Introduce basic algebra at seven, argues study
At seven, pupils should know their tables up to 10 and be introduced to basic algebra, says a study.
The draft primary maths curriculum for England "should be more demanding", says Prof David Burghes in a pamphlet for right-leaning think tank Politeia.
Primary teachers need better maths skills and more should take maths AS- and A-levels, added Prof Burghes.
A senior civil servant said a long-term possibility might be to require all would-be teachers to study maths to 18.
Speaking at the launch of the Politeia document, Stephen Rogers, team leader for raising standards in maths and science at the Department for Education said: "We are currently working on developing a new suite of qualifications for maths.
"These will serve many purposes - one of those is we hope that it may become a requirement for any teacher, particularly primary teachers."
However, he made it clear there was no intention to make this compulsory at this stage - it would be a decision for the future.
Prof Burghes, of Plymouth University's Centre for Innovation in Mathematics Teaching, said the current demand for teachers to have a C grade at GCSE "just doesn't do it", adding that a higher qualification would give teachers "more confidence" about the subject.
He said that the government's maths curriculum was "on the right track" but said that learning multiplication tables earlier, along with an early introduction of the concepts behind algebra and probability, would help put pupils in England on a par with countries such as Finland, Japan and Singapore, where standards are higher.
The pamphlet - Primary Problems for the New Curriculum: Tougher Maths, Better Teachers - argues that slight modifications to the curriculum could make it "more demanding, more aspirational and more rewarding".
Prof Burghes says that throughout the curriculum the phrase "pupils should be taught to" should be replaced by "pupils should be able to".
For example, he says, at eight pupils should "be able to recall and use multiplication and division facts up to and including 12 x 12 multiplication tables" and be able to solve simple algebraic equations based on times tables.
At 10, pupils should be expected to be able to solve linear equations, while 11-year-olds "should be able to calculate theoretical probabilities for outcomes with dice, number wheels and spinners".
Prof Burghes's suggestions include teaching inequality signs such as < and > to seven-year-olds.
He also suggests pupils should not be taught fractions until they are eight.
He argues that the requirement that 10-year-olds be required to work with "increasingly large numbers" be deleted, saying it is not the case that "the bigger the numbers you work with the better you are at maths".
A spokeswoman for the Department for Education said: "Pupils leaving primary school aged 11 currently only learn up to their 10-times tables. But the new curriculum will make sure that by the age eight or nine, pupils will know tables up to 12. This will match places like Massachusetts which do the best in international tests.
"What is most important is raising standards and making sure all pupils get a good grip of the basic concepts. That will mean children are better placed to make progress at secondary school and start to study areas like algebra.
"We are thinking about how to get more teachers with post-16 maths qualifications into primary schools to teach maths. We are not thinking about requiring all primary teachers to have post-16 maths qualifications."
Speaking at the event, mathematician Tony Gardiner said the proposals scared him, as many countries with strong mathematics education "start slower and do less".
"It's like building a tall building. You have to spend a long time pouring in concrete so that you can build high later."
He added that not differentiating between teaching a concept and expecting children to have mastered it risked confusing and frightening teachers and pupils.