Swiss and Japanese pupils always do well in international studies of children's maths performance. But such surveys invariably fail to offer explanations for their high average attainment levels, writes Julia Whitburn.
Having conducted detailed observations of maths lessons in both countries, I have concluded that there are five broad areas in which common characteristics can be identified.
In both Switzerland and Japan, arithmetic accounts for approximately 80 per cent of the curriculum. Shape and space, measurement, and data handling occupy a smaller part of the curriculum than in the UK; algebra is included as a form of generalised arithmetic.
Word problems play an important part and indeed in both countries pupils are introduced to arithmetical processes by means of contextualised word problems, concrete materials and visual aids. Only when understanding of a process is secure will abstract notation be used.
There is also a greater focus on mental and oral arithmetic, with a later introduction of formal written algorithms. Pupils are, however, introduced at an early stage to strategies for mental calculation. No calculators are used in primary school; indeed, it is rare to see any in secondary schools either.
Second, teachers' manuals are used to a much greater extent than in England. Manuals are detailed and carefully developed by teams of experts, and given extensive trialling in schools prior to publication. Of course, with experience, teachers adapt the materials as they wish, but a sound basis and lesson structure is provided for teachers who wish to follow it. Frequently pupils in Switzerland are provided with work books for consolidation and practice, and children in both countries are expected to do far more examples for practice than is required in English textbooks. Progressive steps will be small, and carefully and logically sequenced.
A third factor is the emphasis on whole-class teaching methods. These require a high level of participation from pupils. New concepts or operations are introduced in several ways - using concrete materials for younger children, and visual aids as appropriate - including high-level "challenging questioning", sufficient waiting time for answers, and a requirement for pupils to give oral answers clearly and coherently using the correct mathematical vocabulary.
Pupils are expected, and are willing, to listen to their classmates. Children frequently come out to the front to demonstrate or explain on the board or the overhead projector. Mistakes are not ridiculed by others and are regarded by the teacher as a bonus for providing an opportunity for positive learning and clarification of misconceptions.
The fourth issue is classroom seating, which is regarded as important in both countries. In Switzerland, a "horseshoe" arrangement of desks and chairs is seen as the optimum classroom lay-out, permitting sightlines of communication. In Japan, children are more likely to be seated in pairs - using a boygirl combination as far as possible. Grouping of desks into fours or sixes is used for handwork and art, but not for "academic" learning. In fact, several research studies of primary schools have shown that time on task increases significantly with the introduction of any seating arrangement that does not involve small groups. Research by Wheldall and Olds has also shown that mixing genders increases time on task.
Finally, in both Switzerland and Japan, all pupils within a class have the same learning experience, and great efforts are made to move all children forward together. If necessary, children will be given additional help or explanation by the teacher, either in a group or individually. When written work is introduced, high standards of presentation are required.
There is, however, another feature common to both Switzerland and Japan which facilitates learning; not just in mathematics, but across the whole curriculum. This is the role played by the kindergarten or nursery school in preparing children for formal schooling.
The kindergarten curricula in Switzerland and Japan emphasise the importance of developing social behaviour and co-operation amongst children. Of secondary importance is the development of such skills as auditory and visual memory, co-ordination, attention span, precision and accuracy, and facility with speech. Academic learning, such as reading and writing skills, and recording of number, are judged to be the province of the primary school.
There is no doubt that this kindergarten experience provides an excellent preparation for later learning, so that when children attend formal schooling they are ready to listen, "know how to answer questions", and make sounder progress.
It is not clear that the Desirable Outcomes for Learning published by the School Curriculum and Assessment Authority last year will help nursery classes to perform such a preparatory function. Indeed the importance given to academic learning in the pre-school years by that document may add to the difficulties already faced by nursery teachers.
Julia Whitburn is a senior research officer with the National Institute of Economic and Social Research.