The number of times I hear ‘I’m no good at maths!’, ‘I hate it’, ‘I’m not a numbers person’ is too many to count. The upsetting thing is, it’s often said with a smile, a shrug, an acceptance that it’s normal. As educators we know too well what a challenge this is to overcome.
Maths is a fundamental part of everyday life. It’s a global language. It underpins many essential life skills and can also be the key to many of life’s biggest questions. For something so indispensable, we should definitely seek to master it and just as importantly have fun with it. I believe that maths can and should be enjoyed by anyone and everyone!
I feel very fortunate to have had a series of training and development days with a fabulous mathematician, Jennie Pennant, a member of the University of Cambridge’s NRICH team. She has a magical way of demonstrating how maths can be fun, engaging, stimulating and most importantly accessible to all.
At the heart of making maths accessible is the use of ‘low threshold – high ceiling’ resources. This means that the mathematical problems we work on do not require a large amount of prerequisite knowledge. Take the ‘Button-up’ problem created by Bernard Murphy of NRICH for the National Young Mathematician’s Award (an annual venture between Explore Learning and NRICH). This offers a starting point where everyone feels able to give the problem a go:
My coat has three different buttons.
Sometimes, I do them up starting with the top button. Sometimes, I start somewhere else.
How many ways can you find to do up my coat?
How will you remember them? Do you think there are any more? How do you know?
When we remove barriers for our students, amazing things can happen. Suddenly, you start seeing children demonstrating mathematical thinking, making predictions, using conjecture, thinking systematically and logically – even if they are not quite sure what those terms mean yet! Once we create an environment where confidence is raised and interest piqued we have an opportunity to challenge further:
I have a jacket which has four buttons.
Sometimes, I do the buttons up starting with the top button. Sometimes, I start somewhere else.
How many different ways of buttoning it up can you find?
Look back at the number of different ways you found for buttoning up three buttons and four buttons.
Can you predict the number of ways of buttoning up a coat with five buttons? Six buttons…?
Now we’ve hit a new level. The answer isn’t immediately obvious, but it feels accessible. The brain is sensing a challenge. The reward that we receive when completing challenges such as these, can be greatly satisfying. It’s taken some effort yet we’ve enjoyed it.
To facilitate these moments here are some top tips:
- Language – listen out for the ‘I can’t do it’ statements, arms folded, head in hands and respond with ‘You can’t do it YET’. I love using this and whilst some children need a further nudge, it can often be enough for getting them looking at the problem again.
- Step back – this is probably the hardest change to adopt. It’s so tempting to step in and coach the steps a child should take to solve the problem. Resist and step back. There is not one correct method of approach. The reward comes from the personal journey of discovery and yours from watching it unfold.
- You’ve found something that doesn’t work – brilliant! – we want to celebrate the mistakes. In fact get the student up in front of the class to explain what didn’t work. ‘Thank you James, that’s been a really helpful discovery, that’s helped us all avoid a pitfall’.
- Sharing discoveries – equally the group should benefit from their peer group’s discoveries. However, it’s important that the student knows how to explain their theory first. A theory can only stand up if you can convince others as to why it is true. So talk this through with a student and listen to their explanation before sharing the learning with the whole group.
- It isn’t a race – the best problems are those that create more questions. What if we changed this or that? There’s no need to rush to an end point and close the problem. Equally it’s important to allow students enough time to feel satisfied that they understand.
Whilst there is still a heavy emphasis on computation in our curricula, I believe we can find many interesting ways of covering these skills within the problem-solving arena. In doing so, we not only develop a student’s fluency in mathematics but also a large set of essential skills that form the backbone of problem solving.