# Answers at the touch of a button

Evidence that British pupils (although to a lesser extent in Scotland) are up to two years behind many of their European counterparts in several areas of mathematical competence, not least in basic numeracy, has led to a ban on using calculators in one paper of the key stage 2 tests. From 1997 this will be extended to a "non-calculator component" in key stage 3 tests.

Nick Tate, head of the School Curriculum and Assessment Authority, claims that calculators are being over-used in the primary classroom, while OFSTED argues that, on the contrary, open access to calculators does not lead to dependence.

Calculators are part of everyday life and they are here to stay. They have become relatively cheap and, as with most developments of the microchip, are likely to become even cheaper and yet more powerful.

The national curriculum requires key stage 1 teachers to introduce pupils to their use, both for exploring numbers and as a means of tackling problems. Later, pupils are expected to use a calculator to explore patterns, and to handle data manipulation.

GCSE examinations contain questions which can only be realistically attempted with the aid of a calculator. Similarly at A-level, questions on statistics, for example, use real data which must be manipulated by a calculator with the results then being interpreted by the candidate. The debate at this level is not about ordinary calculators but about the more sophisticated ones which include computer algebra systems software that can do symbolic manipulation. These are now banned.

Properly used, the calculator can be a great asset to learning mathematics, but it is essential that other skills in mental arithmetic, estimating, and degrees of accuracy are not neglected, so that pupils can make effective use of them, and not just use them for finding the answers to arithmetical problems.

Where to go and what to look for

* There are now three main suppliers of calculators: Casio, Texas Instruments and Sharp. Competition is fierce, and although many models seem similar, there are differences in robustness, key action, displays and functions. Companies like Oxford Educational Supplies carry a good range, at competitive prices, even for small quantities. Oxford Educational Supplies, Unit 19, Weston Business Park, Weston on the Green, Bicester OX6 7SY

* Many teachers prefer solar-powered models which of course remove the problem of battery replacement. They also present less temptation to the student who needs a spare battery for his Walkman. The technology of solar power has improved so that low light levels are now much less of a problem. If you prefer battery models, try to use those in which the battery compartment is secured by screws.

* Watch out for the quality of display - this is important, especially with graphic calculators, and make sure the display does not have a small angle of view. With some calculators a slight movement of the head is enough to distort the graph on screen. Key action is to some extent a matter of personal choice, but for younger pupils, the more positive the keys the better.

* The scientific calculators used by older pupils now offer a large range of functions, including trigonometrical and statistical calculations. Some have the facility to display and work with fractions. Opinions are divided as to the desirability of this. My own view is that it is not necessary, but properly used, it can help pupils to understand better the manipulation of fractions.

* Graphic calculators are being used increasingly in key stage 3 and 4 classrooms, and the market for machines suitable for this age and up is moving fast. Casio recently introduced a machine that uses different colours for plotting graphs (the CFX 9800G). I am sure this is the way forward, but the quality of the display is not yet good enough to warrant the extra price Pounds 130, but this will drop in September, according to Casio, when it brings out a new generation at Pounds 89.99.

* At the far end of the price spectrum is the new TI-92, a combination of palmtop computer and graphic calculator, which is likely to become a coveted possession, but at Pounds 200 is not yet within everyone's reach.

For younger and older pupils, one model stands out but for 10-16 year olds there are three which represent good value for money.

Age 5-10

Casio SL-450L

Pounds 5 (approx).Casio, Unit 6

1000 North Circular Road

London NW2 7JD

This is the most robust model for this age range, which will stand up well to hard use and is probably also the easiest to use. It has a hard plastic case, and the keys are large and well-spaced. It is solar-powered, which means no problems with batteries, and it works well in even low levels of light.

The display is large and shows up to eight digits, with dashes being automatically inserted to show thousands and millions. The addition key is sensibly placed at the bottom right of the keyboard, and is larger than all the other keys.

Apart from the four function keys, the calculator has percentage, square root, and sign change keys. There are three memory function keys, with the M+ and M- keys both working cumulatively, in other words numbers are added to or subtracted from the memory by using these keys rather than over-writing what was previously stored.

An overhead projector model (OH-450L) is available, which enables teachers to demonstrate easily the use of the calculator.

Age 10-16

Casio FX-85S

Pounds 9 (approx). Casio, Unit 6

1000 North Circular Road

London NW2 7JD

The most recent additions to Casio's range of scientific calculators include what they designate as VPAM (Visually Perfect Algebraic Method) display. This means that you can enter a calculation just as it is written (eg for sin 30 you press SIN 30=).

The FX-82 has been upgraded to the FX-82 Super, but it does not have the VPAM feature, so I recommend this model instead. Although it has only an eight-digit display (with two for exponents), compared to the 10 of the FX-82, this is sufficient for work up to GCSE. This model does have the advantage of being solar-powered with a battery back-up. The keys are rubber, robust and well-spaced, with clear colour-coded function keys.

There are 206 functions, ranging from fractions to hyperbolic trigonometric functions. Permutations and combinations can be easily found, and the statistical functions include linear regression. The mode in which the calculator is being used, and the function key used are displayed in a small font above the digits on the display.

Age 10-16

Sharp EL-531GH

Pounds 4.99. Sharp, Sharp House

Thorp Road, Newton Heath

Manchester M40 5BE

This calculator uses an entry system similar to VPAM, which Sharp calls DAL (Direct Algebraic Logic). This too allows the user to enter calculations as they are written, and pending operations are shown on the dot-matrix function display.

This is a cheap but well-made calculator, with hard keys and a hard slide-on case. The keys are well spaced and clearly labelled, although their feel does take a little getting used to. The display is good, with large digits (10+2, ie 10 main digits plus two for exponential displays). The equals key is large and well placed at the bottom right.

The list of functions supported includes fractional display, hyperbolic functions and permutations and combinations. The statistical functions are, however, restricted to those involving single variables.

Another strong point of this calculator, in addition to the good range of functions at a very good price, is the claimed life of 11,000 hours (around five years) from the standard batteries.

Age 10-16

Texas Instruments TI-40 Solar

Pounds 14. Texas Instruments

Kempton Point, 68 Staines Road West Sunbury on Thames, TW16 7AX

This is the relatively new, solar-powered version of the Galaxy 40X, which has been a popular choice in secondary schools. There are some differences between the two machines, not least the fact that this version is in the now more usual "portrait" shape rather than the "landscape" of the Galaxy machine.

The 10+2 digit display is clear and a large yellow second function key is centrally situated. Texas does not use a system like VPAM or DAL, but its Algebraic Operating System (AOS) multiplies and divides before adding and subtracting when multiple operations are entered.

Operations are shown on the display, and there are nine distinct error messages. Fractions are catered for, and an integer division key allows the result to be shown as a quotient and remainder rather than decimal format. Pi can be displayed and used as a symbol in radian calculations or in other functions. Statistical functions are limited to single variable calculations. An OHP version and guide are also available.

GCSEA-level

Texas Instruments TI-82

Pounds 55. Texas Instruments, Kempton Road

68 Staines Road West

Sunbury on Thames TW16 7AX

At this stage, a graphic calculator has become almost essential. There are many good models, but this one has several features which single it out.

The display is large, and clear, at 8 lines by 16 characters. You can split the screen in order to show both the graph and the function or table of values on which it is based. The functions of the machine are fairly easy to access through the use of "drop-down" menus, similar to those on computers. The manual is good, with an introduction which allows you quickly to get a feel for the machine and the way it operates.

Zooming and tracing functions each have their own keys, and graphs can be saved (up to 10 rectangular functions). The range of calculations and associated graphs possible is impressive. For example, two variable statistics, including polynomial regression, maximums, minimums, derivatives and integrals. It is also possible to store up to 37 programs in the 28K memory, and to link the calculator to PCs or Macs via a separate cable.

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