Professor Peter Mortimore, new director of London University's Institute of Education, said figures in the chief inspector's report showed that nearly a third of lessons for 7 to 11-year-olds were not up to scratch.
However, Chris Woodhead, the chief inspector, said last week that standards were rising because of government reforms.
Mr Mortimore, whose research has been widely quoted by education ministers, said in his inaugural lecture: "My view is that we have simply not raised standards high enough. I appear to be more worried about standards than he is."
The Office for Standards in Education, which Mr Woodhead heads, was not severe enough on poor maths teaching, Mr Mortimore said. Unlike Mr Woodhead, he did not argue that trendy teachers who refused to use whole-class teaching were the main reason for low standards.
Instead, Mr Mortimore said that primary school teachers' lack of knowledge, particularly of maths, was one of the main reasons for the problem.
"Our recent research evidence shows that the years of junior schooling are important for the whole school career. Yet we know that in many primary schools the subject is being taught by teachers who not only lack formal qualifications but who are, in certain cases, insecure in their grasp of basic principles."
Mr Mortimore called for a new emphasis in schools on maths and reading, but added that this should not be achieved at the expense of a broad curriculum.
Policy-makers, he argued, should use the services of university researchers more, and researchers should learn more about schools instead of concentrating on esoteric debates that did nothing to improve teaching or learning.
n Some 700 jobs have been lost in the past two years because of cuts in funding for ethnic minorities, according to a survey released yesterday. A further 637 are at risk this year, says the Commission for Racial Equality and the Association of Teachers and Lecturers.
The study shows that teachers are convinced of the value of Home Office funds for ethnic minority English language teaching - section 11 grants - in raising standards and combating racism.
Herman Ouseley, the commission's chairman, said: "It will be a sad waste if the Government fails to realise that real progress has been made with this particular educational policy.
"There is growing concern that some ethnic minority children will no longer have full access to the national curriculum."Reuse content