The Australian Mathematical Society Annual Meeting this year included a public debate on the topic “Is the traditional mathematics blackboard lecture dead?” I was on the affirmative team, arguing that the traditional blackboard lecture is in fact dead. Below is some approximation to my remarks. Being a case for one side of the argument, and in a context of an event as much for entertainment as for serious discussion, the below is a small part of my views on the matter.
We lost the debate rather convincingly — and arguing against blackboard lectures to mathematicians is a rather unpopular cause! — but nonetheless it was an entertaining event raising some important issues for tertiary mathematics educators. I thank my colleagues Birgit Loch and Marty Ross for their valiant prosecution of this unpopular cause; congratulations to Adrianne Jenner, Heather Lonsdale and John Roberts on their victory; and to Adam Spencer for moderating.
* * *
We’re here to debate whether the traditional blackboard mathematics lecture is dead.
We are asking whether something despised, deserted, and largely replaced, is dead. Is a corpse dead? Yes, a corpse is dead. Nonetheless, we can still debate the question.
Now I would dearly love this corpse to be resurrected — at least, in its better forms. But resurrection is well beyond my pay grade, and I look forward to my colleagues on the other side bringing forth its second coming.
In our affirmative case, I‘ll be laying out the issues: what the traditional blackboard lecture is, and how it’s dead or dying.
Birgit will provide the proof around attendance, technology, and how traditional blackboard lectures have been replaced.
And Marty will be summing up and sledging the opposition.
* * *
So what does a traditional mathematical blackboard lecture look like?
The students shuffle in, notebooks open. Some of them have understood the material. Most have not — we all know this, because we mark their exams. The lecturer mumbles incomprehensibly into the blackboard. The students are bored; probably the lecturer too. The lecturer copies their notes onto the blackboard. The students copy the notes from the blackboard into their notebooks.
In this way, traditional mathematics blackboard lectures are a transmission channel for maths notes. This gives maths notes a very good reproductive advantage. The same cannot be said for the lecturer.
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Now, not all traditional backboard lectures are that bad, although as we all know, often they really are. A knowledgeable lecturer joyfully expounding the subject they know and love, in all its depth and beauty, can really shine.
But this is not what most people experience.
And how could it be – when most peoples’ experience is of first year units, where students enrol with imagination beaten out of them by a thousand algebra exercises, ever-decreasing background knowledge, ever-increasing financial stresses, ever-decreasing attention spans, and we have to complete their secondary education, fix their miseducation, and teach the actual intended content, if they ever turn up to lectures, in a tightly constrained timeframe, with limited resources, cramming in those fundamentals we’d be embarrassed for students not to know in the no time left before the end of semester?
The tragedy is that for most students, this is our only chance to get them into mathematics, and we lose them. They don’t learn much – even what mathematics is. And those are the ones who pass.
These circumstances make a mockery of our goals as mathematics educators. How can we nurture that free creativity, that tightly constrained logic, that we recognise as the glory of mathematical thought – that joy at playing with new ideas and problems? No, in these circumstances, the traditional blackboard lecture reinforces all the worst of secondary schooling: regimented curriculum; passivity; boredom. But now at scale.
Tertiary education is a mass social institution. University maths departments teach thousands of students each semester. The bulk of these students have only ever taken lower level subjects where they’ve gotten a taste of the traditional blackboard lecture and then run a thousand miles away.
And it is this, the mass social phenomenon that we mean by the traditional blackboard lecture. It is this tradition which is dying. It is already dead. And there is no reason to mourn its demise.
* * *
Let me turn to traditional blackboard lectures as they currently exist, in my own experience, at Monash.
Well, they don’t — at the first year level. They are literally dead, as a matter of cruel hard fact. Large first year classes are taught in lecture theatres with no blackboards at all… or whiteboards, for that matter.
However… I don’t know if I should say this, but some blackboards actually remain at Monash.
There is a small holdout, a rebel building, camouflaged in 1970s mission brown. It is, so I’m told, slated for demolition. No doubt soon it will come into view of the death star. The building next door is already gone.
But in the meantime, traditional blackboard lectures are still taught on this holdout rebel planet. In these theatres — these arenas! — the chalk still flies, the dusters still dust, the blackboards sail up and down in banks of threes.
I lectured there as nearby buildings crumbled around me — literally. Lemmas were interrupted by jackhammers, propositions by demolitions, and proofs were built up as roofs came crashing down. Now there’s a postmodern metallic learning space next door.
All that remains, for us, of the traditional blackboard lecture, is this forlorn mission brown outpost. And it is really a metaphor for tertiary mathematics education today.
Support for traditional lectures has crumbled. Their time is past. And whatever we think of them, we need to think about what will take their place. Because if we don’t decide for ourselves, there are plenty of others willing to decide for us.
* * *
Now, just because something is dead does not mean it is bad. Evariste Galois is dead, but he was awesome. And so it is for traditional blackboard lectures: some were good; but most, in practice, were bad; and all are dead or dying.