The publication on Tuesday of Chris Woodhead’s third, tentatively upbeat, annual report was ambushed by another row over extrapolation - a word that looks likely to be engraved forever on the chief inspector’s heart.

Why, ask Mr Woodhead’s critics, is it acceptable for the chief inspector to assert that there are 15,000 bad teachers (now revised to 13,000), basing this on an extrapolation from the numbers of poor lessons observed, but not all right to point out that if only 1 per cent of lessons have been given the bottom two grades under the new inspection framework, then there must be considerably fewer bad teachers in our classrooms?

Mr Woodhead told Liberal Democrat spokesman Don Foster, who raised the question, that “our database cannot by design identify individual teachers ... so it is not possible for the Office for Standards in Education to convert the proportion of lessons of any grade into a number of teachers”. He also explained the discrepancy by suggesting that his own inspectors had become contaminated by educational orthodoxy, accusing them of being too soft on bad teachers: “We do have a problem with inspectors coming to the right judgments with reference to grading teachers 6 or 7; this is a manifestation of a general problem in education.” He said on Tuesday that he had written to all inspection contractors telling them “that we expect inspection teams to carry out guidelines to the letter”.

Figures released by OFSTED on Tuesday show that out of 2,862 inspections carried out since April, only 88 teachers have been given grades 6 or 7.

Woodhead’s attack on his own inspectors has provoked a furious response. Bill Wright, general secretary of the 2,000-member National Association of Educational Inspectors, Advisers and Consultants, not renowned for its militancy, said: “He has got himself into a corner over that figure of 15,000 bad teachers and now he is trying to suggest that somehow inspectors are failing in their duty.”

Sheila Russell, NAEIAC’s president, suggested that the low number of lessons graded 6 and 7 may be due not to reluctance on the part of inspectors, but to the fact that the teachers concerned are told that they are at risk of a low grade before their second lesson is inspected.

All this has generated a confused picture because inspection data from the new framework and the 1-7 scale, which was introduced in April, is not included in the annual report, although observations on general trends since April are.

In his written commentary on the report, the chief inspector seems at pains to highlight the green shoots of recovery, fertilised by a more “questioning culture” in schools, and is more careful to be seen to be balancing negative observations with positive praise.

The overall percentage of lessons judged to be unsatisfactory or poor has fallen from 18 per cent last year to 16 per cent. As primary schools become more familiar with the national curriculum, standards are rising, albeit slowly, and improvements in secondaries are reflected in GCSE results. But the number of bad lessons is still far too high, he goes on, showing that “the old orthodoxies continue to exert their influence in too many classrooms”.

The general position on standards is similar to last year: about half of all primary schools need to improve, as do two-fifths of secondaries. One in 12 primaries need “substantial improvement” at key stage 1 and one in six at key stage 2. Again he draws attention to the dip in performance in KS2, particularly in Years 3 and 4. Primary school teachers still do not do enough direct teaching, wasting time “on unduly complex organisational arrangements”. He comments favourably, however, on an increasing trend for primary classes to be divided into sets by ability.

So what’s new? Mr Woodhead’s comments on the strong correlation between failing schools and inadequate headteachers - 3,000 heads are condemned - have attracted banner headlines this year, although he is hardly the first to underline the connection. Leadership is poor in one in seven primary and one in 10 secondary schools, according to the report, news that has inspired John Major to suggest that the new qualification for aspiring heads ought to be made compulsory for all heads.

David Hart of the National Association of Headteachers was unimpressed, accusing the Government of “policy-making on the hoof”. “The fact that 90 per cent of secondary heads and 86 per cent of primary heads are demonstrating leadership qualities is a vote of confidence ... (Mr Woodhead) is rapidly becoming the Cassandra of the profession.” On the vexed question of the number of incompetent teachers, he said “OFSTED gives the very distinct impression that it is moving the goalposts in order to justify its original conclusions. ”

Information technology, says the chief inspector, is causing grave concern. Standards are weaker in this subject than any other, particularly at KS2. At secondary level there has been a “substantial decline”; the main problem being teachers’ own lack of confidence.

The chief inspector’s list of new plans in the report is a good indication of the issues that he and OFSTED believe to be the most significant. A disproportionate number of special schools are substandard, and almost half of schools for pupils with emotional and behavioural difficulties are unsatisfactory. Ofsted will be focusing on this and on the fate of excluded pupils, the quality of in-service training, and an overview of the quality of secondary education in the coming months.