Let me explain, using the national curriculum levels as a rough measure of attainment.
Imagine that a bright pupil leaves key stage 1 at, say, level 3 for mathematics and then leaves key stage 2 after having achieved level 6. Under a value-added approach, the school would get credit for improving the pupil's attainment by three levels. However, if a less able pupil moved from level 1 to level 2 during hisher key stage 2 education, the school would get credit for improving hisher attainment by only one level.
But does the school deserve three times more credit for its contribution to the bright pupil's progress than for what it has done for the less able pupil? Under my proposed value-multiplied approach, in both cases the school should get the same credit for increasing the level of attainment by a factor of two. This is clearly a fairer way of assessing the school's contribution to the pupil's progress. Which of the two examples above is really the greater achievement in terms of the educational challenge involved? Having taught mathematics to pupils at both ends of the spectrum, I know which I would find to be the more straightforward teaching task: pushing on the brighter pupil every time.
Give me a mathematically capable pupil at level 5 at the beginning of Year 6 and I would be pretty confident that I could get him to level 6 by the end of the year. Give me a pupil of the same age who has struggled to get to level 2 and I would consider it an achievement to get him to level 3 by the end of Year 9.
In a value-multiplied system the credit for moving pupils from level 2 to level 3 would be 1.5 (since 2 x 1.5 = 3), whereas the credit for moving pupils of the same age from level 5 to level 6 would be only 1.2 (since 5 x 1. 2 = 6).
The ratio of the final level to the starting level is clearly a much more appropriate measure of the school's achievements than the difference.
The expectation in the structure of the national curriculum assessment framework is that some of the very brightest pupils will reach, say, level 9 by the end of key stage 3, while some of the less able may only get to level 3. Making the assumption - obviously a big assumption - that the level descriptions represent equal intervals of progress, then, assuming steady progress across nine years of schooling, the brightest pupil has a potential of moving forward by one level per year, whereas the less able pupil may only be capable of one level every three years. It is clear, therefore, that under a value-added system schools would unfairly continue to get extra credit merely for recruiting brighter pupils.
Under my value-multiplied system, the school gets as much credit for a little bit of hard-earned progress with the low-attaining pupil as it does for a much greater step forward by the high-attainer. Such an approach to measuring a school's performance is essential if we are to encourage schools to improve standards across the whole ability range.
Derek Haylock is a senior lecturer in education at the University of East Anglia, Norwich