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On the level;Mathematics

Geoff Faux claims national tests are a poor indicator of pupil achievement and exert downward pressure on standards.

The Government says it wants to see three out of four children achieving level 4 in the mathematics national tests at the end of primary school. Will this raise standards?

This is not a simple question. The tests do not exist in isolation. They are used for purposes other than measuring the skills, knowledge and understanding of individual children.

A primary head recently wrote to me, saying: "Raising standards is judged to be synonymous with pushing children up through the levels. Heads and teachers feel a lot of pressure to increase the percentage of children achieving the higher levels year on year. Key stage 2 teachers are no longer satisfied (or fear it is not good enough to be only "average" - who wants to be average?) with level 4, but are going for level 5."

The pressure is real and comes from three sources:

* the internal system for target-setting. The school sees itself as an improvingdeveloping school, so compares its results with those of previous years * comparison with other schools (many of which will be putting themselves under the similar pressures). Public accountability from league tables is a serious pressure * selective secondary school demands, by which primary schools are judged locally.

It seems outside influences, rather than professional judgments, lead decision-making. Pupils step up a level as soon as teachers consider they have grasped the previous one, even though plenty of work is available to deepen its foundation. Pupils risk being fed a poor diet, which provides minimum standards within the specification of the level. There is no time to consolidate, enrich or develop quality.

As pupils move from one key stage to another, national test results are used as an indicator of achievement. But the level score fails to show whether or not earlier important material has been covered properly.

To try to understand how the tests could be pushing quality and standards down, I looked at the key stage 2 tests for 1997 and grouped individual questions to show the level they test in the national curriculum in the 1995 Order (see figure 1, right).

A student answering all the level 2 and 3 questions correctly, but no level 4 questions, would score 31 per cent (25 out of a possible 80). The mark scheme last year awarded level 3 to students scoring between 18 and 39 per cent - a range of 21 marks. This suggests a confidence interval of +- 10 per cent in the measuring instrument. It leaves aside the question of how a pupil who has scored, say, 25 per cent feels about his or her personal mathematical competence when unable to answer three-quarters of the questions correctly.

A pupil last year who answered all the level 2, 3 and 4 questions correctly, but no level 5 questions, would have scored 76 per cent (61 out of a possible 80). The mark scheme awarded level 4 for the range 40-61. So level 4 was awarded on 50 +- l0 per cent. But a pupil could achieve 50 per cent by answering two-thirds of the level 4 questions correctly. You get the level for being successful in around two-thirds of the listed items.

Is this mark scheme a fair measure of achievement at each level? The answer must be no. The more I analyse this test the more I become convinced it is not the test that is at fault but the national curriculum model that proposes learning can be split into eight (or 10) developmental steps that needs to be rethought.

If the attainment targets were reformulated to focus on some of the big ideas in mathematics that pupils need to be familiar with and secure in at the end of each key stage, and the test was an instrument to measure that security, standards could be raised.

We need to look at the national curriculum structure as well as the way information is gathered about performance using end-of-key-stage tests. A sensitive and well-designed instrument that focused on the important milestones in becoming competent and confident in mathematics could raise standards. Sticking with the current eight-level scale and national tests and asking teachers to increase the percentage of children scoring level 4 at age 11 is a sure path to Lake Woebegone.

* Geoff Faux is a former maths adviser now working as an independent consultant

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