I’m going to let you in on a big secret about how to get good at mathematics. You might not learn this in school but there IS a quick way of learning mathematics; it’s been known for hundreds of years but seldom talked about and it’s this – hard work.

If that’s not really what you wanted to hear and feel disgusted that I would say such a thing then please do not continue reading this post as I don’t want to waste any more of your time; if you would like to know what my reasons are for believing that hard work is THE QUICKEST way of learning mathematics then please read on…

Unfortunately many of my students get conned during their school maths classes; they’re told “quick and easy” or “cheaty” methods of doing everything from simple multiplications and percentages to trigonometry and integration. It has to be remembered that these cheaty methods were devised by people that understood the theory in the first place – a good example that springs to mind is the CAST diagrams method for solving trigonometric equations (which I don’t encourage using). If these methods are then shown to people that don’t understand the theory from which the cheaty method comes then, sooner or later, you end up with big problems – yet this is done year in and year out in many schools by many teachers and tutors alike in an effort to try and circumvent the hard work aspect of learning mathematics. Teaching these cheaty methods from the outset eventually leads to spectacular failure and lack of understanding as it shows students how to do something in a very limited and narrow range of cases and doesn’t usually provide any kind of flexibility or ability to adapt to unfamiliar situations. Sadly, students are duped into believing that they don’t need to know the theory and develop an unhealthy expectation that maths can always be reduced to cheaty methods.

Here’s the thing – if you understand the theory you can adapt very easily to new sitiuations, solve a wider range of problems and generally enjoy the learning process more because you get more out of it. If you rely on cheaty methods you have to learn a new method of solution for each and every “type” of question that you encounter. To start with this might not be too much of a problem – at GCSE for example you will only really encounter a fairly limited range of possible questions – but further down the line at A Level the doors are flung wide open and if you don’t have some understanding you’re up the proverbial creek without a paddle.

By teaching along these short-sighted lines you encourage an expectation within a student that everything can be reduced to a cheaty method. Which it can’t. From my personal experiences as a maths tutor the largest category of people that fall victim to this way of thinking are those wanting to do the QTS Numeracy test. I’ve lost count of the number of times that I have been asked to provide some tuition for the QTS Numeracy test but insisting that I just tell them all of the “cheaty short-cut methods” to do the questions which they’ll get on the test (by the way; I don’t know beforehand exactly which questions you will get asked on the test; and even if I did I wouldn’t tell you). I’m happy to show people how to take short-cuts provided that they have a sufficiently high level of understanding in the first place. If they don’t understand the basics then we are both wasting our time and I may as well go and talk to a brick wall for a while because they will not understand when or how to apply such short-cuts.

I understand what I’m doing when I do maths but it isn’t because I learned all of the short-cut ways of doing everything. Quite the opposite – I learned to understand what I was doing by working hard and then the cheaty methods become trivial facts; in fact they almost become redundant. By understanding what I’m doing I see where these cheaty methods come from and how they work – better still I can make them even more “cheaty” if I want to in some cases. There is NO WAY to cut out the understanding when learning mathematics and the understanding can only come about through hard work. You have to be prepared to use your own brain to solve problems and not leave yourself at the mercy of some miscellaneous method that you don’t understand but which you keep your fingers crossed that you’re using it right and that it will give you the right answer. Is that really a good way to learn?

IMPORTANT!!! By trying to avoid the hard work of learning to do mathematics properly you will end up spending (wasting) more time, energy and effort trying to get to grips with loads of shot-cut, cheaty techniques that you don’t have any understanding of and will most probably forget every couple of weeks and have to keep re-learning. So hard work really is the quickest way to learn mathematics – not really what you want to hear is it? But that’s how it is.

There is a place for short-cut methods when it comes to mathematics; they can sometimes take the pain out of an otherwise lengthy and tedious calculation but they should NOT under any circumstances be a complete substitute for learning through hard work to acquire the necessary level of competence. You wouldn’t expect to become a world-champion 100m sprinter without hard work would you? And nor would any sprint coach who knew what they were talking about tell you that you could become world champion without a lot of hard work. Leading people to believe that all mathematics can be simplified to such a point where you just need to follow a nice cheaty method is cruel and if you do it and encourage it then shame on you!

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