The easy route to the root of a quadratic equation
It is basically a graph-drawing program, but is also much more than that. Pip Huyton, an advisory teacher at the Davidson Centre in Croydon, is enthusiastic about its ability to help pupils bridge the gap between an algebraic and a graphical realisation of a situation.
When used in coursework projects, it can take away the drudgery of repetitive drawing and can allow pupils to explore the underlying mathematics. Pupils can work at their own speeds, following their own investigations, with teacher intervention when necessary. Pip Huyton has used the program with low attainers and says that one of its great attractions is the equality of access it permits. She sums it up as "excellent value for money".
Second on the list is a program that was not devised for use in mathematics teaching, nor indeed for education: Microsoft's Excel. One of the more interesting developments in using IT in mathematics has been the increased use of spreadsheets. There are many things you can do with a spreadsheet; for example, you could use it to record the results of a simple probability exercise, updating it as more and more repetitions are made, and using the graphing facility to display the results.
With older pupils, spreadsheets have been successfully used to explore functions and iterative processes. Angela Bannerman, head of maths at Woodcote High School, is convinced that using spreadsheets has helped her pupils to develop their reasoning skills. Recently some of them were working on the volumes of cones and used Excel to enter the formula so that the effects of changes in the parameters could be easily seen. Searching for square roots, or for the roots of a quadratic equation, can also be easily accomplished with a spreadsheet, where the steps in the iteration are made clear.
The ability of spreadsheets to display results graphically can also be exploited to great effect. The National Council for Educational Technology publishes Thinking about Spreadsheets (Pounds 2.50), a guide to the classroom use of the software. The council has also just published a very clear, free booklet, Primary Mathematics with IT.
I have been following the results of the trials of Independent Learning Systems with great interest and have seen RM's SuccessMaker being used in several schools. Everyone reports positive benefits from its use. Pupils' motivation has increased, and understanding seems to have been greatly helped. The head of maths in one large secondary school told me that there had been a definite improvement in the numeracy of weaker pupils after only a few sessions and that this seemed to be sustained over time.
The program gives instant feedback, with explanations where necessary, and its superiority to previous computer-aided learning systems lies in the way in which it identifies pupils' weaknesses and provides further work on them.
One of the best places to start looking for useful material on the Internet remains that of the Shell Centre at Nottingham University, although I should warn you that I have often found it slow. A welcome addition is the page run by Bryan Dye, entitled MathsNet, which has lots of links to other sites, arranged by topic. SMILE, well known and respected for its software, has at last set up its own site, which also provides a forum for teachers of mathematics.
John Conway, the English mathematician perhaps best known for his invention of The Game of Life, is now based in the United States. He has a wonderful page full of games and puzzles such as the colouring problem. This site provides many possibilities and ideas for GCSE or A-level coursework.
Fibonacci numbers have always held a fascination for many pupils, partly because of their occurrence in nature and partly because of their links to other topics such as the Golden Section. The site on Fibonacci at Surrey University is well worth visiting. And for further exploration of the links between mathematics and art, try the site run by the Kennedy Centre. I learned a lot as well as having fun - what greater recommendation could there be?
* CONTACTS:NCET, Milburn Hill Road, Science Park, Coventry CV4 7JJSPA Tel: 01684 833700 * Web sites:Conway: http:www.cs.uidaho. educasey931conwaygames. htmlFibonacci: http:www.ee.surrey. ac .uk PersonalR.Knott Fibonaccifibnat.htmlKennedy Centre: http:artsedge.kennedy-center.orgMathsNet:http: www.paston.co. ukusersmathsnetShell Centre: http:acorn.educ.nottingham.ac.ukShellCentSmile: http:www.rmplc.co. uk orgssmileindex.html