The Teacher's Guide. Pounds 3.50. 0 521 46811 6, Cambridge University Press. Mathland is a curious, yet somehow strangely familiar, adventure playground for the numerate explorer. It is a cross between early computer adventures, such as the L-Game from the Association of Teachers of Mathematics, and those branching teenage novels whose story is determined by the reader's response to particular situations.
In the Novice Version, aimed at pupils in key stage 3, you enter a maze through the Gate of Hope and head straight for the Tower of Galileo, where a tall giraffe presents you with a problem. A correct answer attracts points and directs you to the page with the next set of instructions. This leads on to another problem and so your journey progresses.
At most locations you can use points to buy help if you get stuck. You are encouraged to keep a map of your journey - indeed it is essential if you are eventually to escape from the maze. Your final points tally determines your assessment by the Magic Mathematician.
The puzzles are relatively straightforward and familiar. At Newton's Apple Tree you are asked to find the smallest number (not 1) which is a perfect square and a perfect cube. At the Cliff of Copernicus a clever cat gives instructions in code: TOSUPOERARVNGTETEYN.
("think about factors" says the cat).
The Expert Version, aimed at older pupils, including sixth-formers, follows the same format but involves trickier tasks. For example, the familiar Frogs problem is lurking in the Well of Weber and when you reach the summit of Mount de Moivre you have to help a nanny goat use 24 miles of wire to construct a rectangle enclosing the largest possible area.
Both books include notes, for example on the mathematicians whose names appear on the maps, and suggestions for extending the ideas in some of the problems. The Teacher's Guide has hints on using Mathland in school, photocopiable map sheets, a network to unravel the routes through the books and solutions to each of the problems.
The pupils' books are pocket sized, illustrated with line drawings and despite their complicated structure, pretty accessible. I've no doubt that some pupils will find this sort of approach very appealing. Others will not.
Equally, some teachers will find them a useful variation on their normal approach to maths. But what struck me was the amount of clever thinking that has gone in to structuring the book. A group which involved students in designing and making their own Mathland really would stimulate some exciting mathematics Linton Waters is County Inspector for Mathematics for Shropshire.