Finding your feet in a world of numbers
The ability to use and apply mathematics may be required at various levels. Recently a typist, of middle age and considerable experience in a variety of offices, faced the problem of having to enter three and a half into the field of a database where the expected entries were 0, 1, 2, or 3. "Enter it as three point five", was the advice offered. "Oh, I don't know point five." "Well, you are happy with writing Pounds 3.50 aren't you? Isn't that three and a half pounds?" "Oh, yes, but that's point five zero . . . What happens if I have to enter three quarters?" What was the nature of the maths curriculum she studied in the good old days when standards were standards and everyone left school fluent in "the basics"?
Twenty years ago - when that typist was in school - few teachers and advisers in the field of special educational needs recognised their responsibility for facilitating "numeracy" in the pupils they were working with. The matter of literacy filled their view to the exclusion of all else.
Teachers with an interest in maths did not condescend to teach those exhibiting more than average learning difficulties, and many teachers working in the area of learning support feared the subject. If a mathematical component of the curriculum was considered, the stress was on "basics" - the number skills required some 50 years before - and the aim was to turn pupils into effective calculating machines.
Over the years much has been done, not least by the Mathematical Association, in setting up the Diploma in the Teaching of Mathematics to Low Attainers, to encourage exchanges between maths and special needs teachers. Yet now more than ever there is a need for taking flexible approaches with slow learners.
With the growing unpredictability of future careers, the explosion of knowledge and the changing structure of society, it may be impossible to predict patterns of work over the next decades. But whatever is learned in school will need to be reworked in a whole succession of jobs and other changing life experiences. Such transfer of knowledge is most difficult for those with special needs.
Evidence suggests, for example, that pupils judged to be "autistic" need to learn their skills in the setting where they will be used.
A student who sat on a British Medical Association working party on medical education complained that the education of medical students does not lay enough stress on problem solving, which is what the practice of medicine should be about. A problem-solving approach is needed in all areas of education, including special needs, and especially in maths. We need to have not only a large number of people who have a sufficient feeling for number to set up the calculations to be performed, but for the population as a whole to have enough of a feel for number to be able to make sense of the results.
That part of the national curriculum labelled "Using and Applying Mathematics" is vital to all pupils. Will it be neglected, especially for those who show the least aptitude for maths under the current barrage of paper and pencil tests and assessment tasks?
It is relatively easy to prepare any pupil to perform a simple task under precisely defined conditions - and such standard tests can be created in abundance under the label of mathematics - but at what cost to pupils' preparedness for the problem solving which will inevitably face them in the climate of rapid change which lies ahead?
It is so important that we continue to leave space for all learners to make decisions, communicate and develop skills of reasoning as far as is appropriate for each individual. It is no coincidence that these aspects of education - and life - are encapsulated in the first programme of study in the latest revision of the national curriculum.
Opportunities which the typist referred to earlier would not have had within her schooling were lacking partly because the relevant machines had not been invented. Neither pocket calculator, now obtainable for little more than the price of two loaves of bread, nor spreadsheets were available. Both provide the chance to find out more about numbers and how they work.
A quick highlight, and click on a format menu, can change Pounds 3.50 to 3.5 or 3 or . . . effortlessly, leaving the person in control of the mouse and keyboard to question why these expressions might all be synonymous, or even connected. Now the user can "use and apply mathematics", making decisions, communicating findings and reasoning.
A basic calculator can also readily involve pupils in finding myriad number relationships, as data can so easily be generated. A useful example is that of constructing all the fractions possible from four given digits, say 1, 2, 4 and 8, and then finding out more about them. Using a calculator to turn the fractions into decimal notation allows for their entry on to a number line with consequent surprises such as 12 is the same as 48 and 24.
Most pupils who cannot see why this should be true are now ready for assistance from their teacher because they feel they need to know. In the past such relationships would have been told, practised, tested, and retained or forgotten, according to the facility the pupil had to memorise such facts.
So far we have not even mentioned the value of developing a sense of shape and space for a better understanding of the world in which we live. Consider: why are we surrounded by cuboids? What are the properties that make them so all-pervasive in human constructions? A superabundance of cartons of all shapes and sizes is available for study.
Nor have we considered the importance of an ability to use logical procedures to approach the ever greater problems which will confront the human race as it moves into the next century. Are those with special needs to be denied a part in this process? Fostering an excitement in maths and the confidence to use it and apply it, rather than providing training to pass standard tests, is what maths education should be about for all pupils.
o Mary Clark and Rachel Gibbons are on the editorial team of Equals (formerly Struggle), published under the auspices of the Mathematical Association to address the needs of low attainers. Mathematical Association, 259 London Road, Leicester LE2 3BE. Tel: 0116 270 3877
Showing Off statements
1. In one week the school tuck shop sold the following items: 12 Mars Bars, 6 Twix, 15 Lion Bars, 9 packets of Polos, 0 KitKats, 11 Milky Ways.
2. Your parents have agreed for you to hold a party but you must organise it. You must present your plan to them.
3. Mrs Craggs likes carrots, potatoes and leeks. Mr Caisley likes turnips, parsnips, carrots and leeks. Mrs Dundas likes parsnips and potatoes. Mr Conroy likes turnips, potatoes, carrots, leeks and parsnips (and everything else).
4. As you walk into your bedroom you could show the layout, size and contents like this. . .
5. Peter is 1.32m tall and weighs 52kg. Anne is l.lm tall and weighs 41kg. Mike is 1.12m tall and weighs 65kg. Jo is 1.40m tall and weighs 59kg. Mary is 1.50m tall and weighs 61kg.
6. Telephone call - Pick up the receiver, dial the number. If it rings continue, if not put the receiver down and try again. If someone answers then carry on, if not then try later. Put the phone down. If you want to ring someone else start again.
8. The caretaker monitored the temperature in the school hall for a morning. This is what he found; 06:00 am : 7xc; 07:00 am: 9x c; 08:00 : 14x c; 09:00: 16x c; l0:00 am: 19xc; 11:00 : 24x c; 12:00: 27x c.
9. Gosling Family - John Gosling and his wife Olga had three children; Tim, Tom and Tina. Tim manied Jan but had no children. Tom married Fran and had two children: Rita and Peter. Tim a married Mustapha and had one child Oliver. Oliver married Helga and had a son called Wayne. (Naturally he became a football hooligan) 10. Mr Conroy works for his pocket money. In six weeks he earned the following amounts: Pounds 2.67, Pounds 1.90 , 73p, Pounds 2. 09, Pounds 0.82, Pounds 1.32.