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# Introduce basic algebra at seven, argues study

Some key concepts should be introduced earlier, argues the pamphlet

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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."

'More confidence'

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".

## Equations for eight-year-olds

• Which number does each letter represent? Fill in the missing numbers
• 5 x a = 25 a =
• 7 x b = 42 b =
• c x 4 = 36 c =

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.

Basic concepts

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.

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This entry is now closed for comments

• rate this
+2

#### Comment number 106.

A lot of young children are taught simple algebra but it is not called algebra. They have questions such as 4 + _ = 10 and they have to fill in the missing number.
But it would be lovely to have more primary school teachers who had specialised in maths or science and it would be even better if we had some more politicians who had a Maths/Science background

• rate this
+5

#### Comment number 101.

Teaching maths is complex and it's vitally important that the building blocks are built first - and different children will gain understanding at different rates. Try to shortcut this then 'learning' by rote does not work when things get more complex. Teaching and learning is complex. Then there's the whole issue of having enough teachers in our current hostile culture towards the profession.

• rate this
-3

#### Comment number 70.

I am all for children being 'pushed' to do the best of their capacity.
Our children are not being 'stretched' enough and is resulting in poorly educated generation who lapse into a moral malaise and decadence.
The only thing that worries me is that the 'teachers' are poorly educated themselves and it will be the blind leading the blind.
The education sector is in need of major reform (no NUT's)

• rate this
+17

#### Comment number 57.

I'm studying a Masters in Physics at University and STILL don't know my times tables by heart, I got an A* at GCSE Maths and an A at A-Level, but I was NEVER good at timed mental arithmetic tests, including times tables. Mental arithmetic tests made me feel like I was terrible at maths, I think too much emphasis is put on learning them, and not enough on HOW to work them out.

• rate this
-4

#### Comment number 33.

It is ridiculous how much children are pushed at such a young age at the moment. Release the pressure on both teachers and children and it will help them build confidence that will help them as they enter and grow through their teens. To think that increasing class sizes, cutting budgets and increasing the amount children are expected to know by a certain age is beneficial is crazy.

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