Building risk taking and resilience

“I want to do something a bit different with you in maths today. It will probably feel pretty weird to start with, but go with me, because I want to give you an experience of what maths is like once you finish school.

Often school maths tends to be focused on getting the right answers to questions that look pretty similar to ones that you have seen before, usually pretty quickly. That’s very different to maths outside of school. In the real world no one wants you to answer questions that they already have answers to. It’s not a job. We have computers for calculating.

What we need humans for is to figure out what calculations to to, or even what to try in the first place. We need people to find patterns and experiment with problems, then we program computers to do all the easy bits like adding up and multiplying.

So that means that today our maths lesson is going to be a bit different. We are going to try experimenting, rather than just calculating. That also means that we will have some different rules today.

1. The answer is not worth any points – guessing is.
   This is not going to be maths that you already know. It is stuff that you haven’t been taught yet. So I’m not expecting you to know it before we begin. Instead, I want you to make a conjecture – that’s fancy wording for having a guess. Each conjecture you make scores a point. If you don’t know what to try, deliberately guess wrong and test that out – it might give you an idea to try out next.
2. Whatever you guess, you have to test.
   When you make a conjecture, you have to try it out and see if it works. The testing process scores a point, whether your conjecture was right or wrong. If you are right, then you still have to prove it, but then you need a harder question. If you are wrong, then make a new conjecture and score yourself another point. Test that one out… and keep going.
3. Change your mind as many times as you want – score a point for each thing you try.
   If a question is a really good hard one, you might need to try lots of things to figure it out. Each one that you try scores a point. You can number your guesses, or change colours for each one so that I can track it. Once you are happy with it, draw a star and I’ll know where to look.
4. Feel free to work together and copy if you want.
   Once you have had your own first guess at each question, you are welcome to work together if you want to. Just make sure you all write it down and you are all thinking hard. The answer itself is not worth any points anyway, so if you and your friend want to write the same one down then that’s fine. If you can think of two ideas, just try them both and get double points. In fact, if you are really scared about it then you can copy off me – but then I get the points for the guess. Instead, you might want to ask me for a wrong answer to prove wrong, because once you’ve tried that you might have your own idea to try next.
5. No erasing mistakes – use a check box to show you have evaluated them.
   When you realise you were wrong, and you will, then I don’t want you to erase that or you lose the point. Maths is about proving and also disproving ideas. When you change your mind, that is something called “evaluating”. Draw a little circle, like a check box, and put a tick in it so that I can see that you found the error. That’s really important – we actually mark that as part of a strand of maths called reasoning – so please don’t rub it out.

At some point you will probably work it out. Remember that you still have to prove it, otherwise it doesn’t count, but at that point come and get a trickier one so that you can think again and score more points. When you get stuck, I’ll ask you some questions to help you to think it through.

And one more thing, I will definitely show you how to work it out, but that will probably happen tomorrow rather than today. I want you to have as long as possible thinking about it. Also, in the real world you don’t often get to the answer in one day – hard problems take time, and experimenting, and trying the wrong thing first, and working together. And maths today is going to be real.”