Teaching Students to Write Mathematics II
Back to posts after the fun and games of updating my website and blog.
The second video on the Teaching Student to Write Mathematics DVD is by Franco Vivaldi from Queen Mary, University of London. He covers more than just techniques of encouraging mathematical writing. One point of interest, starting at about 9:00 in the video below, is the following slide:
Teacher versus student
The point here is to emphasize the difference between what lecturers see as important – theorems and definitions – and what students see as important – examples. I showed this part of the video during my CETL-MSOR talk and mentioned a student talk earlier in the day where students had said that what they want from lecturers is examples, examples, examples. (I probably came across as a bit more critical of them in my talk than I had intended!)
Although Franco’s point is far from new, I think the slide is well worth showing as it gives a wonderful visual and clearly makes the point. (On the video he says that theorems and definitions are just a beam of neutrinos for the students!)
By the way, I think Franco should add an extra box of examples that comes before and points to the theorems and definitions box since I believe that examples come before theorems. After all it is better to give some examples of groups before defining a group.
Further on Franco also makes a point I keep trying to make to my students: Mathematics is about concepts and not processes. I’ll blog about this at a later date but basically the idea is that pre-university exams in this country give students the idea that maths is about processes. Hence, differentiation is about the process of differentiation, i.e., I give you a function and you use product rule, quotient rule, etc to find the derivative. Of course, differentiation is about something deeper than that.
I’ll look at this video and the other one at some time when it’s not nearly midnight! Meanwhile, have you and your colleagues – or the Leeds University Mathematics Dept as a whole – ever thought of setting up, or helping with, one of these new ‘free schools’? Just a thought that crossed my mind with these places being rather in the news at the start of the new school year. I think they’re allowed quite a lot of latitude and it might be an opportunity to introduce your ideas on approaching and writing mathematics far lower down the age range.
Hi Humphrey,
One problem with setting up a “free school” would be that we know nothing about running a school! (And judging from the Swedish experience the same is true of many people actually running free schools.) Obviously we could help with such a school rather than set it up or run it but either way I suspect that we don’t have the resources – in time or money. Also, the impact of working with a single school is rather small. Producing a DVD and uploading videos is good place to start with the revolution!
Yes, see what you mean about finding time and so on. Good luck with the DVD. The only people I know in the teaching profession are a highly dedicated special-needs teacher (‘challenging behaviour’) who works usually on a one-to-one basis, and the head teacher of a local primary school. However I’ve sent them the link to this part of your blog so we’ll see what happens – you may get an enquiry. I do remember doing formal Euclid proofs (complete with ‘QED’) at what would now be upper primary age which has probably given me the idea that proof’s important.