This report is the third of a series of Standards and Quality reports dealing with individual subjects in the secondary school. It makes evaluations based on the published performance indicators used by HMI in all school inspections. This series should be read in conjunction with the more general survey of Standards and Quality in Scottish Schools, of which the most recent edition covers the period 1995-1998.
Much of the mathematics teaching in Scottish secondary schools is effective. Many pupils make good progress and the most able achieve high standards. Over the ten year period 1985-1995, for example, there were significant increases in the numbers of pupils achieving quality awards at Standard and Higher Grades. However, this report shows that too many pupils at all stages fail to achieve their potential in mathematics. Improved attainment will require better account to be taken of pupils' individual needs and prior achievements, improved course planning, and more effective teaching and learning. The national advice and guidance to allow mathematics teachers to improve these aspects of their work has been available for some time, in the form of the 5-14 National Guidelines (SCCC 1991), national performance indicators in How Good is Our School? (HMI 1996) and Improving Mathematics Education 5-14 (HMI 1997). The key is to implement this advice and to learn effectively from the great deal of existing good practice, a point which echoes concerns raised in other reports, particularly with regard to S1/S2.
At all stages, there are departments which provide high quality mathematics education, and where pupils reach high standards of achievement. There are, however, too many departments where there are significant weaknesses in provision at one or more stages.
In S1/S2, too many mathematics departments have been slow to implement the 5-14 guidelines, work is often not well matched to pupils' needs and many pupils could make more rapid progress to higher levels of achievement. Many education authorities have responded well to the 1997 HMI report on mathematics and are now encouraging and supporting schools in implementing its recommendations. Teachers are being advised to spend more time in direct teaching and to put more emphasis on improving numeracy through mental calculation. Many schools have also followed national advice on matching work better to pupils' abilities through extending setting by attainment in S1/S2. However, these features of good practice are not yet sufficiently widespread. National Tests have recently been revised to place more emphasis on mental calculation and written calculation without the use of a calculator. All schools should immediately implement national testing in mathematics in S1/S2 in order to confirm teachers' judgements about pupils' progress and identify areas of weakness.
In S3 to S6 some aspects of provision, such as course construction and meeting pupils' needs, are generally better than in S1/S2. However, too many S3/S4 pupils gain only a Foundation Award because of unchallenging courses. Many lessons neglect the need for high standards of numeracy and too few pupils are required to think for themselves. The introduction of non-calculator papers in examinations at Standard Grade and beyond should encourage higher standards in mental and written calculation. The type of interactive teaching, working directly with individuals, groups or the whole class, as recommended in Improving Mathematics Education 5-14, needs to be extended into S3 to S6. The new courses being introduced under the Higher Still programme are designed to support this kind of teaching approach. Appropriate use of ICT is another way of making teaching more stimulating, and teachers of mathematics should respond positively to the recommendations of the report Advanced Calculators in Mathematics Education (SCCC 1998).
In several key respects, the management of mathematics provision should be improved. The quality of self-evaluation is poor in the majority of departments. There should be a greater emphasis within mathematics departments on working together, and with others, to identify what improvements are required and the steps that must be taken to secure these improvements. Departments will need support from senior managers, and from local and national agencies to ensure that these improvements can be achieved.
This report will be of interest to a broad range of readers, including education decision-makers at national level, education authority directorates, senior promoted staff in schools, and school boards and parents. Above all, it should help teachers of mathematics as they seek to improve the quality of the educational experiences and attainment of pupils in mathematics.
D A Osler
HM Senior Chief Inspector of School