A draft framework is due to be published at Easter with a final version ready by September, but the primary national strategy team has published some early ideas for consultation.
They include Year 3 pupils adding the 3 and 4 times tables to the 2, 5 and 10 times tables they learn now.
Tim Coulson, director of the national numeracy strategy, said: "If we want to see greater progress we need to do better in Years 3 and 4.
"It is not about drilling children in their tables, but at some stage children do need to know them. We're suggesting it should be by the end of Year 4 rather than the end of Year 5."
Maths teachers want the frameworks to be slimmed down and more time for consolidation allowed. Sue Johnston-Wilder, chair of the Association of Teachers of Mathematics, said: "We'd like to put some elastic in it so if a child is ill or a teacher is ill there is less of a sense of catch-up.
"One of the biggest problems in maths is anxiety and panic. Where the strategy works well you have confident youngsters, where it works badly the kids fall to pieces.
"We have to emphasise the confidence of those youngsters. It is almost more important to have confidence than to have any one bit of mathematics under your belt."
Jonathan Wren, maths co-ordinator at Grinling Gibbons primary, Deptford, south London, said: "There is quite a bit of peripheral stuff - there are some strategies for different pencil and paper methods which seem insanely complicated."
Comments on the strategy website from maths subject leaders in Harrow say more time is needed to consolidate topics and Wigan maths subject leaders want more links to other areas of the curriculum and examples for gifted and talented pupils.
The government target is for 85 per cent of 11-year-olds to reach the expected level 4 in maths this year. In 2005, 75 per cent of pupils reached the grade.