An often overlooked aspect of mathematics at GCSE and A Level is presentation. How to present solutions doesn’t usually get much attention – there will be those who naturally present their solutions in a neat and organised way, there are those who will eventually figure out that they need to present their solutions in a neat and organised way and then there are those who don’t realise the importance.

I think good presentation of solutions is one of the most important aspects of mathematics – in some ways even more important than the content. Think about it this way – if someone wrote a book and they didn’t pay any attention to their word order, their grammar and spelling was completely wrong or they didn’t indicate when they were moving from one subject to another in a clear way – then even though they might have some brilliant ideas in their head they have not been able to present their story, arguments and ideas in a coherent way. Would you be at fault for not understanding what they intended to say? Would it be your job to unscramble their words? In this case is the intended content (however brilliant) as important to you as the presentation? Probably not. Yet many GCSE and A Level maths students will pay little or no attention to their presentation. My advice to my students is not to present a page of indecipherable heiroglyphics and symbols as a solution…ever! It is up to you as the author of your solution to make sure that it is presented well and can be understood.

But why is the presentation of solutions in mathematics so overlooked at these levels? Well for a start off it could be because ‘How to present your solutions’ is not a chapter in any of the maths textbooks and a lot of people will only learn what is in a chapter of their set textbook so if it’s not there then it doesn’t get learned. But I think mainly it’s because it is difficult to get to grips with in some cases; it’s difficult to articulate exactly how to present solutions in a concise way. There are many conventions and unwritten rules that mathematicians will obey when writing out their solutions. Some of these conventions can seem a bit arbitrary, and in some cases contradictory, and so this can be a bit of an issue for people who like a fixed set of written rules to abide by; for example it is much more usual to see $2x$ rather than $x2$ or $x^{2}+2x+3$ rather than $2x+3+x^{2}$ even though there is nothing, strictly speaking, wrong with either expression in both cases. It’s easy to make a mistake when learning the conventions and to feel silly when you realise what you’ve done – but unfortunately this can’t be used as an excuse for not trying.

There isn’t any standardisation with how to present your work and solutions and in some ways everyone has their own little idiosyncracies and preferences when it comes to writing out their solutions – I know I do. So how do you learn how to present your work well? The answer for me was to observe other people; look at how other people set out their working, particularly your teachers or lecturers; analyse the layout of model solutions in textbooks; find what you like and what you don’t like. There is a lot of trial and error involved and your presentation is something that will change over time. Your presentation may be quite rudimentary to start with but you need to analyse the layout of your own solutions; check whether you think your solutions would be comprehensible to someone else; write and re-write solutions to problems until you’re satisfied with what you see – you’re not necessarily focusing on the content of the solution but on its layout.

Something that can really raise the standard of your presentation is using words to explain what you’re doing throughout your solution. For some reason, people feel that once they get into a maths lesson or exam that words are forbidden. This is simply not the case. I’m not saying that you have to write paragraphs explaining in minute detail each and every thing that you do – but a couple of short sentences here and there really help someone reading your work to understand what’s going on. Using words is a good way to give a short conclusion to your solution; even though you might know exactly what you’ve done in your solution and what the implications are, you still need to point these out using words in some cases.

There is no perfect way to present your solutions; there is no set of rules to just follow. Sometimes you will receive some criticism for your presentation style but as long as the criticism is constructive then you can take it on board and either change your style or not. Just because someone criticises your presentation doesn’t mean that it’s wrong – just that it’s not to their liking. But is your work is clear and can be understood then you have a good style; it can always be improved in one way or another, but all the same it is a good style. It takes conscious effort of your own volition to learn how to present your work but whatever you do, don’t overlook your presentation.

 

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