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Standards and Quality in Secondary Schools 1995-1999: Mathematics

2. STANDARDS OF ATTAINMENT

HM Inspectors made three judgements about pupils' attainments:

• the quality of classwork;
• standards of pupils' work compared with national standards; and
• the overall quality of attainment, taking into account coursework, attainment related to national targets and examinations, the quality of learning and how well their needs were being met.

Comparisons with national standards were based on reference to levels defined in 5-14 National Guidelines in Mathematics and on SQA examination statistics. The mathematics departments inspected between 1995 and 1999 for this survey were representative of the national patterns of performance for Standard Grade, Higher Grade and CSYS mathematics.

Standards of attainment in S1/S2

In many schools, pupils coped well with coursework but, particularly in S1, much of the work was familiar and undemanding. Although work was often neatly presented, pupils required more practice in writing out their solutions to problems in a logical sequence of steps. The standards pupils attained in their coursework were very good in 20% of departments, bearing in mind these frequent shortcomings in the challenge of the tasks set. In a further 65% they showed more strengths than weaknesses. They required significant improvement in 15% of the departments inspected.

In around 10% of departments almost all pupils attained the appropriate 5-14 levels of attainment for their stage. Most pupils reached appropriate levels in an additional 30% of departments and the majority of pupils in a further 35%. In the remaining 25% of departments, appropriate levels of attainment were reached by less than half of the pupils.

The overall quality of attainment, which takes account of all factors, showed more strengths than weaknesses in only 45% of departments and was very good in 5%. There were some important weaknesses in 50% of departments including a few where the overall standard of attainment was unsatisfactory. In general, overall attainment in S1/S2 should be improved. aspects requiring improvement are shown in Box 4.

Standards of attainment in S3/S4

The quality of coursework was very good in 10% of departments. It showed more strengths than weaknesses in 70% and important weaknesses in 20%. In many departments, pupils at Standard Grade, particularly those aiming for a Credit Award, presented their work well, completed clearly argued accounts of investigations, worked at a good pace in class, responded with enthusiasm to teacher questions and conscientiously completed homework on a regular basis. Where weaknesses were identified in standards of coursework, they usually included untidy and inaccurate work, with incorrect calculations left uncorrected; or too slow pace of work leading to inadequate experience of problem solving.

National performance in Standard Grade mathematics is shown in Box 5. The pattern of awards, with many pupils gaining only a Grade 5 Award at General level, supports the evaluation made by HM Inspectors that too many Foundation/General courses were pitched at the lower level of attainment. Pupils receiving a No Award had usually not completed the required number of investigations or attended for the examination.

The overall quality of attainment, taking account of a range of factors, including comparison with national averages and with the performance of other departments in the same school, was very good in 15% of the departments inspected. It showed more strengths than weaknesses in 35%, and some important weaknesses in 45%. Overall attainment was unsatisfactory in a small number of schools.

Where the quality of overall attainment showed weaknesses, improvements in aspects of the following were required:

• in Credit level work, more facility and accuracy in algebra;
• in General and Foundation level work, more confidence in written and mental calculation without the use of a calculator; and clearer setting out of working and explanations of how solutions were arrived at;
• at all levels, better development of skills in solving challenging problems.

Standards of attainment in S5/S6

Standards of coursework were very good in 10% of departments. They showed more strengths than weaknesses in 60% and some important weaknesses in 30%. In most cases, HMI found that the standard of coursework in Higher and CSYS classes was very good, or had more strengths than weaknesses, but there was a lower standard in many NC classes, where pupils sometimes lacked motivation and made slow progress. The strengths and weaknesses of pupils' performance in coursework are set out in Boxes 6 and 7.

National performance at Higher Grade is shown in Box 8. Around 11% of the S6 cohort were presented for at least one paper at CSYS. 2% gained Band A; 3% Band B; 3% Band C; 2% Band D; and 1% Band E. The number of pupils who received no award was negligible.

Percentages of S5/S6 pupils achieving full success in NC modules varied widely, both nationally and in the sample of schools inspected. These large variations were caused mainly by differing presentation policies, although some of the differences in successful completion of NC modules can be related to the quality of the teaching programme.

In judging the overall quality of attainment in each department, HMI took into account both the way in which pupils' needs were met by the presentation policy of the school and by the general quality of learning and teaching. This involved consideration of the balance between Highers, CSYS and NC modules. The overall quality of attainment in S5/S6, taking account of these factors and comparisons with both national averages for Higher mathematics and the performance of other departments in each school, was very good in 10% of departments. It showed more strengths than weaknesses in 35%, and some important weaknesses in 55%. Unsatisfactory attainment in S5/S6 was found in only one department. As at other stages, overall attainment should be improved.

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