Memories of things to come
The first graphic calculator to sell in large quantities in the UK was the Casio fx7000g and this soon found its way into the bags of A-level students, often to the bewilderment and annoyance of their teachers. At the same time the Hewlett-Packard HP-28C calculator, with superior mathematical functions, but less impressive graphics, appeared on the US market. MESU (now the National Council for Educational Technology) funded a curriculum development project directed by Ken Ruthven on graphic calculators at A-level, which was based on regional groups of teachers mainly using Casios, with a few using HPs.
Shortly after this project, Texas Instruments brought out the TI-81, which combined many of the best features of the Casio and HP products at a very competitive price. Soon after, Sharp had a couple of models also competing. So, with the major calculator manufacturers committed, the developers of new A-level projects such as SMP 16-19, Nuffield Advanced Mathematics and MEI were able to formulate new syllabuses, materials and examinations on the premise that all students taking such a syllabus would have access to their own graphic calculator.
Quite quickly new approaches to familiar aspects of sixth-form teaching became standard Q for example, it was easy to plot the graph of: y = (x+h)n Q xn h for some small value of h as a way of introducing the derivative of xn. The presence of certain additional features such as matrix operations allowed some syllabuses to include new material.
On the whole examination boards did not seem to be too worried about students using such calculators in examinations Q provided they (the calculators) could be demonstrated to have had their memories cleared!
In February 1993, the then Department of Education and Science held a conference on maths and information technology with representatives from HMI, Association of Teachers of Mathematics, Mathematical Association, NCET and other bodies to help formulate future policy on IT in the 5-16 curriculum. At the same time NCET announced a scheme of pilot projects using portable computer technology. Through this scheme several schools were able to experiment with using graphic calcul-ators, and pocket-book computers (some with Derive on Rom cards), with key stages 34 as well as some at key stage 2.
New styles of working began to emerge, both in class and at home, with some students taking school calculators home. For example, many investigations lead to number patterns. The tables of numbers can be entered as data from which scattergrams can be drawn. Then graphs can be superimposed, first "by eye", and then by investigating what the various types of regression equations offer.
When the Department for Education and Employment announced its revised plans for Grants for Education Support and Training IT funding to LEAs in 1993, money earmarked for hardware could include graphic calculators. As well as the devolved funding to schools for hardware, materials and training, the DFEE made funds available for central support for IT in secondary maths. This funded a round of courses for LEA personnel involved in setting up local GEST projects, as well as the production of support materials.
The resulting IT and Maths Pack has been reprinted and is available from ATM or MA at Pounds 15. The DiGEST newsletter was set up with joint editors from ATM and MA. Subsequently the Mathematics and IT at Work booklet was produced, and this is available from NCET for a 75p stamped addressed envelope. This year the ATM and MA have received financial assistance in running weekend and twilight courses for teachers.
Feedback from these GEST activities shows that about half the participating schools are starting to use graphic calculators with key stage 34 classes. The more recent Casio fx-7700 GE and TI-82 models have been the most popular because of their ease of use with simple menus, and their connectivity both with each other and with peripherals. Recent developments include Casio's introduction of colour liquid crystal displays, TI's introduction of the cheaper TI-80 and the more powerful TI-83, and Hewlett-Packard's HP-38G with infra-red communication.
Improved interconnectivity now means sets of programs andor data can be easily downloaded into a class set of graphic calculators. Last year TI brought out its Calculator Based Laboratory (CBL) which is a hand-held data-logger with a set of probes from which data can be downloaded to a TI-82. There is, then, plenty of scope for cross-curricular developments between maths and subjects such as science, technology and geography.
TI has broken new ground in the design of the TI-92 by asking the writers of the well-known computer algebra system Derive and the dynamic geometry software Cabri to produce versions which are held in Rom. Thus the TI-92 has all the functionality of an advanced graphic calculator together with these two powerful built-in pieces of mathematical software. In this case the educational community has not been caught unawares by such a development. For example the School Curriculum and Assessment Authority has led the way in encouraging debate on the effects of such developments: * on examinations, particularly at A-level, through discussions with the GCE boards * on the core and new syllabuses, through a working group and * on education more widely through its Mathematics 16-19 conference held in December. At least one examination board has a well developed proposal for a pilot A-level course in which students will have access to the TI-92.
The professional associations are also doing their bit. The ATM published a discussion paper on computers and algebra at A-level, Micromaths publishes regular articles on hand-held technology and computer algebra, and the MA will shortly publish a book on the implications of computer algebra for mathematics 14-20. Many conferences and courses now devote sessions to hand-held technology.
The manufacturers are also investing considerable effort and money in keeping the educational community well-informed, in sounding out their opinions, and in providing support for training. For example, both HP and TI have well-developed training programmes for teachers in the US, now spreading into Europe.
Currently, the main educational attention to the impact of computer algebra systems (also known as symbol manipulators) is being directed at A-level, an increasingly politicised arena.
Present practice in higher education is very varied with some of the more established universities set firmly against the use of hand-held technology of all sorts, and others embracing it. Industry and commerce seem to be making considerable use of many IT products, including computer algebra, in solving mathematical problems. As yet very little attention has been given to the use of symbol manipulators at key stage 4 or below, but this is bound to come.
It has taken us a long time to come to terms with the way the widespread availability of simple calculators may affect the mathematics curriculum Q and this still remains a political hot-potato. The changes in all areas Q graphical, statistical, algebraic, geometric Q are vast. Most have been assimilated but computer algebra will no doubt bring out extremes of view and we can but hope that the ensuing debate will be based on informed judgments, and not on emotional reactions.
Adrian Oldknow is professor of mathematics and computing education at the Chichester Institute of Higher Education. He chairs the DFEE Central Steering group which supports the GEST work in IT in Secondary Mathematics, and the Mathematical Association's subcommittee on the implications of symbol manipulators. The opinions expressed are his own.