Squaring the bubble
Concept cartoons are problematic-style drawings which present a range of viewpoints about subjects involved in everyday situations. The brainchild of Brenda Keogh and Stuart Naylor, lecturers in science education at the Institute of Education at Manchester Metropolitan University, they have been used successfully in science lessons. I have adapted them for maths sessions and found them to be a unique means of teaching, learning and assessment.
Concept cartoons are crafted to access children's ideas, to puzzle, prod understanding, kindle discussion and instigate mathematical thinking. These highly visual learning tools provide a child-friendly framework that acts as a springboard into topics and ideas. They can be used in one-to-one teaching, focus-group work or whole-class discussion to find out about children's ideas and the reasoning that underpins them. They are particularly effective for children with special educational needs and those who lack confidence in putting forward their views in a mathematical context.
The dialogue between the characters in the cartoon draws children into a mathematical world and involves them as active participants in a challenging setting. For example, the concept cartoon illustrated here provides children with a variety of viewpoints about a common everyday shape. Some of the statements are accurate while others reflect misconceptions that may need teasing out. Most children are familiar with the shape but generally speaking will know it only as a square or quadrilateral. This cartoon can easily be developed into a whole lesson on "square thinking".
Draw five children looking at a square with phrases as shown in the illustration. One bubble should be empty for children to complete. Then ask the question: "What other names could you call this square window?" Use the definitions listed below to help children structure their thoughts. As you say them, they can work out whether the shape satisfies the definition given.
* Convex polygon - a plane shape with straight sides and many angles.
* Quadrilateral - a four-sided polygon. The sum of the angles of a quadrilateral is 360 degrees.
* Parallelogram - a quadrilateral which has pairs of opposite sides equal in length and parallel, and the opposite angles are equal in size. The diagonals bisect each other.
* Tetragon - a plane figure of four angles.
* Rhombus - a quadrilateral with four sides of equal length. Opposite sides are parallel and opposite angles are equal in size. The angles bisect each other at right-angles.
* Oblong - a rectangle which is not a square.
From these definitions we can say that the shape above has six names. It is a convex polygon, a square, a quadrilateral, a tetragon, a parallelogram and a rhombus. These are best remembered alphabetically as CP, S, Q, T, P, R.
There are many good reasons to make up your own concept cartoons to use in maths lessons. They enhance classroom practice and improve children's motivation.
Co-ordinating a whole-school approach to using the cartoons is worth consideration as a way to raise attainment and improve assessment procedures. They can help children and teachers to understand learning needs and they enable teachers to identify links between assessment, learning and teaching.