the past decade and continue to show "significant weaknesses" at one or more stages, HM Inspectors complain in their state of the nation report.
Maths teachers join colleagues in science and English in taking a pounding from the inspectors and overall the verdict is, could do considerably better.
Douglas Osler, senior chief inspector, writing in Standards and Quality in Secondary Schools 1995-1999: Mathematics, bemoans that too many pupils at all stages fail to achieve their potential, although much teaching is effective, and not enough teachers and departments come up to expected standards.
"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," Mr Osler states.
Not unexpectedly, the first two years of secondary are particularly criticised, a common HMI theme. Too many departments have been slow to implement 5-14 guidelines, work is often not well matched to student needs and many pupils could make far more rapid progress.
Mr Osler praises local authorities for responding well to the 1997 report on maths. "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."
Equally unsurprising is the advice that all schools should implement national testing.
In the middle years, too many S3-S4 pupils only gain 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," Mr Osler states.
Calculators should not be banned, as some reports have suggested, but should be used more sparingly to improve mental and written calculation, a recommendation from the 5-14 maths report.
Interactive teaching, working directly with individuals, groups or the whole class, should be extended to classes above S3. New courses under Higher Still will help this, Mr Osler continues. He also advises greater use of ICT to create more stimulating teaching.
Turning to management, the senior chief calls for substantial improvement and slates self-evaluation as poor.
Many courses in S1-S2 were not well planned, the inspectors report. Only 10 per cent were very good and 50 per cent were good. Things are better in S3-S4, where 10 per cent were very good and
60 per cent good, and better still in S5-S6, where 80 per cent were very good or good.
In S1-S2, most departments still placed too little attention on mental calculation, problem-solving and enquiry skills.
At Standard grade, courses were generally well designed. Weaknesses included low expectations, slow pace and not enough time on problem-solving. In S5-S6, most courses had more strengths than weaknesses.
Standards of attainment
Many schools struggled in S1 to provide demanding work. The standards pupils attained in their coursework were very good in
20 per cent of departments and in a further 65 per cent were described as good. But 15 per cent of departments "required significant improvement".
Overall attainment in the first two years needed attention in half of the 92 departments inspected.
In S1-S2, pupils need to improve in mental calculation; fractions, decimals and percentages; algebra; and solving non-routine problems.
At Standard grade, attainment was very good in 15 per cent of departments, good in 35 per cent and only fair in 45 per cent. Credit work needed to focus on accuracy in algebra and at General and Foundation levels more confidence is needed in writing and mental maths without a calculator.
In the upper school, 10 per cent of departments were very good, 35 per cent good and 55 per cent only fair.
Learning and teaching
From S1 to S6 the quality of learning was very good in 5 per cent of departments, good in 55 per cent and fair in 40 per cent. The quality of teaching was very good in 10 per cent, good in 75 per cent and fair in 15 per cent.
On assessment, 40 per cent of departments had weaknesses to address, especially in S1-S2. National tests were sometimes badly used and most departments had inadequate evidence to provide reports to parents which conformed with national guidance.
Accommodation and facilities had more strengths than weaknesses in 50 per cent of schools and were very good in a further 30 per cent. Weaknesses include absence of a staff base, inadequate storage and too few dedicated classrooms.
Only one department showed good practice in staff development and review and fewer than 10 per cent had done a full staff review.
Management and quality assurance
Principal teachers' leadership was very good in 20 per cent of departments and good in 55 per cent but "it is of concern that almost 20 per cent of principal teachers showed some important weaknesses in leadership and 5 per cent were found to be unsatisfactory". 'Many lessons neglect the need for high standards of numeracy and too few pupils are required to think for themselves' WHAT TO WATCH FOR IN THE CLASSROOM
* Hard-working teachers and good teamwork in most departments.
* Good pupil response and relationships with staff in most classes.
* Well organised assessment in S3-S6.
* Good range of courses in S3-S6.
* Teachers who are good at explaining and questioning in groups and classes.
* Some schools had very high standards of attainment, especially in S5-S6.
* Well designed courses in S3-S4 leading to good Higher courses.
* Teachers need to raise expectations and improve attainment at all levels.
* Direct teaching should be increased in S1-S2 and some S5-S6 courses.
* Pupils need a more active
role in lessons, being set more challenging problems.
* Better alignment of assessment and reporting to guidelines.
* From S1 to S5, more emphasis
on mental and written calculation without a calculator.
* Need for more systematic