There’s an old saying that practice makes perfect; it’s very easy to trot out this old saying every now and again without really thinking about it. Does practice really make perfect? I don’t think so. Of course there is the argument that you would need to define what you meant by perfection and whether perfection is something that can ever be attained; I don’t really want to get into that right now – I want to look at this from a more practical perspective.

I completely agree that practice is important when learning a new skill; mathematics being no exception. You have to practise mathematics by doing mathematics and it takes a lot of hard work and enough time to get good. When you first start learning a skill, whether that’s playing the piano, playing tennis or driving a car, your technique will probably be fairly bad. For some things you will, over time, automatically gravitate towards better and more efficient techniques – from my own experience it’s almost like your brain is sifting through all of the possible ways that you’ve done something and choosing the optimal way on your behalf. I remember this happening when I used to train for the long jump all those years ago – some aspects of my technique just came about automatically and I didn’t have to think about them too much such as the leg shoot at the end of my jump; I didn’t need to consciously learn this – just practise it.

But what about when your brain doesn’t do this automatically or if your brain chooses (on your behalf) a poor technique? Simply rehearsing and practising a skill with a poor technique, no matter how many hours you toil away at it, will only reinforce that poor technique and your progress will quickly grind to a halt. If you don’t realise that you have a poor technique then it may not come to your attention until a later time when someone points it out to you – but it’s surprising how many people will practise something in complete knowledge that they are using a poor technique. In this case practice will not make perfect…no matter how much you practise.

Mathematics is a skill like anything else and as such, to really become confident and competent at mathematics (of any kind) you have to practise – but you have to make the effort to use good techniques and not just fall back on ‘comfortable’ but poor techniques.

Mental arithmetic is a good example of this – particularly in relation to the mantal arithmetic part of QTS Numeracy test. I have provided tuition for many people preparing for the QTS Numeracy test and I think the reason that the majority of them felt that they needed tuition was because of their poor mental arithmetic (MA) skills. The reason that their MA skills are seemingly so poor is because of their technique; it isn’t a good idea to try to do long multiplication or long division in your head using methods that are primarily written methods. I point this out to people and introduce them to more ‘mental arithmetic friendly’ methods of doing calculations – after all they’re wanting to improve their MA skills. This means that they sometimes have to re-condition their brains to use this new technique as a first option when doing mental arithmetic rather than what they have been using until now. But many will choose to ignore what I tell them and continue to practise using their ‘comfortable’ yet poor techniques. The result – well…unfortunately they don’t make much progress. The ones who take on board what I say, are willing to work through the initial discomfort of using the new technique but ultimately make it part of their general approach have much more success.

It’s not just mental arithmetic where I see this – I see it with people learning to solve algebraic equations, trigonometry and problem solving in general. But it also extends into anywhere that a skill of some description is being learned – in all of these cases, just practice alone does not necessarily make perfect. At some point you have to make a conscious change to your technique and approach by learning (or even re-learning) a skill using good (or better) techniques and being motivated to practise these good techniques perfectly each and every time if you want to progress beyond a certain level. I’m certainly not the first person to say this but the saying shouldn’t be “Practice makes perfect” but more “Perfect practice makes perfect”.

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