My good colleague allowed me to distribute these extracts from his emails. They are quite interesting, in my opinion.
I have now come to the conclusion that if you want first year students to learn how to write mathematics properly, it is necessary and fully sufficient to spend two hours face-to-face with them, in front of a blackboard, and have them write any form of silly proof such as: a uniformly continuous function is continuous.
But they must hold the stick of chalk and write, and you must correct real-time every single f*****g comma.
I can mark homework week after week and am stupidly dedicated at that; but homework, even good-willed, will not force the lost ones to make any progress, as opposed to the above. Just a face-to-face two hour session, correcting every move.
What a gain of time it would be to simply teach them the trick! How delightfully readable would their papers be afterwards! And what a side-benefit for the whole society!
Why do we then not do this?
As you see I completely gave up on conveying intuitions to 1st year students. Not to mention my own research for the time being.
This term my teaching duties are in a small branch the University has in *******. Classes of 20; students are dedicated, which is not unprecedented. But we can afford being dedicated to them, which is.
So unfair to the crowd in *****! [However] it is not impossible to implement.
Of course the professor who lectures in front of 100+ (30+ is already quite too much) cannot afford it.
Our TA’s should be assigned such — pleasant — duties, could we rely on all of them.
For all I request is two (2, TWO) hours per student, not per student per year. The cost is reasonable.
And the savings are huge; homework and exams become less of a pain: you only have to grade the contents, not return every-single-mark-my-word-bloody-time to the difference between “if… then…” and “therefore…” (a linguistic ability quite useful in everyday life). Which I do in written form, every-single-mark-my-word-bloody-time.
This, for the student who will spend in the average two or three years studying or trying to study mathematics, takes overall more than two hours.
I can report on this more in the future. One of my duties (in *****) will be to mark and comment on exams for people applying to become secondary school teachers. We actually run a full course entitled “How to write mathematics”. It is a year 5 class!
I have not suggested my idea there yet.