I know that many teachers firmly advocate learning to play a piece slowly even if it's quick. I was wondering what you thought were the pro's and cons of doing this.

I am all in favour of practising smaller problematical sections slowly, even very slowly; but I don't like to ask a pupil to learn to play a whole fast piece at a slow and steady speed. I find that so often it's not possible to get it up to the tempo it needs without big problems. You may well find a fingering which will work perfectly at a slower tempo which just isn't feasible at faster tempo. Similarly, the kind of touch and phrasing that works at a slow speed may not sound right when it's faster. And then of course there's your entire conception of a piece. I had a girl pupil once who would take home a piece a week and come back with it learnt, but although it was always flawless at a slow tempo, I just could not bring it up to speed with her. Her whole "feel" for the piece was something completely different.

So although I may take a piece phrase by phrase, whether I'm teaching it or learning it, I try to get the proper feel for it at its intended tempo as soon as possible, even if it means initially there will be a lot of stumbles. You can always go back and analyse why those stumbles are happening and eliminate the problem.

I just wondered whether I'm alone in this.

This is exactly as I learn a piece

Will reply more when I have more time but essentially my teacher's approach is the same as yours