How to make computers count
Five years ago, Trevor Fletcher, former HMI, wrote: "Future ages may remember very little of the details of 20th-century teaching, but they know that it was the time when the computer came into mathematics and into schools; and I hope they will remember that teachers seized the opportunity and used it well. " Do not feel guilty if you have not helped to make Fletcher's prediction come true - just read on, and take heart from the fact that very little can go wrong.
Remind yourself why you want to use IT: it's not because the national curriculum expects it; it's because it can enable pupils to explore many facets of mathematics in greater detail and often with more accuracy.
The National Council for Educational Technology's free guide, Mathematics and IT, is a short pamphlet giving six examples of the ways in which IT can provide opportunities for maths students. The NCET also publishes The IT Maths Pack, covering four different aspects of IT. The Mathematical Association has also produced a good overview .
There are three main ways of using IT in mathematics: commercial packages designed to teach or illustrate a particular aspect of mathematics; general packages, such as spreadsheets or drawing programs; and programming, usually in Logo or Basic.
The first is best for the beginner. There are many programs available - many of them, unfortunately, of the drill variety. Have a look at SMILE, which in the past few years has started to make packages that run in Windows, among them Investigations, Angle Estimation and A Sense of Number. For younger pupils, Maths Workshop from Br?derbund and Hooray for Maths from Lander offer worthwhile activities.
One of the more interesting developments in IT in maths has been the increased use of spreadsheets. There are many things you can do with a spreadsheet. You can use it simply to record the results of a simple probability exercise, updating it as more repetitions are made, and using the graphing facility to display the results.
With older pupils, spreadsheets have been used to explore functions and iterative processes. The well-known max-box problem can be elegantly investigated. Searching for square roots, or for the roots of a quadratic equation, can be accomplished with a spreadsheet where the steps in the iteration are made clear. The ability of spreadsheets such as Excel to display the information graphically should be exploited whenever possible.
One of the earliest uses of micros in mathematics was to explore geometry. Your pupils can be introduced to concepts of angle and distance by using Logo to move turtles, either on the screen or "actual" turtles on the floor or table. Older pupils learn about transformations by using packages such as The Geometer's Sketchpad (from Capedia) or Transform (from SMILE).
Please don't forget the power and simplicity of Logo. Besides its application in geometry, it can be also used in number work, algebra and more: there is even a "microworld" for post-16 students to investigate Newton's Laws.
Don't forget the Internet. One of the best places to start is the Shell Centre at Nottingham University.
* NCET, Milburn Hill Road,Science Park, Coventry, CV4 7JJATM, 7 Shaftesbury Street,Derby DE23 8YB MA, 259 London Road, Leicester LE2 3BESMILE Centre, 108a Lancaster Road, London W11 1QSBr?derbund Software,PO Box 63, Hartlepool TS25 2YPLander Software, 74 Victoria Crescent Road, Glasgow G12 9JNCapedia Ltd, Harford Centre,Hall Road, Norwich NR4 6DG http:acorn.educ.nottingham.ac.ukShellCentComputers in theMathematics Curriculum (1992), The Mathematical AssociationISBN 0 - 906588-28-6