The originators of Concept Cartoons are my colleagues Brenda Keogh and Stuart Naylor. Their success in using them in science education (see www.conceptcartoons.com) prompted me to think about how to use them in the maths classroom. I wrote an article in The Times Education Supplement promoting concept cartoons in maths called ‘Squaring the bubble’ and Millgate House Education asked me to write a book. The concept cartoons book and CD will contain 120 concept cartoons.

Concept Cartoons in Maths is receiving a lot of interest from colleagues around the country which is very encouraging. As part of this exciting project I have been working with a group of teachers from the city of Edinburgh. Sharing in their expertise is helping us to create the best possible set of resources before we publish. The book and CD will now be available in 2007 but before then we will be producing a set of 20 concept cartoon posters.

Edinburgh Development Group:

Peter Gorrie, Quality Improvement Officer, City of Edinburgh Council
Geraldine Forsyth, Clermiston Primary School
Anne Pettit, St. Cuthbert’s Primary School
Gilly Hewitt, Flora Stevenson Primary School
Diana Williamson, East Craigs Primary School
Lee Carson, Queensferry Primary School
Eileen Forrest, The Royal High Primary School
Sylvia Campbell, Juniper Green Primary School
Margaret Thorn, St. Catherine’s Primary School
Evelyn Gajardo, Trinity Primary School
Laura Brandon, Carrick Knowe Primary School

Click here to see an example of a Maths Concept Cartoon

What are Concept Cartoons?

Concept cartoons are problematic style drawings or visual arguments that use a cartoon-style format with conversations inside speech bubbles. The characters within a concept cartoon all have different ideas and learners are invited to join in the conversation by saying what they think. They provide learners with a context for sharing ideas and are written to prod and probe mathematical understanding.

The aim is to stimulate cognitive conflict and thought friction so that learners are challenged to compare and contrast a range of opinions and ultimately voice their own. Concept cartoons naturally invite discussion and learners contribute quite readily justifying their reasoning as they go.

So, a concept cartoon involves talk and a lot of it. This isn’t broadband teaching characterized by quick-fire questions and ping-pong exchanges. No, this is assessment for learning at its best. Children are given the time to talk and use their own search engines in consultation with others. What is said by learners is all important because this helps to shape the learning agenda and guide future learning. Blindly and uncritically following a bullet point agenda helps no one. Concept cartoons make a positive difference because learners are dynamically implicated in their own learning. A concept cartoon is a bit like a swimming pool. Why? Well, learners can jump into one and splash their ideas around and we as teachers are there to support and facilitate. Of course, this doesn’t mean doing the swimming for them - they have to do that by themselves.

Concept cartoons have many important features. First of all they have to be a visual experience but not one that is crowded with snazzy and jazzy images. A concept cartoon doesn’t contain any gimmicks because it’s the conversations and concepts we’re interested in. A concept cartoon doesn’t contain much text either. We don’t use paragraphs where a sentence will do the job. It’s about keeping it simple, keeping it short. Importantly we want concept cartoons that are pragmatic, authentic, creative and where possible embedded in the everyday. A concept cartoon will draw on common misconceptions and aim to build from these. We look to action research to help us here.

What really stands out about a concept cartoon is the equality of statements and opinions presented. We make sure that every child is heard no matter what they think. If it’s real and relevant to them then it’s not our job to dismiss or degrade what is said. There is a place for valuing different types of thinking and concept cartoons help us to see just how children view the world around them. Concept cartoons are likely to contain misconceptions but they also contain mathematically acceptable viewpoints – sometimes there might not be a single right answer. Finally, none of the concept cartoons contain any contextual clues, there are no facial expressions and no one character dominates. This is an equal playing field where the question is What do YOU think?

When using a concept cartoon there are some obvious classroom management issues to consider and using them is normally quite straight forward. The following guide hopefully makes this obvious:

• Introduce the topic
• Provide a concept cartoon to focus on
• Brief individual reflection
• Encourage small group discussion
• Class feedback on alternatives
• Discussion of how we could investigate
• Small group enquiry
• Share outcomes of enquiry
• Whole class discussion
• Draw ideas together
• Consider how learners’ views might have changed

It sounds simple enough doesn’t it? But what do you do and what do the children do?

What do I do?

For us as teachers we act as facilitators, scaffolding the thinking process to promote reflection, offering feedback and engaging children in active learning. We sprinkle and infuse some food for thought ideas and eye opener jolts to keep children on their toes. We challenge misconceptions we may encounter so that children who enter the classroom with errors and fallacies don’t leave the classroom with them. That doesn’t necessarily mean we intervene directly and ‘tell’ children the answers. What we can do is set up learning opportunities for children to discover things for themselves. Children need to have ownership of their learning and that means we have to step aside rather than kidnap and hijack the learning process. We make sure that we coax and chivvy reluctant learners by promoting their involvement. We have to make sure that children realise that they too have a responsibility for their learning and that it isn’t all going to come from us: it’s a reciprocal process. A key feature of formative assessment is that as teachers we find ways of making learning active and getting children to speak out and express themselves. The success of a lesson using concept cartoons will depend on a commitment to low level intervention and that means facilitating from the perimeter but being at the centre of things at all times, still providing the structure and pace but allowing the lesson to breathe.

What do the learners do?

Express, discuss, argue, use each other as sounding boards and share expertise. If formative assessment was a stick of rock then the word running through the centre of that rock would be talk. We also want children to argue. We want mathematical arguments because this is promoting challenge and constructive conflict. Children have to be active, agile and alert. If they are then they are more likely to be engaged, enthusiastic and enterprising. If learning is to be efficient then children have to be active agents and active participants in their learning. A silent classroom is rarely a supportive learning environment. Children have also got to take risks. They’ve got to get on their bikes without stabilisers and have a go. If they fall off then they get up and try again. So, if they have an idea, then should run with it and see where it takes them. Children also need to make decisions. Concept cartoons are about making choices and that means comparing and contrasting, looking for evidence and justifying their reasoning.

The value of concept cartoons is obvious. They kindle conversation and kick-start thought friction, they extract misunderstandings and insecurities, they mobilise and energise an enquiry and chains of thinking. They also promote genuine partnership, foster cognitive activity and importantly don’t cost the earth. Concept cartoons promote thinking skills because they inspire talking points. They use safe, non-threatening situations and characters, set up disagreements with a collision of ideas and provide us with opportunities to offer dollops of feedback. They’re a minds-on approach to learning and promote a think tank philosophy whereby children are encouraged to analyse, reflect and evaluate. So, what we are doing is encouraging children to be resilient, resourceful and receptive learners.

Concept cartoons can help us elevate talk to support thinking, learning and assessment in a very significant and creative way. They act as argument builders and discussion points but they are not the only talking tools available to us. There are many other formative assessment techniques to choose from and we should add them to our repertoire of strategies to ensure that we are providing children with a range of learning opportunities and experiences. See Active Assessment: thinking, learning and assessment in maths for a range of examples. This book will also be available in 2007.

Notes and references

I am interested in setting up a debate and discussion about using concept cartoons in maths and welcome comments from colleagues. Over to you - what do you think?
E-mail: john@johndabell.co.uk

Published articles relating to concept cartoons:

Dabell, J. (2004) Squaring the bubble, Times Education Supplement Teacher, 9th January, 2004.
Dabell, J. (2004) Concept cartoons, Junior Education, July 2004. Scholastic.
Dabell, J. (2004) Using concept cartoons, The Mathematics Coordinators File, 16, pfp publishing
Dabell, J. (2005) Active assessment, Teaching and Learning, January/February, 2005. Questions Publishing.
Dabell, J. (2005)Concept cartoons, 5to7 Educator, February, 2005. Mark Allen publishing.