As Mr Woodhead presented his annual report on schools he said the proportion of unsatisfactory lessons has fallen substantially, from 25 per cent five years ago to 8 per cent in the past 12 months.
But he also insisted that his estimate of around 15,000 weak teachers was based on hard evidence from inspections. It suggested that 6,000 primary teachers are not up to scratch. However, the figure for secondaries of 9,000 had to be treated with caution because it was based on a sample containing a high number of weak schools.
The figures are available for the first time as in the past 12 months school inspectors have graded teachers on a seven-level scale. Those rated 5,6 or 7 are regarded as unsatisfactory or worse.
Mr Woodhead said he did not want to dwell on weak teachers. Inspections suggested that only 3.2 per cent of primary lessons were consistently unsatisfactory.
In secondaries, the proportion rose to 5 per cent, but that data was taken from the second round of inspections where 40 per cent of schools had already been identified as having failings.
However, the report also suggests that 50 per cent of primary teachers (around 100,000) taught mostly good lessons and the proportion of good or very good teaching has risen by 5 per cent.
Only 34 per cent of secondary teachers were judged to be teaching mostly good lessons, 74 per cent taught lessons that were at least satisfactory.
The figures for primary are based on 19,000 teachers who were observed teaching on five or more occasions. The 6,000 teachers in secondary schools were observed for three lessons.
Mike Tomlinson, director of inspections at OFSTED, said it was difficult to explain why teaching quality had improved, while the number of weak teachers had not seemed to change.
Mr Woodhead said it was disturbing that 2,300 primaries and 510 secondaries were led by people incapable of giving them a sense of purpose. He added:
"Too many heads do not really know what is happening in the classrooms. This is a fundamental weakness."
David Hart, general secretary of the NAHT said " the vast majority of heads and teachers are performing miracles". Peter Smith, general secretary of the Association of Teachers and Lecturers, said Mr Woodhead's praise was "too little, too late".
Nigel de Gruchy from the NASUWT condemned the focus on incompetent teachers. "It seriously dissuades able young graduates from contemplating teaching as a profession," he said.
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