Ofsted says that pupils at all levels must be stretched
Maths teachers in England are being sent booklets with advice on how to teach their subject after a report identified weaknesses.
School inspectors Ofsted has warned that about half of schools need to improve the quality of maths teaching.
The booklets aim to improve teaching by "shifting it away from a narrow emphasis on skills".
Maths results at primary and secondary level are improving, but ministers recognise more needs to be done.
Ofsted's report on maths teaching, published at the end of last year, said too much of it was "taught to the test" and that this did not equip pupils for their futures.
The new booklets - one written for primary schools and one for secondaries - are designed to help improve pupils' understanding of maths and how it is applied in everyday life.
Ofsted says that more pupils should be achieving higher grades in the subject.
"Strategies to improve test and examination performance, coupled with teaching that focuses heavily on preparation for the qualifications, does not equip pupils for their futures," says the booklet destined for secondary schools.
It goes on to describe features of good and satisfactory teaching.
In successful teaching, the booklet says, "Teachers monitor all pupils' understanding throughout the lesson, recognising quickly when pupils already understand the work or what their misconceptions might be, for example, circulating to check all have started correctly, to spot errors and extend thinking."
But the National Union of Teachers did not welcome the booklet.
Its head of education, John Bangs, said, "Teachers don't need Ofsted breathing down their necks about what they should or shouldn't do."
Christine Gilbert, Ofsted's chief inspector of schools, said it was vital to equip children with confidence in a subject which was so relevant to their adult lives.
"I hope these booklets will help teachers ensure that every child gets the best possible mathematics teaching."
In a report at the end of 2008, Ofsted said results were improving in both primary and secondary schools, but that understanding of the subject was not.
It said that secondary schools in particular were less effective in developing pupils' understanding of applying maths to new situations or solving problems.
The government has said it is putting £140m into maths teaching in schools to raise standards, and said there was "no reason" why tests should result in a narrow focus or uninspiring lessons.