Why do standards of attainment seem to be consistently higher in continental schools than here? Helvia Bierhoff, in the National Institute of Social and Economic Research discussion paper Laying the Foundations of Numeracy, describes some fundamental differences in approaches to teaching the subject. One of these which has been highlighted in the media is that in Britain children are allowed access to calculators from an early age, whereas pupils in Switzerland and other countries such as Japan and Korea, which also do well in international comparison, are not allowed calculators until age 13 or 14. Over-reliance on calculators is put forward as a very obvious reason for our pupils' lack of success.
Banning the use of calculators might seem the answer to raising attainment, but I don't believe so. We need to look more closely at some of the other findings of the research before deciding whether there could be more fundamental reasons for our pupils' lack of success. Mental arithmetic, for instance, is given precedence over formal pencil-and-paper methods until the age of nine. Pupils are helped to an understanding of the whole number system and encouraged to develop efficient ways of working in the head. Teachers on the Continent also manage to keep the class working together. They encourage pupil interaction by the sharing of ideas and working on a blackboard or overhead projector, whereas in Britain there is a reliance on individualised learning.
As a teacher of considerable age and experience, I began to wonder whether there could be historical reasons for these very different approaches. Could it be something to do with our Imperial system of measures? Before the introduction of metrication in this country, most of the mathematical work in junior schools consisted of paper and pencil exercises involving the conversion of pounds, shillings and pence, or inches, feet and yards, etc. Most of us entered secondary education with a fair knowledge of number bonds and multiplication tables, gained from constant "mechanical" practice. At my primary school mental arithmetic was tested weekly - a form of torture for most of us, we just hated maths - but I do not recall being taught to work mentally.
Of course, on the Continent, where the metric system prevailed, a different way of working was established. This was based on a more oral tradition involving the use of mental arithmetic in a systematic way in order to develop a sound understanding of place value and number notation.
With the coming of metrication in Britain we did not follow the ways of working established on the Continent. We did not use the time to work orally, to encourage pupils to develop mental strategies or provide opportunities for consolidation. Rather, we took the opportunity to introduce "new maths" which included work on sets and tessellations and probability. This led to some more interesting mathematics but probably at the expense of fluency in basic arithmetic.
The Cockcroft Committee maintained that "mathematics is a difficult subject both to teach and learn". It encouraged the proliferation of individualised schemes of work Qwhich are now known to hinder, not help pupils' progress.
When we eventually had a national curriculum the broader view of maths was maintained, even for primary pupils. Number is just one of five attainment targets. It was recognised that pupils need to have experience of working mentally, with paper and pencil and calculators. Attainment target 1 recognises the importance of developing mathematical language and communication (pupils need to discuss mathematics with their teachers and each other) in a similar way to that on the Continent. However, it was left to teachers to decide how best to teach the new curriculum, whereas their colleagues on the Continent are provided with schemes of work and collections of pupil exercises directly related to their national curriculum. Number work is paramount, particularly in the early years. There are fewer topics to be covered and a longer period of time is spent on each topic. The aim is to ensure consolidation by most of the class before moving on.
To raise attainment, we need to shift the emphasis from paper and pencil work to more oral work and interaction with the teacher. We need to encourage the use of discussion and more mental arithmetic, using ways similar to those used on the Continent. But let's not return to the dreaded mental arithmetic tests so many people remember with horror.
The calculator can be a very important tool in developing skills in mental arithmetic. As we are reminded in the original maths non-statutory guidelines: "Calculators provide a fast and efficient means of calculation, liberating pupils and teachers from excessive concentration on pencil and paper methods. By increasing the options available to pupils . . . and by saving time in making calculations, calculators offer an opportunities to increase standards of attainment."
As a teacher introduced to ways of working with calculators during the time of the Calculator Aware Number (CAN) project, I was pleased to read that recent research had shown that open access to calculators does not lead to dependence on calculators and can in fact improve numeracy. However, this did not seem to apply to eight and nine-year-old pupils, and this causes me some concern. It could be that this is the critical age for constant practice with number bonds and multiplication tables so that they are retained permanently. Teachers assure me that they find working with calculators very worthwhile and children respond very favourably to using them. Pupils should not become dependent on them. Lots of other work should be done when calculators are not available.
Calculators can be regarded as an essential part of the "basics" which everyone seems to want us to teach. Used appropriately, calculators can help pupils to explore number notation, become familiar with number relationships and I know no better way of illustrating the place value system that the Skittles game. Pupils have to enter, for example, a three-digit number and "knock down" the digits to zero to a given rule. Using the constant key can illustrate the patterns created when, for example, 10 is added to a number. Using calculators certainly helps young children to develop working with numbers instead of holding on to counting-on methods of computation for too long. Teachers can encourage trial and improvement with questions such as "can you find how to . . .?" so there is a meaningful discussion about number relationships. "Broken key" activities allow pupils to suggest alternative strategies for working. None of these calculator activities hinders mathematical thinking.
Teachers can set challenging problems using real data. Large numbers can be coped with. Negative numbers which can cause such problems at secondary stage are handled and used in appropriate situations. However, to ensure the correct use of the calculator, pupils need to develop fluency in mental arithmetic, and that is where we have a lot to learn from the way pupils work on the Continent. But, please, let us keep our calculators.
Marjorie Gorman is an advisory teacher in Wakefield