I think it would be hard to deliver this in short videos, and I think that the institution of “the lecture” provides this coherent thread, not to mention an important degree of regularity and structure to student life.

> Does that mean I was failing to take responsibility for acquiring the
> learning I needed? I don’t think so.

Clearly you have the right approach for yourself and you were taking responsibility by making the most of the available resources. That’s the best way!

> If you believe in the inevitability of poor lecturing being the norm,
> as I pessimistically am inclined to do, it becomes harder to be
> confident that the huge investment in lecture courses is an optimal choice.

But would the videos or other resources prepared by a poor lecturer be any better than their lectures? Possibly, in which case this is a wonderful solution. But likely not.

> I imagine that you’re both a good lecturer and a conscientious one.

You can imagine all you like! 🙂

> I don’t think anybody is claiming that lectures need to be got rid of.
> I certainly didn’t get the impression that Jimmy Wales was saying that.

It’s not clear to me exactly what was being claimed because it came second-hand via a journalist. What I didn’t like was the tone and I felt that a counter-case needed to be made. I agree that a dearth of hard data hinders any definite claims either way. I also agree with Jimmy Wales’s comments to the effect that it’s an exciting era of possibilities we’re moving into.

But I think it’s dangerous to suggest that the lecture should be replaced by new methods without introducing them gradually and testing them. Big pedagogical changes have a habit of happening too quickly, particularly in the UK, driven by a perceived need to keep up with change. The fact that universities are providing “inertia in the system” is not a bad thing.

J

Jonny Evans

May 1, 2013 at 9:12 pm

2. Hi Johnny

Greetings from Zurich (johnny here :)). I really enjoyed reading your thoughts on the topic and found many things you say absolutely correct. On the other side I also think that we have reached a point in time where we need to rethink the concept of conserving and providing scientific knowledge. For the sake of brevity let me just list some thoughts which could be thrown into the discussion:

On lectures:
-lectures are not the same as lecturers (or the other way around :))
-lectures indeed bundle the thought process of big groups of individuals and are important from that point of view, particularly on the introductory level (i.e. basic courses and introductory lectures)
-there are indeed boring lectures! we have to admit that

On content
-the quantity of scientific information has literary exploded since the 60s, which is a far bigger problem than we think.
-the scientific content is sometimes closed and not accessible to many due to legal agreements. This is annoying.
-we are still teaching certain things which are outdated.

On technology

On structure
-lectures should be accessible at any time and from any place
-do we really need exams at all levels? I found that master exams at the end of studies were waste of time.
-shorter lectures and longer discussions/thought processes

As I said just a list of phrases which could be thrown into discussion. On the other hand, are we talking about boring lectures or about bad lectures? My point is that just bashing the so called boring lectures is too narrow. The quality of scientific content and its propagation is a complex systemic question, not just who teaches how and is it boring or interesting. Consequently we should have a discussion but just on a different level.

By the way I would love to watch your (boring) lecture on Lie groups and Lie algebras online. Sounds very boring indeed 🙂 Can you provide me the link?

Best regards from Switzerland

Cheers,
Johnny

Johnny Srdjan Micic

May 1, 2013 at 11:07 pm

• Hi Johnny,

> we have reached a point in time where we need to rethink the concept of conserving
> and providing scientific knowledge.

Amen to that! As you say that’s another, much bigger, can of worms. Have you read anything by Michael Nielsen? http://michaelnielsen.org/blog/michael-a-nielsen/ – I really enjoyed his book about this.

> shorter lectures and longer discussions/thought processes

I agree that at ETH, 90 minute lectures are maybe a little too long. I think that taking time from lectures and using it for “discussions/thought processes” might be less helpful than it sounds. Of course lectures involve both discussions and thought processes, but I think you might mean something less structured. Obviously freeform thought processes and discussions (with peers and the lecturer) need to happen all the time, but in your own time. Everyone absorbs things at different rates.

One good model for discussions is to have students learn the stuff and deliver the lectures (like a reading course). This probably works better with more advanced students.

> By the way I would love to watch your (boring) lecture on Lie groups and Lie algebras online.
> Sounds very boring indeed Can you provide me the link?

The lectures will be in the autumn. The notes will be ready before then and I’ll post the link when they’re up!

J

Jonny Evans

May 2, 2013 at 9:47 pm