I just want to talk about something that really holds a lot of people back when it comes to learning maths; something that stops (too) many people from achieving what they can truly achieve – the fear of failure.

The fear of failure and of making mistakes is a very common issue amongst maths students (though, I’m certain that it’s also the case in other subjects as well). Failure (or at least what is perceived to be failure in someones own mind) and mistakes are always seen as a bad thing. Sometimes failures and mistakes are bad things because the consequences may be very severe – but when you’re learning GCSE or A Level maths, the good thing is that no-one dies if you fail or make a mistake; there is no catastrophic nuclear accident; the world continues to turn and the sun continues to rise and set.

Mistakes are a necessary part of learning and doing mathematics at all levels; and the possibility that you might fail to solve a problem is something that you have to learn to accept as this will ALWAYS be the case even if you happen to be called Albert Einstein (OK, he wasn’t a mathematician but you get my drift).

I know that it feels good when you get the correct answer to something and you succeed in writing out a correct solution – but if you only continue to do what you know how to do then you will only ever be able to do what you know how to do; in other words you will stop learning. The possibility of failure is something that I very often have to work very hard to get my students to accept. Sometimes, and this is particularly true of people who have done well with GCSE maths and moved on to A Level maths, students are so used to getting things right first time and without any difficulties, once they’re presented with an actual problem that they have to solve they will give up. The thing is, it’s not that they can’t solve the problem because in many cases they can, but just that they think that if they make a mistake that they have failed miserably and that only ridicule and embarrassment will follow. They are so afraid of making a mistake that they won’t even make an attempt – they just say, “I haven’t been shown how to do that”, or simply “I don’t know what to do”.

As a mathematician (or student of mathematics) you have to be willing to make an attempt at applying your knowledge and accept that you may (and in all likelihood, will) make mistakes; you may even be unsuccessful in finding a solution for some time and you may NEVER find a solution. Have you failed in these cases? No – not at all. You have failed if you make no attempt at a solution; you have failed if you’re not prepared to make the mistakes that you need to make in order to learn.

Sometimes I have to put my students in situations where they HAVE to make an attempt at solving an unfamiliar problem and where they might make many mistakes along the way; I will not give any clues about what to do until a good attempt has been made by themselves to find a solution. Cruel of me? Not really as this is what they’ll have to do in the A Level or new GCSE maths exams so it would be cruel and wrong of me to not do this and only have them do things that they can easily do. By doing this I’m not saying that I expect them to find a full solution and I even say to them that I’m not bothered if they don’t find a solution; what I do expect is that they put themselves out there and try things out; I AM bothered if they don’t make any attempt even if they claim that they don’t have any ideas. I have to get them to understand that mistakes are a natural part of learning and doing mathematics; that no-one is going to laugh at them if they make mistakes; that their otherwise impeccable reputation will remain intact despite their mistakes; and that they will learn more from making these mistakes than by not making them.

I can see their faces contorting when they first write something that they know might be wrong – but this is what doing mathematics is about; trying things out until you find something that works. As a mathematician you’re not expected to be able to blurt out the correct answer or solution immediately upon being presented with a problem. What you are expected to do is to work to find a solution and this means making umpteen false-starts in the process. Once my students accept this fact and free themselves from the fear of failure (whether real or perceived) then I know that they’ve taken a huge step in the right direction.