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”.

In a video that I made recently about ways to improve your QTS Numeracy I mentioned things like using a range of different resources, using things like apps to help you with your addition and multiplications. Drawing on my personal knowledge that I’ve acquired over the last few years as a professional maths tutor in Leeds and successfully tutoring loads of people for their QTS Numeracy test, here are a few free online resources that I think are really useful for those of you out there preparing for the numeracy test. Remember that there are no shortcuts when it comes to learning what you need to know for the QTS – it all comes down to how much you practice and the quality of the practice.

Online Arithmetic Drill – This is a great little tool for improving your multiplications, additions, subtractions and divisions – there really is no excuse for not knowing your multiplications when you’re going in for the QTS Numeracy test! You set what you want to do whether it’s just multiplications that you want to practice or a combination of additions, subtractions etc. set which numbers you want to be asked to multiply, set the time that you want to practice for and away you go – do as many as you can in the time that you have. I personally have this bookmarked on my computer and is one of my personal favourites! My personal best is 107 multiplications in 120 seconds up to 12×12. Try to do 15 to 20 minutes of practice a day for a couple of weeks and you’ll see a huge difference.

Worksheet Generator 1 – This site can produce a never-ending supply of worksheets (dynamically generated) for you covering additions, multiplications, simplifying fractions, addition and multiplication of fractions, rounding, percentages …. the list goes on. Not all of the stuff that’s available will be relevant to the QTS Numeracy test as the site is not designed with QTS specifically in mind but there is some good stuff there that you can really take advantage of.

Worksheet Generator 2 – Another brilliant site for worksheets. This looks like it could be aimed primarily at American schoolchildren so is, again, not specifically designed for QTS. BUT….there are just tons of topics covered. I think the ones that would be most useful for QTS Numeracy would be the sections titled

  • Elementary Math
  • Fractions
  • Decimals
  • Ratio, proportion and percent

Just have a play around with the settings until you get used to it – definitely a recommended site

 

I sometimes get asked by my students if I can do some worksheets for them to practice with – I have done this in the past but if I’m completely honest with you there is really no need for me to do so. I don’t want to sound like I’m just trying to find a way to get out of doing a bit of work, but using these websites you can generate hundreds, if not thousands or even tens of thousands, of questions in the time that it would take me to write out a mere twenty questions and that’s not including the tea-break that I’d probably take half way through and then the time that you would have to wait for me to email it through to you! How can I compete with a computer program that is specifically designed to mass produce questions! And what’s more is all of these worksheets are free, created at the click of a mouse and often have the option for the answers to be generated as well. Maybe it would be better for me to stick to what I’m good at which is the tutoring!

 

 

Here’s the next video in my Ten Ways series – this video is for those of you out there looking for ways to improve your QTS Numeracy. I know that there are lots of people out there who are looking to do their QTS Numeracy test who feel that they’re going to have a rough ride. Well the good news is that as a professional maths tutor in Leeds over the last several years I have done loooooads of tuition for QTS Numeracy so I’ve got a few tips here in this video that might help. It is quite a long video – I didn’t actually expect it to be as long as it was but at least you’ll be getting your money’s worth!

The video, as with my GCSE Maths and A Level Maths videos, is not just giving a list of topics to revise for the test although it does mention a couple of topics that might be particularly useful. I didn’t want to make a video just giving all of the topics to revise because I think there’s already a ton of websites and other videos out there already doing just that. What I did want to do was to bring something unique and new; to share my personal experiences, observations and advice that I’ve learned over the last half a decade or so – no-one else can give you that.

I hope that this helps you out a bit – I’d love to hear any of your comments; your own advice that you can pass on to others preparing for the test and your own personal experiences of the test itself.