John Muir says the debate on maths standards must be put into perspective over 30 years.
Primary and secondary teachers are considering the admonitions and advice in HMI's recent report on mathematics education 5-14. Some of those who were themselves pupils in the fifties will be heard saying "we told you so". They may argue that it did not need the results of comparative international studies or the series of reports from the Assessment of Achievement Programme to point out that standards of performance have fallen.
Unfortunately, the response to Improving Mathematics Education 5-14 may be to blame teachers alone for falling standards. To do so would be to forget previous advice which primary schools have been given by educationists and members of the Inspectorate, either informed by research or directed by politicians, over the past 40 years. As the profession considers the Agenda for Action, with its key recommendations for change to the content and pace of learning in mathematics, I thought it would be interesting to look back over a selection of papers published during that period to point teachers in the "right" direction.
In The Primary School in Scotland, published in 1950, HMI comments: "In the old days classes were so large, with rolls of 70 or more, that the teacher's method had perforce to be that of class instructions. Class instruction should be given no more than its due place in a judicious and flexible combination of individual, group and class methods. Much of the work in arithmetic lends itself well to group or individual methods, from which the weaker pupils in a class gain special benefit. As much of the work as possible should be done mentally; work not so done should be set down on paper. Long and laborious sums should not be given. The teaching of decimals should be postponed until the pupil enters a secondary department." The 1997 paper agrees with some of this - "In all classes there should be regular mental calculations" - but stresses that teachers should "employ whole-class teaching for introducing and consolidating work".
In 1965, Primary Education in Scotland was published and became the bible for primary teachers in training at the time and for many years thereafter. It set the scene for a more relevant and interesting primary curriculum, but there are those who maintain that it marked the beginning of a departure from the "basics", particularly in mathematics. "For many years the teaching of mathematics in the primary school has been almost exclusively concerned with the development of skills in reckoning and the perfecting of routine methods of carrying out computations. Much of the work is of little educational value. The introduction of calculating machines has weakened the vocational argument for intensive training in computation. In order to cope with the variety of activity the work of the class will have to be organised to allow a blend of individual, group and class learning, with the teacher frequently prepared to adopt the role of helper rather than of leader and instructor." Improving Mathematics Teaching 5-14 urges teachers to ensure that "most of their time in class is spent in direct teaching . . . with clearly structured lessons".
The Primary Memorandum, and publications which followed, such as Mathematics in Primary Schools (Curriculum Bulletin No 1, HMSO 1966), gave the clear message that the mathematics curriculum should be broadened to encompass other areas more fully. The school day was not lengthened, so more time spent in other areas meant less to work on arithmetic, for example. Primary Education in Scotland: Mathematics (Curriculum Paper 13, HMSO 1973) had as its aim the "updating and consolidation of the work outlined in the Primary Memorandum" in order to take into account decimalisation and metric measurement. It questioned the continuing prominence of arithmetic and proposed more flexible and broader approaches to mathematics: "Prior to the publication of the Memorandum, four hours per week was recommended for mathematics in the upper school. There is no justification for spending, on average, more than this on mathematics today and there may be some justification for spending less."
The 1997 report reiterates the 5-14 recommendation that "15 per cent of teaching time (3.75 hours a week) should be allocated to maths" but teachers should ensure that this is a "planned minimum time" for all pupils. The calculator age demanded that children should become familiar with the technology and when the instruments became as cheap as pencils there was no reason why their use should not be written into the curriculum. Many of the sentiments at that time were summed up in one of the recommended texts: Primary Mathematics Today, Third Edition, For the Age of the Calculator (Longman 1982): "As soon as children can count they begin to be interested in what a calculator can do. From quite early days they will check their answers to simple additions against those of their electronic device and thus build up memorable sequences. "
But the authors did not say that the calculator should do away with mental arithmetic, as some proposed. They counselled: "The use of a calculator does not diminish the need for an understanding of how numbers behave. If sensibly used, they can add much to the children's understanding of number."
The Committee on Primary Education's position paper on Primary Education in the Eighties said "the use of calculators to strengthen powers of estimation and testing of approximations should be encouraged". The 1997 paper reflects current concerns about over-use of the calculator in schools today and goes so far as to propose that its introduction should be "delayed until last primary or early secondary school". COPE, which again urged teachers to broaden the primary curriculum generally, implied that too much time was being spent on mathematics and reminded them of "the long recommended allocation" (of four hours a week).
Many HMI reports in the eighties expressed greater concern about the quality of learning within environmental studies and the expressive arts than about mathematics. It came as a surprise to some, therefore, that the 5-14 development programme had the review of mathematics high on its list of priorities. The levels and strands laid down were new to teachers and confusing to parents, presented with progression from A to E, the opposite of gradings in secondary schools. To manage the new guidelines and cope with the associated national tests, the levels were linked to certain ages and stages. Now, six years from the publication of these guidelines, research has led to a growing concern that standards are falling, particularly in comparison with pupils in some other countries. The latest advice is that "more should be expected of pupils . . . to improve overall performance".
By referring to a personal selection from a few past publications, some of which seem to contradict what is being proposed now, I am not implying that we should let things be as they are. We must respond to the needs of the time we are in and Improving Mathematics Education 5-14 can help us to do so. If we read it carefully we will not embark on the mass rewriting of textbooks (to the delight of publishers), build bonfires to burn calculators or return to "chalk and talk".
Schools that have "moved on" from a review of mathematics 5-14 must now be given time to look at the recommendations and consider fully the implications, not only in terms of resources and classroom practice, but also of the impact it will have on the pace of developments in other curricular areas. As headteachers contemplate how and when they will do this let us not forget that the 5-14 disease, "innovation fatigue", is still claiming its victims.
John Muir is adviser in primary education with Highland Council. The views expressed here are personal.