Primary teachers' poor knowledge of maths is leading children to become confused and make mistakes, while their colleagues in secondary schools are failing to check pupils' understanding and challenge their errors, according to Ofsted.
The watchdog hopes to help fix these problems by publishing a pair of guides on maths teaching for primary and secondary schools.
"The vast majority of primary teachers have little knowledge or experience of mathematics beyond courses they studied at school, such as GCSE or O-level mathematics," the primary booklet states.
While teachers became familiar with the maths they teach, their lack of experience could lead to mistakes when they explain things or demonstrate solutions.
"Such moments can trigger fruitful discussion and debate," the guide says. "However, when errors reflect teachers' weak understanding of mathematics and are not noticed or corrected, pupils can be left confused and in danger of repeating the error themselves."
The booklets are designed as practical guides for teachers to help remedy the shortcomings in maths provision highlighted in a critical Ofsted report in September.
The secondary school booklet notes that a lack of variety in maths lessons is accepted as the norm by many pupils. A lack of pupil understanding was also evident.
"Many of those observed in lessons were content to have the right answers in their books when they did not know how to arrive at them," the guide says.
Many secondary teachers were not giving sufficient attention to this problem. "Errors or misconceptions are not always exposed: some pupils get the answers from their peers, others alter their answers to the stated correct ones, and some do not progress far through the exercise," the booklet says.
Teachers were not always even aware of the problem.
"Typically, the teacher asks a question, very few hands go up, a selected pupil answers it well, and the teacher assumes that all the class knows and understands. Actually, the pupils' books and discussions indicate that many are unclear."
Many secondary teachers were uncomfortable when pupils asked about the usefulness of maths. But some had clear responses. The booklet cites a teacher who was asked what the point of algebra was. His explanation of its uses included expressing the laws of science and creating computer graphics.
- The booklets can be downloaded at: http:www.ofsted.gov.ukOfsted-homeNewsNews-Archive2009MarchHelping-teachers-make-it-all -add-up-on-World-Maths-Day.