As an advocate of new teaching and learning innovations, I still find myself falling back on the traditional chalk and talk for my own lecturing as well as having to defend the use of such an archaic practice to the powers that be within my institution. Indeed, after a couple of years running Bifurcations, Catastrophes and Symmetry I felt myself yearning to return to the comfort of what I know best, and that using the card system that seemed to work well previous years was almost compelling me to go through the material at a faster rate than I really wanted. Also a few years ago after taking back Differential Equations, a core first year module, we’d overshot admissions so had 400 plus students. Usually taught by the traditional three lectures a week in a large lecture theatre, with blackboards, that year due to larger numbers I was forced (kicking and screaming) into one of the University’s grand cutting edge 500 seater lecture theatres having to use visualisers.
All this started me thinking about why it is that us mathematicians resist the call of the 21st (20th?) century, and why, so far, there has not been a game changing innovation that would banish blackboards to the history books. Perhaps we are just being stubborn dinosaurs and resisting change for no good reason?
That’s not to say that I exclusively, and only, use blackboards. In another module (“Problem Solving”) that I taught for a few years I made the most of some of the University’s flexible teaching rooms, such as the new(ish) Oculus building, where there is not a blackboard in sight. Instead there are varying quality of white/glass boards but most importantly projection screens so I could use Prezi presentations and movable furniture so I can get even a class of 80 students working in groups. The subject matter lends itself to this delivery method however, a typical maths lecture would not necessarily (I have seen some good examples of “flipping the classroom” in maths lectures, primarily in the US, but always with a relatively small number of students). Of course, over Covid lockdowns delivery of material also had to be thought about carefully, but as well as videos and live teaching done using a graphics tablet, I also managed to still make use of the blackboard in my office! See a summary of my approach in a previous post: Covid Teaching – A Late Reflection. [Yes, myself and most of my colleagues in the department have blackboards in their offices, the one in mine I actually insisted was brought down from our old building when we moved into the new one in 2003, it then followed me when I changed office. It’s too big to fit in the lifts and is a proper good quality heavy one, took three porters to carry it from one office to the other!]
There is, of course, the romanticised reasons for the call of chalk. It’s a very tactile way of writing/drawing, easy to make changes, to draw diagrams, and of course it’s a lot easier to tell when a piece of chalk is about to run out. When Warwick started to introduce lecture capture in the main lecture theatres, those implementing the technology were worried that blackboards would be much harder to capture clearly than whiteboards, it became apparent very quickly this was not the case, and in fact the opposite was true. So the argument quickly becomes not whether chalk is preferable to white boards, but whether the art of the “chalk and talk” lecture is outdated.
Through necessity some of my colleagues, indeed some whom you would consider to be traditionalists, have moved over to visualisers to present lectures. In some sense capturing the benefits of the “standard lecture” whilst adding the benefit of a permanent record of their scribbles. The main disadvantage is limited writing space, even with two visualisers it becomes much harder to refer back to ideas covered more than 10 minutes ago. Larger solutions such as an A0 sized writing surface are a promising possibility, although for now the cost would still seem to be prohibitive, and for the purists you still lose the tactility of chalk on board.
Another colleague delivered his entire lecture course on a tablet (as in the old meaning of the term, a writing tablet projected onto screen).
So why not embrace technology? I think it largely comes down to this
Should Universities teach students mathematics or teach them how to be mathematicians?
I think this also captures my views on “printed lecture notes”, and why I dislike them with a passion, but that’s a whole post of its own so I won’t pursue that here. It is very easy to see a lecture as a way of getting information from the lecturer (read lecture notes) to the students. Paraphrasing something I once heard in a talk on the subject, some people think that “lecturing is getting information from the notes of the lecturer to the notes of the students without going through the heads of either”. The other pearl of wisdom I have heard, again paraphrasing because I can’t remember the source, is that “material that is taught in lectures is forgotten almost instantly, but understanding that is taught in a lecture lasts a lot longer”. The latter is why blackboards are such a great medium for mathematics, you can build up to results, draw diagrams to aid the understanding of what’s going on, go back and correct mistakes, or go back and add clarifications, all the while building up to the “big reveal”, the “this is why we have done this”, big chalk flourish underneath to emphasise! Ta da! It’s a performance, and it’s showing how mathematicians (the lecturer) actually thinks about DOING maths, rather than just reproducing a set of lecture notes. The most memorable lecturer I had as an undergraduate was the late David Tall, he took this to the extreme, during the lectures it would seem chaotic, he was always going back to things, changing, annotating, at times you cursed him because you also had to do the same thing to the notes you were taking (this was years before printed lecture notes were even a possibility!). But, every single lecture, when you walked out that room, you understood perfectly what he had done, and why he had done it. Brilliant.
So, given all this, here’s my list of why blackboards are the way to continue teaching mathematics, I’ll probably periodically come back and edit this, but for now:
- Theatre! Giving a good lecture is like performing on stage, you want to make it engaging and interesting. Banks of blackboards allow you move around, swap from one to the other, be more physical in ways that whiteboards don’t and standing at a lecturn using visualisers/slides certainly doesn’t,
- Which allows the “big reveal” in a natural way,
- And allows you to teach how to be a mathematician, not just teach mathematics,
- You know when a piece of chalk is going to run out,
- Unlike whiteboards, blackboards don’t reflect light and are a better choice for good video lecture capture,
- Don’t listen to IT telling you chalkdust clogs up the lecture room computers, first invest in proper chalk (Hagoromo, obviously) and second these days PCs become obsolete and need to be replaced way before chalk dust becomes an issue,
- Chalk is easier to wash off your hands and clothes than pen, and easier to erase off the board,
- More space to keep things visible longer, choose what to rub out, what to keep for later to refer back to (see third bullet point),
- Being able to make mistakes, and easily go back and change things, add things, show students that the process of doing mathematics involves making mistakes or improving things as you go along (again, see point 3),
- Writing on a blackboard naturally slows you down when presenting, erasing boards gives a natural break for the students,
- Drawing diagrams, the more advanced the topic the more diagrams become an art form. Full stop the best medium.
- Also…….
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If it’s good enough for the Doctor…. |
Finally, since we’re on the topic of teaching Mathematics, I thought I’d use the opportunity to finish with one of my favourite quotes on the topic:
Mathematicians aren’t people who find maths easy. They’re people who enjoy how hard it is.
Matt Parker, Standup Mathematician
Photos on this page, top screenshot from “A Serious Man” 2009 (c) Universal Pictures, bottom and featured image Peter Capaldi as Dr Who (c) BBC.
