Extra spending does not appear to have a significant effect on the performance of children in the bottom half of the achievement range, but it does boost the scores of pupils who are above average in maths and reading.
The finding, which will dismay groups campaigning on behalf of disadvantaged children, has emerged from a study undertaken by William Fowler of the National Centre for Education Statistics.
William Fowler told the AERA conference that he had studied the composite maths and reading scores of 10,110 state school children who were tested at the ages of 14, 16 and 18 as part of the National Education Longitudinal Study.
He then compared their scores, which were collected between 1988 and 1992, with the spending levels in school districts.
Information on spending by individual schools in one state - Texas - was also examined, and background information on the children's socio-economic status was also taken into consideration.
William Fowler said that he had set out to try to prove that children who do not perform well on achievement tests are "more sensitive to higher expenditures" but he had found that the opposite appeared to be true. "Money seems to have some slight positive effect upon those students who scored above the median . . . if these results are consistently found, then the current operating assumptions in education may be profoundly altered," he said.
"The competitive position of the United States among other nations has often focused upon raising average achievement, presumably by raising minimum standards. However, if the achievement of students above the median score can be enhanced by additional expenditures, then a new strategy of funding may be in order."
A second paradox thrown up by William Fowler's study was that the individual school spending figure turned out to be less statistically significant than the district total spending figure.
But such apparent illogicalities merely demonstrate how difficult it is to tie down the links between spending and pupil attainment, a point that William Fowler acknowledges.
The next two challenges facing researchers, he believes, must be to produce better estimates of the sums spent on individual children and to produce more sophisticated statistical procedures for "disentangling socio-economic status and school resource levels".