In my opinion skill-automation is the key to accessing higher-level problem-solving skills in mathematics (and possibly other fields of work as well). But what do I mean by skill-automation?

I don’t know if skill-automation is an officially recognised term but I will explain what I mean when I use this term; a skill has been automated when it can be used and applied with very little, if any, conscious thought and effort. Some skills can be automated quite easily, others require much more effort to automate and there may be yet other skills that can’t be automated.

Automating skills is essential in mathematics because it means that you are able to focus your mental energies towards the more intricate aspects of a problem without getting bogged down with trivial aspects. For example, addition of fractions is a skill that can be automated quite easily (and I don’t mean that it can be just done on an electronic calculator or similar device) and it might seem like a very small and insignificant skill and yet, a failure to automate this skill means that whenever you need to add fractions together as part of a problem you have to strain to either remember the way that you’ve been shown or to try and figure it out from scratch. Both of these are a huge drain on mental energy – it’s like having to think about every single step that you take while walking or having to figure out how to walk every time you want to take a step.

The lack of automation of certain skills is something that often frustrates my students’ attempts to solve problems. Some skills that are often not automated to a sufficiently high degree are

  • Addition, multiplication, subtraction and division of whole numbers and fractions
  • Simple algebraic manipulation and re-arranging equations and formulae and solving linear equations
  • Expanding brackets, collecting like-terms and simplification of expressions
  • Pythagoras’ Theorem and trigonometry in right-angled triangles
  • Recognising and solving quadratic equations

Of course there are other skills as well. The point is that once these are automated (which doesn’t take that long) you don’t have to worry about them and you can concentrate on the more challenging aspects of a problem.

So how do you automate a skill? Well it can happen in all kinds of ways – all of which take time to a certain degree – but the main way is through practice and initially, conscious and directed effort. At first the skill will be far from automated and you will have to think very carefully about what you’re doing (think about when a child learns to walk) but through repeated exposure to situations where the skill is required then, if you are paying attention and concentrating, you will find that you start to spot certain patterns – sometimes these patterns may be very difficult to express in words but you acknowledge them all the same. You will start to take advantage of these patterns subconsciously and through necessity as problems become more challenging – the skill is starting to be automated. Continual exposure to challenging problems will cause you to see more patterns which will often be subconsciously incorporated into your problem-solving. Of course there may be a limit to this – a skill may only need to be automated to a certain degree; the law of diminishing returns will kick in so it will make further automation very time-consuming but possibly unnecessary anyway.

The key here is practice – you cannot automate a skill without a great deal of practice and this is often why many of my students have failed to automate these skills – they simply haven’t practiced enough. They complain that they struggle to add fractions together and yet they refuse to practice this skill. Would you expect to learn to play the piano without bothering with the practice? No, it would be absurd to even think that it could be done. Admittedly, adding fractions is not very exciting (and I’m not even going to patronise you by claiming that it is!) but it IS an essential skill to automate if you want to get on to solving more challenging problems; the same applies for other skills. Learning scales is maybe not a very exciting aspect of learning to play the piano – but I would guess that any piano teacher would insist on scales being learned (and automated) otherwise higher-level piano playing becomes a practical impossibility.

So if you want to get on to solving more interesting and challenging problems in mathematics then you’re going to have to get these basic skills sorted first – there’s no way around it I’m afraid!

Over the last few months I have been working hard to produce some videos that I have uploaded to Youtube covering several topics on the A-Level Maths and Further Maths courses. The video at the start of this post will take you to a Youtube playlist of my A Level Further Maths tutorial videos, and through my Youtube channel you can view all of my A-Level Maths tutorial videos (and many more videos besides).

In my videos I usually try to address specific problems which, through my years of tuition, I have noticed that people often have. In other words, the videos that I make are not just ‘going through’ a particular topic in the same way that they are covered in the classroom or in the typical textbook; I make a real effort to emphasize the specific issues that people get stuck with. I don’t really make videos (at least not any more) that just ‘go through’ a topic – if I don’t feel that I have anything positive and fairly original to add to the noise that already exists then I just don’t make the video.

I am always keen to know what problems people have with their maths studies – there’s always new issues that crop up that, even after all these years of tuition. I want to help people come to an understanding of these problems so I can help people overcome these problems. If there is anything that you would like me to make a video on then please let me know – if (and I emphasize the ‘if’) it is something that I can make an original contribution to then I will be more than happy to make a video on it for you – just let me know. On the other hand, if you just want to ask a question about anything that is presenting a problem for you with your maths studies then please get in touch and I will be very happy to help.

I would be very grateful if, after watching my videos on Youtube, you would like and share my videos and subscribe to my channel – this really helps my videos get viewed by more people and gives me a bit of motivation to keep on keeping on making more videos.