Power to the pupil
I know that there are some people out there who think fun in mathematics is a contradiction in terms, and I can understand that point of view if your experience of mathematics has been limited to endless hours of calculation with no apparent purpose.
However, as Simon Singh, the author of the recent best-seller, Fermat's Last Theorem, pointed out in an article in The Guardian, mathematics is concerned with a search for truth and elegance. As a non-mathematician, he had come to appreciate the creativity which mathematicians must necessarily use to make advances in the subject. At a school level, we are not trying to push back the frontiers of knowledge (except that of our students), but if we do not allow students to experience a little of that beauty and creativity we shall have failed them.
There are many ways in which ICT can be used to promote exploration and creativity, and there will be plenty of sources of further advice available during Maths Year 2000.
Logo can of course be used to stimulate students of all ages, encouraging them to explore mathematical ideas in the context of learning how to control the on-screen turtle (or a robotic one attached to the PC). A program such as TAG's MicroWorlds uses Logo commands and allows pupils to construct simulations using mathematical ideas. Sounds and simple animations can be added to enhance the models and I have seen some wonderful examples of pupils creating their own worlds. Similarly dynamic geometry software (for example TAG's Geometry Inventor) provides an environment in which students can create images and speculate about what might happen when they change some of the parameters.
As the Association of the Teachers of Mathematics pointed out a few years ago, one of the most important freedoms offered by such programs is that of being able to make mistakes. By allowing students to explore without having to rub out errors in their drawings on paper, these programs encourage a more questioning nature as well as helping to appreciate how beautiful geometry can be. If you wish to explore more ways in which to use animations, the MathsNet website has some very useful links, including one to a source for Constructor Set, the animation software.
The Fibonacci sequence leads to some very elegant pieces of mathematics. Indeed there is currently a poster on the London Underground (on the lines of "Poems on the Tube") encouraging commuters to explore these numbers. Fibonacci numbers have always held a fascination for any pupils, partly because of their occurrence in nature and partly because of their links to other topics such as the Golden Section. It is relatively easy to get students to write a short program or spreadsheet to explore the sequence. The website on Fibonacci at Surrey University is well worth visiting for further ideas.
Mention of the Golden Section naturally leads to exploring other links between mathematics and art, and a good place to start is the CD-Rom Art and Mathematics. This is suitable for older secondary students upwards, and I can strongly recommend it as a fascinating exploration of the influence of maths on the visual arts. For a further exploration of the links between mathematics and art, try the site run by the Kennedy Centre.
Another well-known example of mathematics and art comes from the Mandelbrot Set of images which illustrate the behaviour of fractals. The mathematical relationships governing fractals can be understood by sixth form students, but younger students can understand the iterative (repetitive) processes involved and can certainly appreciate the beauty of the images produced.
There are many very good sites now on the Web which provide not only more ideas for teachers, but also challenges and resources for students. One of the best places to start, with links to other good sites, is that of the Centre for Innovation in Maths Teaching at Exeter University. MathsNet, as well as its own good puzzles and animation pages, also has lots of links to other sites. John Conway, the English mathematician perhaps best known for his invention of the Game of Life, is now based in the USA, and he has a wonderful page full of games and puzzles such as the colouring problem.
The Beauty Principle states that if a theory or principle is beautiful or elegant then it has a high probability of being true and useful. Using ICT creatively in mathematics can help children to appreciate that idea.
Ian Wilson is headteacher at Ryder School, Walton-on-Thames, Surrey
Centre for Innovation in Maths Teaching
NRICH online maths club
MicroWorlds and Geometry Inventor, both from TAG Developments
Price: pound;69 and pound;79.95 respectively
Art and Mathematics from REM