A grey area: the importance of colour in representations

Emma Hill is maths subject leader and Year 3/4 teacher at Georgeham Primary School in North Devon. Georgeham Primary is a small school with around 100 pupils, taught in mixed age classes. An experienced maths lead, Emma was her school’s lead participant in a Teaching for Mastery Work Group with the Jurassic Maths Hub in 2019/20. In 2018/19, they took part in a separate, local project (called an Innovation Work Group) that she reflects upon here:

I was recently involved in a small research project about the use of colour in maths. We were looking at how colour could support pupils’ understanding of maths, but also how the use of colour, if not considered carefully, can make understanding more difficult. An interesting idea and, as I visualised the fairly haphazard and mismatched collections of maths equipment we had in school at the time, one that I felt I probably needed to be thinking more about.

The project aimed to find out how different children respond to colour in maths visuals, and also how they might use colour to represent their thinking, so we were constantly trying out ideas and then talking to children about their experience of what they were being shown.

Our starting point was in KS1 looking at representations of numbers using counters in different colours.

Which of these representations makes ‘seven’ easiest to see without counting, and which harder?

During the discussions that followed, I was amazed at just how different each child’s experience of something so simple could be. For some children the first thing they noticed was the colour of the counters. For others the position and layout of the counters, whether they were the same size and shape, or even the gaps between the counters, was far more important. None of these would have been things that I would have spent much time considering, yet they all impacted on the children’s experience and understanding.

Over the course of the project, two key ideas emerged for me. First, if we are pushing the children to follow our own understanding closely, we could actually be making things more difficult for them. Take the simple example above of representing seven. If I see seven as the ‘five along the top plus two more’ then this colour layout supports my understanding:

However if the child sees the seven as the group of four on the left plus three more, then my use of colour in the configuration above makes their reading of seven more difficult. The configuration below supports their understanding.

Sometimes I might need the children to see it the same way as me, but in other lessons my understanding could get in the way of theirs.

The second realisation had implications beyond colour. As the images or resources are seen so differently by each child, I needed to be taking much more time to check that we are all working on a shared understanding of the representations we are using before starting. For example, when we were using the hollow plastic Base 10, it came out in the discussion afterwards that one child thought the 1,000 block was 600. The model is hollow, so physically it is constructed from six of the hundred blocks to form its six faces. Seeing it through the child’s eyes, it had the weight and sound of six of the 100 blocks (which it obviously is!) so why wouldn’t he think it was 600!?

Being involved in a maths research project is a great opportunity to spend time talking to children about their experiences and understanding. This project has made me consider all aspects of the resources and images I am using to support maths understanding much more carefully, not just the colour. Our Base 10 is now a single colour and made of foam (which has the added benefit of making no clattering noises!). So now the 1000-block is solid, so literally equivalent to 1000 of the 1-blocks and proportionally correct in both size and weight.

In my classroom, I am determined to continue to make more time to really talk to the children about their experience of our maths lessons because I will only really know what they are seeing if I ask them – regularly!

Sam Malyn, Year 2 teacher and maths lead at Northam St George’s CE Infant School, also on the project, adds:

I am now regularly thinking during planning, and when delivering my lessons, ‘What is it I want the children to see?’. The extension to this thinking is to be considering ‘What else might they see?’ or ‘How might they see it differently?’.

This was reflected in our discussions during this research. It was fascinating to see the variety of ways that children can interpret an image and it is so important that we are open minded enough to see concepts from their point of view.

The children were very forthcoming with their ideas about how colour and presentation of an image can help their understanding. It is important that we as teachers think very carefully about why we are using that colour or image. Are we using it to help them notice something, such as using different colour ‘ones’ to assist with counting? Or are we using colour to reinforce understanding about relationships of number?

A poster-evaluation of the project can be seen by clicking on the image on this page. Dr Ruth Trundley, who led the project, will be presenting a session on it at the ATM conference in 2020.