Magical mathematical tricks raise a cheer from pupils participating in this circus roadshow, says Chris Olley.
The circus is in town. But this is no ordinary circus; no daring tricks on the flying trapeze, no lions tamed with a stick and top hat. This is a circus of hands-on tricks and puzzles, games and activities. The small number of entertainers are there to explain the activities and to set them going. The rest is up to you.
The Magic Mathworks Travelling Circus was set up 12 years ago by Paul Stephenson, a former head of maths and deputy head. Originally he planned to write a book about what he calls "manipulatives" - big, solid mathematical activities that you can really get a feel for.
He ran in-service training sessions for teachers, who urged him to go out and work with pupils. He did, and as the collection of manipulatives grew, the circus was born. It now turns up in one of a fleet of three vans filled to the brim with plastic crates of bean bag frogs, yellow plastic balls which build up into pyramids, a tower of Hanoi made out of nesting wicker baskets, and much more. Unsurprisingly, the book remains to be written.
I visited the circus at Ribbleton Hall High School in Preston. It was booked for a numeracy summer school by its organisers, maths teachers Gerry Hornby and Paul Stemp. The circus arrived at the end of a week in which pupils had been halving, doubling, partitioning and practising the rest of their numeracy skills in the classroom. Paul Stemp and Gerry Hornby wanted to break up the balance of the course and give their pupils a more loosely structured day. After a full hour working through the activities, everyone stopped for a drink, and there was a cheer when the time came to get started again.
Some of the activities were familiar: the tower of Hanoi, a game of Nim, Handshakes, Frogs, Fibonacci numbers; others less so: an old record player with a mirror in the lid to experience opposing rotations, a silver cocktail shaker which turns a trapezoid co-ordinate grid into a rectangle, wire framework solids that produce beautiful shapes when dipped in washing-up liquid solution.
To most pupils all the activities seemed new, even if they had seen them in another form in the classroom.
For instance, one girl who was moving into Year 7 for the new school year was trying hard to understand the concept of the "handshakes" problem - a group of people arrive at a party and each shakes hands with everyone else. How many handshakes are there in total?
I left her with one of the helpers explaining how it worked using a large board with five evenly spaced pegs to wrap elastic bands around, each band representing a handshake.
A short while later she ran over to me carrying a large whiteboard on which she had drawn a circle with 12 points with all of the handshakes drawn in. "It's 66," she said with excitement. "That's what I guessed it would be!" The teachers said they had found activities and approaches to try out in their classrooms, and were convinced of the value of providing a variety of experiences. Moreover, they had seenseveral examples of young people being genuinely inspired by a piece of maths - not a common classroom experience.
Looking around the activities, it became clear that something subtle was going on. The girl who had been so excited over the handshakes problem was building a pyramid by stacking plastic balls on top of each other. With each new layer she counted the number of balls on each face. The numbers turned out to be the same as the numbers in the handshakes problem. This was not accidental.
Paul Stephenson has designed the activities in groups according to Zoltan Dienes' principle of multiple embodiment (Memoirs of a Maverick Mathematician, Minerva, 1999). The numbers of handshakes are 1, 3, 6, 10, 15... the triangle numbers. The stacking pyramids also produce triangle numbers, as do many other activities.
Different transformations: rotation, reflection and enlargement, appeared in many different ways. Other number sequences recurred, as did relationships between shapes. Pupils were making connections between their experiences and building bridges between the often compartmentalised statements in current syllabuses.
In a three-hour morning session it is difficult to get too far with connectionism, so the activities are laid out to maximise the variety of experiences. However, Paul Stephenson also runs workshops lasting from two days to as much as a week. Over these longer periods the activities can be grouped on common structural themes. Then it becomes possible to engage pupils more deeply in the nature of maths, looking at different appearances for the same underlying structure.
* The Magic Mathworks Travelling Circus runs as an incorporated charity with private sponsorship and money from COPUS (Committee on Public Understanding of Science). For more details contact Paul Stephenson at Old Coach House, Penypwllau, Holywell, Flintshire CH8 8HB. Tel: 01352 713014.
Chris Olley is a maths educationconsultant