Maths v. Music Education

I was debating Computer-Based Maths education (CBM) with a sceptic before the summer and he brought up the analogy of music education to support various claims he was making of maths.

As I understood his central point it was that practising hand calculations is akin to practising music pieces--it's simply the way to learn to play. Also there was some attempt to draw the analogy between listening to music and CBM, whereas playing was like traditional hand-calculating maths.

I think music education can teach us quite a bit but believe his analysis and conclusions were wrong.

We need to start from outcomes. What do we hope to achieve from people learning maths and music?

For most people, music is enriching. And for some, generating that music adds enrichment. For a few, it may even be financially enriching too, if they become professional. But I don't think that latter case is why most people study music.

The objective of learning an instrument is to play music. And practising playing music is a direct requirement to achieve that. It usually starts very early--as soon as you can string notes together, you're off trying to practice simple pieces. You are also supposed to practice scales and arpeggios. In my case I wasn't very punctilious at scales, primarily because I didn't see the point. If it had been explained that getting really good at the Eb major scale would aid my playing of an Eb major Haydn piano sonata, I would have been much more interested. In fact no association was made between the scale being practiced and the key of the piece I was trying to play.

Back to maths. My argument for CBM is that practising hand-calculating doesn't relate to the real-world outcomes in any direct way. It's not akin to practising a piece of music because the real-world outcome is disconnected. In fact my adversary in the debate agreed completely with my analysis of real-world maths: that it's computer-based. He just believed practising hand-calculating was the way to get there. I don't. In fact for all the reasons I've gone into before, I think it's detrimental for a start because it de-prioritises much more important, much more real-world outcome-connected material.

Far from just learning that practice is important, we should learn from music education that repeated practice or experience of the actual outcomes (in maths--real-world problem-solving) is vital. CBM aims to do just that.

We shouldn't forget that one big difference between music and maths is compulsion. For the most part you only learn an instrument if you (and/or your parents) want to. Everyone is made to learn maths. In music if you want to play pieces, you need to practice them; that motivates you. In maths, if you have no idea why you'd learn it, can't see an outcome you're interested in, why would you practice? And in fact the practice prescribed is largely dissociated from outcomes you'll face; so you'd have a point!

There's something else music can teach us--about how assessment works. (Lord) Jim Knight pointed this out to me. At least in the UK, you take a "Grade" exam when you're ready, not along with everyone else whatever your level. The exams are closely tied to the outcomes, mainly playing pieces live to examiners. There's some sight-reading (you'll need that if you want to learn new things), some scales and some questions on listening to music. Most people do well in the exams because they're ready, yet they are still highly-regarded, not dumbed down.

Why not adopt this sort of model in maths?