At Parliament Hill Girls School in north London, eager children sit in groups around board games. They are in the middle of the strategy project, an annual exercise to develop analytic thinking and justification (as in AT1, using and applying maths). Over three weeks, the Year 7 pupils play games from various continents and explore the difference between games based on luck, those based on strategy, and those with a combination of the two. After playing and analysing, the children devise their own game and explain it to the others.
The project evolved from a multi-cultural maths workshop in 1993. In creating a multicultural maths classroom, Bridget Perkins, head of maths at Parliament Hill, bought some maths games, including the popular African Ayo or Wari (available from Oxfam shops). It is highly successful, says Ms Perkins, in motivating children and in raising the status of strategic thinking.
Classes start by discussing and drawing a line continuum between strategy and luck. The pupils research the games they know and those in the shops and explore whether chance or skill is preferred. Generally, games with at least an element of chance are considered most enjoyable - "more relaxing, the luck element adds fun and you don't have to think all the time," says Ms Perkins.
The games played are Shut the Box, from France; Kungser, from Tibet; Bottoms Up, a kind of adapted Connect 4; Serpent, a Nim-type game from Asia; Four Field Kono from Korea; Mu-Torere, a Maori game from New Zealand,and Wari from Africa. Versions used appear in the book Strategy Games by Reg Sheppard and John Wilkinson (Tarquin Publications). All are fairly simple and cheap to reproduce.
After everyone has had a turn playing the games, the children are asked to comment on strategy and on why, say, going first or second may affect a player's chances of winning, or why picking up a certain piece is a successful strategy.
Positional thinking, the importance of clear aims and steps to achieve them are clear gains not only when it comes to talking about maths but also in individual thinking.
Although students do not discuss algorithms directly, they are working around the concept and becoming equipped to deal with notions of creativity in mathematics. Ms Perkins says: "Later on, when they do more open-ended activities, they are better at them and approach them more seriously. It raises the status of logical thinking. "
After playing games, the students develop their own and submit them to the acid test - being played and analysed by classmates.
Ananda Gill and Wendy Wilson from Year 7 wrote about their games-playing, "We had a chance to adapt the rules and see which game worked best." They liked the version of Connect 4 embodied in Bottoms Up.
After trying out their own games, the students researched the history of chess through books and CD-Roms. Many were astonished to find it had a non-European origin, having been developed in India. Chess is seen as a high-status activity and this reinforces the point of mathematical thinking within a pastime. As Ms Perkins says: "It is a big issue to make maths more interesting and exciting in the classroom. "
She sees one of the benefits of the project as raising the confidence of her students, many of whom still believe girls cannot be good at maths. "We have to work hard at helping them believe they can be good mathematicians, " she says.
Maths staff at Parliament Hill have realised it is not always the ostensibly brightest students who do best at games. Sometimes students who have wide general knowledge appear more able than they are, whereas the play of logic required by a particular game shines a bright light on the "pure" ability of other, less obviously able students.
Games are part of everyday life and so are easy to talk about. Indeed, games with which children are familiar, such as chess, draughts or ludo can be played at the school's lunchtime board games club. Ms Perkins herself is a keen games player, whose enthusiasm is infectious. To counter the danger that because the games are so familiar, parents and children may not understand the serious mathematical gain involved, parents are kept informed in the weekly home bulletin.
In an era when a debate about forcing standards up seems to dominate, Ms Perkins likes to quote Martin Gardner in Mathematical Puzzles and Diversions: "The interest of great minds (like Einstein and Leibniz) in mathematical play is not hard to understand, for the creative thought bestowed on such trivial topics is of a piece with the type of thinking which leads to mathematical and scientific discovery. What is mathematics after all but the solving of puzzles?"
Inspiration in a SMILEUse of puzzles in schools is gaining ground. Recently, the expanding SMILE Mathematics project ran a puzzle competition to celebrate 25 years of publication. Sponsored by Texas Instruments, Oxford University Press and Circa, the competition asked pupils to solve four puzzles and contribute one of their own.
A total of 951 students entered, many from schools which do not use SMILE.Two schools decided to run their own puzzle competitions. At Chulmleigh Community College in Devon, which won one of the prizes for most entries, 6O of the 15O who entered for the SMILE competition were keen enough to want to try the Sharp UK competition.
Samantha Hancock is head of maths at Chulmleigh Community College. The school came just below the national average in its maths GCSE grading last year and has adopted SMILE for its Year 9 and l0 students as part of an attempt to raise standards.
SMILE's formula of short, discrete tasks is well suited, says Ms Hancock, to increasing pupil enthusiasm.
The competition was popular with all the groups. Over two weeks, lower ability sets (Years 9 and 10 are set for maths) took enormous pleasure in counting all the possible combinations of pentominoes in a set; high-achieving students were put on their mettle by the fifth question, which asked students to design their own puzzle. "I can set a harder one than that," they proclaimed.
Maths word searches, crossword puzzles and getting the calculators out to test out number relations fed their enthusiasm for "doing that great competition again".
The maths staff were pleased with the way the questions, which spanned several basic number concepts, backed up the curriculum work on primes, cubes and squares. Now, says Ms Hancock, "I've started ending lessons with a few puzzles, such as number bingo. It's been a bit of an inspiration, really."