There is to be a new emphasis on maths play in England's nursery schools and 13,000 maths specialists to spearhead better primary school teaching.
The government accepts the findings of a review it commissioned from a team led by Sir Peter Williams.
It will take 10 years and £187m to train the specialists, expected to be drawn from existing teachers.
More help is proposed for youngsters who are struggling. Parents' support is seen as crucial to the whole scheme.
The proposed maths specialists would not necessarily be the existing mathematics coordinators in schools, and smaller schools might have to share.
The proposals assume that 3,000 specialists could be found straight away next year.
It will take another 10 years to train the extra 10,000 - which the report acknowledges will "result in inequalities".
They will be paid an extra £1,000 for each of the three years it takes to train, to attend summer schools, plus £2,500 on completion and another £2,500 when they are awarded a Masters degree in maths teaching.
Culture
The report also argues for more qualified teachers in early years settings, to give pre-school children a better start in maths.
The main recommendations are:
The aim is to counter the prevailing culture in which, Sir Peter says, the UK remains one of the few advanced nations where it is socially acceptable - even fashionable - to profess an inability to cope with mathematics.
But his team's report concludes firmly that it is teachers, not parents, who determine what children learn - especially as the way mathematics is taught has changed greatly since most parents went to school.
Better training
Sir Peter says he and his panel saw some excellent teaching while visiting schools.
But children are highly attuned to uncertainty on the part of their teachers - who have a wide curriculum to get through in primary schools.
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The report says the basic requirement of trainee teachers that they have a grade C GCSE in maths should stay for now but be reviewed, with a view to raising the hurdle.
Initial teacher training in maths is not good enough, it says. But the most practical way forward is to improve the ongoing training of practising teachers.
The review team noted that English teachers get five days a year training.
In Scotland, teachers get an extra week for personal "continuing professional development", and that should be a long-term aspiration for England too, they said.
National strategies
The government will be pleased to hear the report say that the introduction of the National Numeracy Strategy in the late 1990s had transformed maths teaching.
In turn, the proportion of primary school leavers attaining Level 4 of the national curriculum in tests, as expected for their age, had risen from 59% in 1998 to 77% last year.
But the report calls into question the effectiveness of the revised national primary teaching frameworks and suggests they should be reconsidered and made more "user friendly" for teachers. This is being done.
Launching the report at a National Centre for Excellence in the Teaching of Mathematics conference, England's Schools Minister Lord Adonis said everyone had their part to play in helping children to understand numbers and their importance in the world.
Shadow education secretary Michael Gove said the review had failed to grasp the seriousness of the state of maths education in England, with nearly a quarter of 11-year-olds failing to reach the minimum level of maths to enable them to cope with secondary school.
"The government has failed to grasp the nettle and replace methods of teaching which have failed with tried and tested methods used in countries that have much higher levels of maths achievement," he said.
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