Despite the scares over falling standards there is no systematic research on what schools can do, says Donald Macnab
IN ALL THE attention to the state of mathematics in Scottish schools, there is a missing dimension. We are not short of reports pointing to declining standards of achievement, a relatively poor international ranking and the need to take remedial measures. Most recently, HMI's Standards and Quality report has underlined aspects of unsatisfactory performance.
But the lack of a research agenda for mathematical education means that one element of informed debate is not available.
There are isolated studies by individuals or bodies like the Scottish Council for Research in Education, but these do not amount to an agenda. The absence of such an agenda not only impinges on our understanding of factors affecting effective mathematics teaching and learning, it results in certain questions remaining outside the currency of debate.
Scotland certainly is not lacking in curriculum initiatives and guidance, but these are not normally underpinned by an explicit body of research evidence. For example, the 5-14 guidelines state that they are based on a wide-ranging review of good practice.
Outside Scotland, there is an extensive range of research activity, but importing research has two major disadvantages. First, the research may not relate particularly well to Scottish contexts or may be perceived not to relate. Second, and more importantly, it tends to create a dependency culture and leaves Scotland outside the debate on the range of active research issues and consequently without direct influence on it.
If one looks at the major UK players in mathematics education research in terms of published work, all are working in England. The obvious question is, why?
Several general answers might be put forward. It could be argued that as England has a much larger population than Scotland it is more able to sustain a substantial research activity. Some might say that Scots are a more pragmatic people than the English, and suspicious of theoretical approaches to education.
Again, it might be said that Scotland is a more close-knit community than England in which consensus is more easily attained and implemented, or that central control of education is greater in Scotland than in England.
However, these answers, individually or in combination, do not fully explain why other small countries, Denmark for example, can support an internationally recognised research activity in mathematics education.
The real answer must be elsewhere, within the psychology and outlook of the Scottish educational community which does not see any need. In general, and excluding attainment surveys such as the Assessment of Achievement Programme, educational research in Scotland is for the most part concerned with a mix of social, political and holistic issues - with topics such as bullying, special needs, curricular planning coherence and integration, school ethos, to name a few - in which mathematics, if dealt with at all, is treated within the curriculum as a whole rather than as an investigative area in its own right.
There also is a wide divergence between university departments of mathematics, concerned with teaching and research in mathematics as an academic discipline for the relatively few, and schools, concerned with basic mathematics education for the many.
The teacher education institutions - now amalgamated, or about to be, with universities - are not yet staffed for substantial research activity into the subjects of the school curriculum. Schools tend to shy clear of involvement in research initiatives in mathematics education which they see as a distraction from their main function of teaching.
These reasons, of course, only attempt to provide an explanation why there is no Scottish research agenda, not why one is not needed. There is certainly no shortage of topics for inclusion in such an agenda.
For example: aims and purpose of mathematics teaching, in primary schools, in S1S2 and for national examinations; methodological approaches to teaching mathematics in primary and secondary schools; effective classroom learning environments for mathematics; mathematics and cognition - the development of thinking skills; mathematics learning and the psychology of the individual pupil; nature of mathematical knowledge and understanding - internal structures and learning processes; the development of meaning in mathematics education; curriculum development in mathematics teaching and learning; curriculum management of mathematics education, at school, education authority and Scottish Office Education and Industry Department level; teachers' belief systems and attitudes on the teaching and learning of mathematics.
The plethora of books and papers on mathematics education over the past decade demonstrates both the variety of thinking and the lack of consensus. The Scottish education system provides an important context in which the issues can be subjected to scrutiny and development, thereby bringing a unique perspective to the debate.
If we believe that Scottish education, and in particular mathematics education, has the positive qualities that are so often stated, then we should be bringing a Scottish perspective to bear for the benefit of the rest of the UK and elsewhere. If we believe that Scottish education is in need of significant improvement, then there is an even greater need for a home-grown research programme.
Either way, the status quo should no longer be an option.
Professor Donald Macnab is senior research fellow, Northern College, Aberdeen. He is engaged in developing research initiatives in mathematics education and welcomes responses to the views expressed.