Where I teach, we have engineering programs that are three years of length. Students take two, perhaps three mathematics courses, the two first being Linear Algebra and Calculus. Each course are seven weeks and run in parallel with another course. So the mathematics content is basically half of a semester of mathematics. That’s not very much – in fact it is very little.
Such educational programs are common in Sweden, they are called “högskoleingenjör”. A translation into English would perhaps be “College Engineer” if that makes any sense.
The amount of time spent on mathematics cannot be increased, at not least in a discrete step corresponding to one more course. The main reason is the competition over time with all the applied courses. At my institute, a sort of “tug of war” has been going on for as long as I have been there and there is now a sort of “armistice” at the line of two, in some cases three, courses. Some colleagues still hope for, or argue for, more courses. That is in vain. I may be a bit drastic here – but you get the point.
Now what can you do with calculus in seven weeks in parallel with another course? I couldn’t understand that fourteen years ago when I started teaching calculus at my place. I did a pedagogical experiment with two colleagues that tried to address the problem. It failed miserably (I must tell the story eventually). After some years I started to teach other stuff and almost forgot about the problem. Then I few years ago I decided I wanted to come back to teaching mathematics. Now I see that the problem remains, if it hasn’t got worse. It seems – I cannot prove it with data – that the incoming students know even less mathematics now as compared to ten years ago. They basically have no usable mathematical understanding or skills. Again I’m drastic and there are exceptions.
Well, who cares? I care for two simple reasons: (1) Society needs engineers and engineers ought to know some mathematics. (2) It’s my job and I don’t my job to a constant frustration. These reasons can be elaborated – and perhaps they should – but again you see the point.
To simplify, I would say that the traditional way to teach engineering maths is to teach various calculational skills (like integration) with a little dash of understanding and proof and trying to motivate the subject from its application. It doesn’t work, although many teachers refuse to acknowledge that. Again I may by slightly drastic.
That’s one reason I’m looking for a new way of doing it. But I stop here.