Last term, in my advisory role, I completed my round of discussing with schools their targets for pupil attainment in 2003. LEAs are now “armed” with more information than ever before. Like many others, North-east Lincolnshire has a fully populated and up-to-date database, showing every pupil and their attainments in their last end-of-key-stage tests.

In its “autumn package”, the Department for Education and Skills has helpfully provided an analysis of national data to show what proportions of pupils achieve particular key stage 2 levels, given their earlier KS1 levels. LEAs are able to produce similar tables for individual schools and the authority as a whole.

These progress tables are useful to schools in appraising their progress and setting targets. The combined table below, for mathematics, puts three figures in each cell. The top left figure shows a particular school, the middle figure shows the LEA, and the bottom right figure shows the national data.

Progress between KS1 and KS2 Clearly, pupils in the school are making progress over KS2 at a better rate than the national or LEA rate. Notice that all those who enter this school with level 3 achieve level 5 by the end of the key stage. All those who enter with level 2a or level 2b achieve level 4 or better. Sixty-three per cent of those starting with level 2c achieve at least level 4 and nearly half of those with level 1 achieve level 4.

I estimate that the national target may be met only by all level 2c entrants achieving level 4 and at least 80 per cent of those at level 1. On this comparison, this is a high-achieving school. I want to congratulate them and tell them their progress rates are commendable.

To improve further their points score they have to move more pupils from the left-hand side of this table to the right. But here lies the snag. It means, among other things, the school must move some of its level 4 into level 5, and some of its level 5 into level 6.

In my conversations with secondary schools, I am being told that already some of the KS2 assessments are insecure. They are measuring where a pupil can reach by standing on tiptoe and with full body stretch. I can just touch the ceiling in my house this way but it does not mean I am very tall. There is a difference between extended height and normal height.

Progress should be measured from normal attainment, not from what can be forced on a particular day. Learning builds on what is consolidated not on what is tentative. The tiptoe reach of attainment at the end of KS2 is not the same as the platform for progress in learning for KS3.

I believe this can be generalised to any key stage transition where results are reported and carry with them high stakes in terms of teachers’ performance management.

What needs to be done in primary schools? We need a level 5* which measures a secure platform for further progress and requires:

* a depth of understanding with level 5 content

* an ability to apply level 5 content in a range of contexts;

* a relational understanding of concepts within level 5 which demonstrate learning connections across maths - and beyond

* an ability to reason mathematically within the content prescribed.

Level 5* must be awarded additional points to satisfy the league-table addicts. A secure platform merits higher recognition than tentative reach. More importantly, it should be awarded additional points to prevent superficial content skating.

This is not radical. Some levels are already broken into the three parts of (c), (b) and (a). Perhaps the (a) assessment could satisfy the criteria above. The (c) assessment might include the criteria of demonstrating:

* emerging understanding of the level content

* an ability to apply the level content in a usual context

* an instrumental understanding of concepts

* an ability to understand a simple chain of reasoning within the content prescribed.

Level (b) would be somewhere between (c) and (a).

Each level could be defined in three degrees which relate to confidence and be ascribed a particular point score. At one stroke, this would give primary schools a motive to secure breadth and depth of understanding and give a clear signal to secondary schools of the platform on which they should build to secure continuity and further progress. A level 5a or 5* would stretch and recognise the achievement of the higher attainers.

I want to be able to tell my primary schools to make their level 4s into better 4s and their level 5s into better 5s. I want to be able to tell my secondary schools that level 4a or 4* is a secure platform and I expect to see level 5a or 6c or 6b as outcomes at the end of KS3. If each level difference is worth six points, then we can aim to make four points progress a year.

This would be one way that assessment might support rather than distort the curriculum and its learning. Current national assessment leads to selecting only those aspects of the curriculum that will be tested. Learning is also put at risk. Effective learning takes place when the learner resonates with the teaching. In less secure learning, the learner merely echoes what the teacher says or does. Assessment should be able to differentiate between resonance and echo and award the former more value than the latter. This approach would contribute positively to the debate on meeting the needs of high attainers where, currently, accelerating through the levels is the only way to secure extra points value.

A broad curriculum, well taught and cross-braced with learning connections, brings the possibility of high and secure structures of achievement. The challenge is to design assessment tools which assist in the building of these structures and do not encourage constructions where height is achieved at the cost of stability.

I am not surprised by the encouraging findings of the Organisation for Economic Co-operation and Development which show England to be eighth in the international league table for mathematics. This reflects the skills and talents of our teachers.

Our national preoccupation with over-simplistic assessment rather than curriculum enrichment is the block to our becoming world leaders.

Current models of national assessment and predatory moves to nationalise pedagogy will strangle the potential of the teaching profession to bring about further improvement. The Association of Teachers of Mathematics, along with other subject associations, wishes to see more learners better served. We wish to see incentives to enrich the curriculum and deepen subject knowledge and understanding. Differentiating assessment within each level in a manner similar to what I propose here would help in this cause.

Peter Lacey is deputy director of education of North-east Lincolnshire, and chair of the General Council of the Association of Teachers of Mathematics, 7 Shaftesbury Street, Derby DE23 8YB. Tel: 01332 346599. Web: www.atm.org.uk