The report deals with 5-14 maths but has major messages for the rest of the curriculum as well. Brian Wilson, the Education Minister, wants its recommendations implemented “as a priority”.

Douglas Osler, senior chief inspector of schools, states in the foreword that schools must set targets that go “significantly beyond the minimum expectations in the guidelines”. Launching the report, which was called for after international and Scottish research showed a sluggish Scottish performance in maths, Mr Osler said schools must realise that the 5-14 targets were minimum standards.

The HMI report on Standards and Quality in Scottish Schools found that most pupils attained minimum national standards in only 75 per cent of primaries and only 65 per cent of secondaries in the first two years. Significant numbers of pupils exceeded the minimum targets in just one in six primaries and one in nine secondaries.

These messages for the classroom about the pace of learning are expected to form a central part of the work of the new ministerial task group on standards, which meets for the first time early next month.

The maths report recommends that most pupils should aim to overtake level A work by the end of primary 2 instead of primary 3, and that most pupils should be working beyond level D by the end of primary 7 rather than simply being content to achieve that target by the end of the session. These adjustments to the existing guidelines are now likely to be extended to the rest of the 5-14 curriculum in an effort to raise standards.

The Inspectorate is keen, however, to emphasise that the Government is committed to the 5-14 programme, including the place of national testing and the new level F to stretch the most able. The fact that changes will be made in the light of experience does not mean there is “open season” on 5-14 guidelines, commented Kathy Fairweather, HM chief inspector in charge of 5-14.

The maths report makes both specific and general recommendations, including more structured lessons, more interactive and participative methods of teaching, integrating homework more effectively into class work, restrictions on the use of calculators and more emphasis on mental arithmetic. Greater attention to arithmetic in the early stages and higher expectations by teachers about the pace of learning are also recommended.

The report was prompted by concern over the “disturbing” performance of pupils in primary and the early years of secondary revealed in the recent Third International Mathematics and Science Study and the Scottish Office’s own Assessment of Achievement Programme in maths.

The international study showed Scottish 13-year-olds in particular were performing well down the international league. Concern about the early years of secondary school was reinforced by the AAP study which confirmed a progressive decline in performance from primary 4 to secondary 2 and falling standards since the 1991 AAP survey, particularly in basic number work.

The HMI report acknowledges the paradox that, despite the worries about the first two secondary years, pupils appear to catch up by the time they are ready to sit national examinations. Ordinary grade A-C awards were achieved by only 26 per cent of S4 pupils in 1985, compared with nearly 49 per cent who gained corresponding Standard grade 1-3 awards in 1995. Higher passes in maths rose from 11.8 per cent to 15.7 per cent over the same 10-year period.

Grant Mathison, HMI’s national specialist in maths, says the recommendations on higher expectations, more effective homework and more structured lessons are already features of maths teaching in the third and fourth years. Their extension to the earlier years, coupled with a tightening of the guidelines in primary, would raise standards still further.

Mr Mathison visited Singapore, Korea and Japan, the three top-scoring countries in the international study. He sat in on classroom work, held discussions with teachers and studied teaching materials. Practice in Switzerland and Hungary, where pupils had performed well, was also scrutinised.

The report concludes that teachers in these countries “have very demanding expectations of the levels of attainment which most of their pupils can achieve”. National guidelines are also set at higher levels than those in Scotland.

Mr Osler says the message of the report is that there is sufficient good practice on which to build, including a positive attitude to maths among pupils. “We are not saying that 5-14 maths is in crisis.”

The key points

* Maths teaching should mostly be based on direct teaching to groups and classes and involve: clearly structured lessons; a good pace of work; clear explanations with effective questioning techniques; high standards of accuracy and neatness; non-routine problems to get pupils thinking for themselves; opportunities to recap what has been taught and the setting of homework.

* Teachers should encourage more interactive and participative learning which should include spending more time in explaining and asking questions and less time in class having pupils engage in individual practice; asking pupils to demonstrate and explain their thinking more often; and making better use of homework so that more work is corrected by the pupils themselves in order that mistakes are revealed and difficulties emerge.

* Emphasis on mental calculation should be increased; calculators should not provide unnecessary support but should be used for well-defined purposes; their introduction should be delayed until late primary or early secondary, and unrestricted access to calculators in S1S2 should be discontinued; exam candidates should be set questions to be answered without using a calculator.

* Number work at the early stages should be increased and basic algebra introduced at level D.

Primary

* More pupils should complete level A by the end of P2 and most pupils should be working beyond level D by the end of P7.

* There should be no more than three attainment groups in any primary class.

* Whole-class teaching should be used for introducing and consolidating work, and attainment groups should be limited at the early stages; group teaching should aim to stretch able pupils leaving teachers more time to help struggling pupils.

* Heads should ensure teachers have a more consistent approach to maths teaching, including detailed course guidelines and advice on the pace of learning; setting of pupils in P6 and P7 is advantageous.

* The planned 15 per cent minimum time for teaching maths is not being met in all primary schools.

Secondary

* Maths departments should not discourage S1 pupils who are well into level E and should reject the “fresh start” approach.

* Broad band setting should be introduced into S1 maths classes as soon as feasible with pupils allocated on the basis of recent assessment.

* Individualised learning schemes should be discontinued in favour of more structured lessons, either for groups or whole classes.

* The teaching time for maths should go significantly beyond the recommended 10 per cent minimum.

* Homework should be set more regularly in S1S2.

Training

* Some teachers will require staff development to adopt more participative and interactive teaching styles, and to deploy the use of questioning and discussion to ensure pupils absorb lessons.

* Teacher education courses should be adapted to support these recommendations.

Platform, page 12

Comment, page 13