Professor Sig Prais, of the National Institute of Economic and Social Research, has reached this controversial conclusion after re-examining data from the Star project conducted in the late 1980s. He maintains that the experiment only benefited six-year-olds and argues that the cost was uneconomical.
Professor Prais also insists that his analysis shows there is no point in conducting more research into the effect of class size on average pupils' attainment. It would be more productive to investigate the benefits of alternative textbooks, more detailed teachers' manuals, other forms of class organisation and teaching styles, and more lesson preparation time for teachers.
He agrees that pupils with special educational needs do benefit from smaller teaching groups - a view confirmed by the Tennessee study - but says that researchers should now try to establish the optimum class sizes for the different SEN categories.
The Tennessee experiment has attracted worldwide interest because it is the largest study of its kind. It followed 7,000 children through their kindergarten year and the first three years of school and cost $12 million (#163;7m). Children were randomly allocated to a class of 15, a class of 24, or a class of 24 that was supported by an assistant.
The study's authors produced evidence showing that children's maths and reading scores were higher in the smallest classes. But Professor Prais, who is best known for highlighting the gap in maths attainment between British and German children, raises new doubts about the Tennessee findings in the latest edition of the Oxford Review of Education.
He refuses to accept that the end-of-kindergarten scores show a clear advantage for small classes because the children's ability was not assessed at the start. But he acknowledges that children in the smallest classes made bigger gains in the first year of school than those in the average-sized classes (the equivalent of 16 days' extra teaching in a school year of 180 days).
Professor Prais, however, suggests that this may be partly because 108 "incompatible" children had been moved out of the small classes at the end of the kindergarten year.
"Moving probable bad eggs out of one basket to another must be expected to improve the recorded average degree of freshness of their originating basket, and lower the average freshness of the destination basket," he comments drily.
He also highlights the surprising finding that in the second year of elementary school the children in small classes made slightly less progress in maths than those in the bigger classes. In the third year the progress rate was very similar.
Over the three years children in the small classes made only 1.6 per cent more maths gains than other pupils, which Professor Prais says is the equivalent of just three extra days of teaching a year. The reading gain was the equivalent of six days.
"Those extra days could be found in the UK in various ways," he says. "School holidays might be reduced, and teachers could be paid for an extra three days of teaching a year, adding under 2 per cent to the wage bill.
"Alternatively, fewer days could be spent by teachers on 'Baker days', or the sports days and pantomime days that often occupy the end of term could be moved to weekends or national holidays, so freeing time for teaching and learning.
"These options need to be compared with the Tennessee alternative based on reducing class sizes to 15, amounting to an additional teaching cost per pupil of about 60 per cent ... In any event, a gain of 1-2 per cent is hardly worth straining for when it appears that Japanese pupils learn at a rate about 50 per cent faster per year than English and American pupils."
Professor Prais says the study indicates that teaching assistants had a negative effect on children's progress, but he questions this finding. "I favour the possibility that the samples of pupils, following their regrouping at the end of their kindergarten-year, were not of equal ability. I suspect that the teaching assistants did much good helping classes with an undue proportion of difficult pupils."
Nevertheless, he says it may be time for English schools to reconsider their policy on classroom assistants. "While there may be doubts about the acceptability of the Tennessee finding, until further research results are available it suggests caution," he warns. "The number of assistants in English primary schools rose by a remarkable 40 per cent between 1992 and 1995. They now account for about one in five of all full-time equivalent adults in schools."
"Class size and learning", Oxford Review of Education, Volume 22, Number 4. Copies of Professor Prais's paper are available from Carfax Publishing, PO Box 25, Abingdon, Oxfordshire OX14 3UE, price #163;10.