Maths Without Limits
Opening Young Minds to Endless Possibilities

(first published in TES – July 2019)

I walked into a colleague’s classroom some months ago and saw this above the board:

“Mistakes are to be expected, respected, inspected and corrected.”

Brilliant! This, in a nutshell, was what we had been trying to teach our children for years – that it is not just OK to make mistakes, but mistakes are actually where the learning happens. So don’t rub them out! Instead, value them and talk about them.

I shared this mantra with a Primary 4 class. Within a day, the class teacher had told me that the children had decided that there was a word missing. Detected! We have to detect our mistakes before we can respect and inspect them. So now we had: Mistakes are to be expected, detected, respected, inspected and corrected!

We tried sharing this with other classes. But there were now too many words and no one could remember the correct order!

Then I had a brainwave. Was there a mnemonic? If you put M for ‘mistakes’ at the beginning you would get MEDRIC. Not very memorable…

Was there a word for mistakes which began with C, I wondered. Then we would have CEDRIC! The thesaurus revealed the answer – the only synonym that began with C: Confusion.

The more I thought about it, the more I realised that this was the perfect word to start our slogan…

Our maths working group met earlier this term, so we discussed CEDRIC. The group unanimously agreed that this was the one thing we should focus on sharing with our children this session. It linked beautifully with all the work we were doing on mindset and, if we could really get the message embedded across the whole school, we reckoned it could be quite transformative.

Step 1 would be to design a CEDRIC character. This was delegated to our primary Year 6 pupils through a competition. Shortlisted entries were voted on by our primary Year 4s and 5s.

Here is our winning design, a combination of two pupil designs that have been combined by a graphic design colleague and branded with our school colours.

Next step was to decide how we would get the CEDRIC message out to the whole school. We’ve decided to do an official launch through assemblies in the summer term. Meanwhile, several of us have been experimenting with our maths classes.

Here’s how it has been working for me so far…

In any real learning situation, confusion is expected. If our brain is being stretched we will sometimes feel confused and we may make mistakes. In order to learn, we need help from others so our confusion can be detected. Peer marking is great for this. If we and others have different answers, there is an opportunity to investigate.

## Don’t be afraid of making mistakes

With the classes I have worked with so far, we have used the 333 approach, where pupils work in threes and compare answers after every three questions using a three-step process: plan together, work apart, check together. Most pupils mastered this part of the process quickly. A few impatient ones needed reminding about team working.

The important next step is that our confusion or mistakes should be respected.  We shouldn’t be embarrassed by our mistakes or hide them or rub them out. Instead, we should get out our favourite colour and put a bright coloured cross next to each mistake. This, the children found more difficult.  Some were used to rubbing out mistakes and changing them – so some retraining was needed to get them to leave a mistake in place, or indeed even put it back again after they had rubbed it out.

The key was to continually remind the pupils (and staff) that the work you do on your own is done in pencil and anything you do with your team is in colour.  Suddenly you have a clear record in your book of what you did unaided and how you improved your understanding with others – great for personal reflection and for sharing with parents.

Having highlighted a mistake, it then needs to be inspected. At this point, we encouraged the pupils to get together with others in their team and talk, in depth, about the differences in their understanding. This is probably the most challenging step in the process – it requires a real change of gear from some children.  The objective is no longer to get through lots of questions, but instead to engage deeply with the thinking of each member of the team.

We encourage our children to use pictures and diagrams to explain their thinking to each other and to write things down. Individual whiteboards are great for this. We are also finding ourselves increasingly giving support with spoken vocabulary and sentences. Speaking maths is a really valuable skill, but, like any skill, it requires much practice.

We are also encouraging the children to explore ideas from different angles until they are all in agreement with their understanding and are all confident that each of the others can explain their ideas clearly to someone else. It is early days yet, but I am confident that, with persistence, we can bring about real change.

Finally, when the confusion is sorted, mistakes can be corrected. But even now, we don’t rub out the earlier mistake. Instead, we keep it as evidence of our learning and write the correct answer next to it – again, using a bright, stand-out colour.

The result – if we do it well – is that we have truly learned from our confusion. And…we have jotters or learning logs where everything that we have learned and clarified is clearly highlighted – clear evidence of thinking, and great for sharing with parents. A teacher’s dream…

P.S. The idea of CEDRIC is not copyright. So feel free to use the CEDRIC slogan in your own school. However, the CEDRIC image shown above is ours. If you want a CEDRIC image to use in your school, why not run your own design competition?

Rob Porteous, deputy head learning and teaching, George Watson’s College, Edinburgh