# How can teachers make maths fun inside and outside the classroom

Ben Sparks shares five top tips for making maths fun and further advice for primary teachers.

## What are your five top tips for making maths fun?

Get hands on

Many aspects of maths can feel abstract, which is of course part of the usefulness and power of maths. That said, there are many ways to include more concrete hands-on moments to really boost pupils’ engagement and learning.

Counting blocks, Cuisenaire rods, geoboards, tiles, 3D models, and more – they’re all useful ways of enlivening the mood, by letting learners literally get to grips with new ideas and tasks.

Don’t have those resources on hand? There are always other physical things around us that can provide a mathematical context, for example:

• invite learners to get out of their chairs and measure familiar objects (are all doors the same size?)
• go outside and time something that moves (how long is that ball in the air?)
• arrange stones in patterns (which objects can you use to fill a square shape?).

Anything which captures the act of ‘actually physically doing’ or ‘manipulating’ can help learners unlock mental versions of maths by linking to real-world tasks.

Paint a picture

One step removed from a hands-on moment is finding a picture that represents the concept you want to discuss. Mathematics has always been represented in pictures, even in ancient times.

Geometry and shape are obviously all about pictures anyway, but apparently, abstract number theory provides useful images too – for example, think how the factors of a number can be drawn as different rectangular shapes. Meanwhile, data is not always easily appreciated in raw forms as lists of numbers, so enhance in-class understanding with graphical forms of charts and plots.

It is hard to think of any mathematical topic that isn’t better understood with pictorial representations. And after all that, simply finding a beautiful image with some mathematical context (such as a flower with beautiful symmetry) is a great way to motivate questions and start vivid discussions.

Try getting your group to photograph natural phenomena outdoors, then discuss the images they’ve chosen and the mathematics they can find. Spirals, shapes, quantities, symmetries; collect them all.

Make it move

There is one aspect of visual maths that has been fundamentally changed by modern technology in recent years. We now have easy ways of making these pictures move. This can change the way children think about mathematical ideas, allowing them to experiment with different scenarios and observe the outcomes. This helps them understand mathematical ideas and the way they generalise, as well as their limitations.

The question ‘What’s changing?’ and ‘What’s staying the same?’ make so much more sense when something is actually moving!

The key thing is that moving images have the power to convey extra information, providing a much more interesting spectacle, and a dynamic starting point for new questions and conversations.

Share the stories

Maths is one of the oldest academic subjects in human history, but it’s common for learners to get through their entire school career and hear nothing of the human stories behind the subject. Even a small amount of research around the origins of ideas can reveal fascinating glimpses of how and why humans have studied and used mathematics for millennia.

Showing students how different techniques were used in different times and places will help them realise why what they are learning now is useful and important – even beautiful.

A classic example could be for students to try to do arithmetic using Roman numerals – not only interesting in its own right, but also pretty helpful in establishing that our base 10 system has serious advantages.

Surprise!

Learning stuff is hard sometimes; it takes effort. One useful way of fuelling that necessary effort is to provoke learners’ curiosity. Maths is full of interesting facts that can be revealed for a big surprise, which in turn motivates further exploration or practice.

A simple mathematical magic trick, performed in a way that surprises your audience, can be disproportionately effective in grabbing learners’ attention. It can also provide an opportunity for a different classroom atmosphere to the standard didactic exchange.

Educators have a chance to incorporate their own personality into a small performance and at the same time spark the curiosity needed to fuel their pupils' learning.

Need an idea? Give this a try:

• On a calculator, type in a three-digit number of your choice.
• Type in the same three digits again so you now have a six digit number.
• It would be preposterous to suggest that I can know what number you have just chosen, let alone its properties (e.g. I can’t know if it’s odd or even).
• But…
• Divide your number by seven. You will get a whole number answer
(Was that a 1 in 7 chance? Are you impressed?).
• Whatever is on the calculator screen now, divide it by 11. You will get a whole number answer. Again.
• Lastly, whatever is on the calculator screen now, divide it by 13.
Please don’t get too upset about the final answer, which may seem familiar…!

## What is the one piece of advice you would give primary teachers when it comes to making maths fun?

Nobody does anything without some form of motivation, let alone anything difficult. Maths can be difficult, but there is always a reason to do it.

Our reasons might range wildly – from needing to solve a problem for some industrial application, or just appreciating the beauty and satisfaction of a piece of geometry – but they are always there. Learners need this motivation too.

Teachers may never head-off all the complaints (‘But it’s hard!’) and questions (‘Why do I have to learn this?’) in any subject, but it is usually helpful to acknowledge the motivation behind learning anything new, before getting too deep in the details.

Things you could try:

• show a surprising fact (for example in the form of a magic trick) to motivate some exploration
• share a beautiful or intriguing image (such as a nice geometric design) – particularly if it’s animated
• tell a background story (e.g. who first thought of this, and why? How is it used?)
• set a challenge (find the most efficient way to do something).

Of course, there will always be the pressure of external (positive and negative) motivations: ‘You’ll get a reward if you do this well’ or ‘Do this or you will fail or be punished.’ While these extrinsic motivations are sometimes undeniable facts of life, there is usually a more helpful intrinsic motivation to be found, which helps learners appreciate the subject itself.

The five tips I suggested previously offer some ideas to help learners in various ways: using concrete and pictorial options whenever they are available, before moving to more abstract ideas. Harnessing the emotional reactions to surprising outcomes, or beautiful images, can help motivate further enquiry.

Best of all, be prepared to rediscover your own mathematical motivations: find a trick that delights you or a fact that surprises you, then share it – and any delight you feel – with your learners.

If you don’t ever show them that maths can be fun and surprising it is possible that noone else ever will.

## Can you tell us a bit about yourself?

• Name: Ben Sparks
• Role: Mathematician, Teacher, Speaker.
• Brief summary of your career: I taught maths in secondary schools for 10 years, while also developing a career delivering mathematics outreach and enrichment workshops and talks. I now work with the Advanced Maths Support Programme, and as a freelancer delivering maths sessions around the world. I also often work with the YouTube channel Numberphile.
• What’s your favourite thing about maths?: You don’t have to take anyone else’s word for anything, you can check it for yourself.
• Why does maths matter?: It’s useful and beautiful, and sometimes both at once.
• What do the children/young people you work with enjoy most about maths?: Realising that mathematical techniques give you the power to understand things that you previously didn’t comprehend, and the power to appreciate beauty in a new way.

#### Additional resources and support from Pearson

Teaching tools are available to support pictorial manipulatives, for example Power Maths.

Our Diversity and Inclusion poster series showcase key mathematicians who have inspired us and positively impacted the way that we live today. Featured individuals range from Katherine Johnson, the first African-American woman to work as a NASA scientist, to Al-Khwarizmi, the man who is considered to have written the first book on algebra.

Pearson has a range of resources that will help make maths learning fun. This includes Power Maths and Maths Flex, which help learners become maths masters.