Introduce basic algebra at seven, argues study

Child doing maths 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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  • rate this

    Comment number 175.

    As long as I can add up and take away that is all I have ever needed.

  • rate this

    Comment number 174.


    even if you estimate the expectation of such a function, is it worth the money for the ticket?, I didn't think so...

  • rate this

    Comment number 173.

    It just had to be a man who named it algebra, one thing on their minds and one thing only.

  • rate this

    Comment number 172.

    @170 Liv I pointed out that the only way to increase your odds is to pick 3 odd numbers and 3 even. Go on, provide the mathematical proof. Please!

  • rate this

    Comment number 171.


    I apologise for the aggression.

    I disagree that the 12X table is outdated, I used to push pupils onto 13 & show them number patterns across the timetables: many recognised square & cube numbers. Learning times table by rote without appreciating number patterns is futile, indeed makes it harder to start on modulus (congruence) or hexa-decimals.

    12 goes into 360 for the Babylonians.

  • rate this

    Comment number 170.

    What for ?

    many educated people seem to have no common sense.

    I recently had a 'debate' with a maths graduate in a pub about lottery statistics and probability.

    I pointed out that the only way to increase your odds is to pick 3 odd numbers and 3 even. He said it made no difference. He is wrong of course.


  • rate this

    Comment number 169.

    When the 7 year olds have been taught basic algebra perhaps they could in turn teach George Osborne basic arithmetic?

  • rate this

    Comment number 168.

    Crap government² + no jobs = UK

  • rate this

    Comment number 167.

    @104. You have somewhat aggresively misunderstood my character limited post. The times tables up to 10x10 are important. The 12 times table isn't-it's out of date, grammar school thinking to make it a priority. As I said, the 15 times table, and the 25 times table are much more important. Effective written methods & problem solving are also the priority.

  • rate this

    Comment number 166.

    Algebra is useful, once learned it works -often subconsciously- as a basis for solving problems.
    But it shouldn't be introduced early. Research and country comparisons show that starting school at 7 is best, and forcing anything too early is counter productive; erodes independent and creative thinking - but I can see our government and their backers might prefer that.

  • rate this

    Comment number 165.

    If arts & humanities teachers had also had to be experts in maths I'd have missed out on some truly inspirational teaching. It's long been known that most people are either left or right 'brained', with the former favouring maths & physics whilst the latter prefer history, English, art etc. Not that Gove cares less, for him it's just repetition of the Tory 'tougher' mantra to generate headlines.

  • rate this

    Comment number 164.

    If X = NO and Y = SOD, what does Z =

  • rate this

    Comment number 163.

    Algebra, as normally taught, is a difficult concept for most 7-year-olds. Possibly the very brightest might cope with it, but for most I would suggest 10 or 11 is a more appropriate age. At 7 the priority surely should be developing a thorough grounding in basic arithmetic. Without that, they will struggle with algebra anyway.

  • rate this

    Comment number 162.

    Sorry, this is all hyperbole.
    In Year 2, we find 'missing numbers' (e.g. 6 X ? = 12). We teach children about the inverse relationship between multiplication and division. Likewise, children are taught to solve 94+?= 175 or 54-?=6.
    Perhaps if we just start calling it 'algebra', everyone would be happy.
    I just wish these 'think tanks' would check the facts before banging on ignorantly.

  • rate this

    Comment number 161.

    159. IanT -- you are not completely metric -- otherwise you would not be using stones for a persons weight or MPH rather then KPH in articles about speeders (as 100mph doesn't sound as bad as 160kph)

    About 12 years after the US started teaching new math - sets and numbers -stores had to get cash registers that made change as the new employees never learned how to do it.

  • rate this

    Comment number 160.

    Serious studies show children's minds aren't ready to process abstractions like algebra at 8.
    Not that UK government cares about research or successful practise. In fact research and country comparisons show kids do best starting school at 7 with no pre-school academics. Forcing it harms mental development. Also shows the less government interference the better.

  • rate this

    Comment number 159.

    Has ther DfE spokeswoman not realised that Massachusetts is an American state and that the USA has not gone metric yet? If we are going to ask children to do lots of calculations with dozens, then why stop at the 12 times table when we could test them on bakers' dozens too!

  • rate this

    Comment number 158.

    All Great Education is about independence and taking charge and control of your own life and livelihood, because if you don't then someone else will -and usually for their own ends. The highest form of pure thought is in mathematics. Plato

    Cantor felt a duty to keep on in the face of adversity to bring the insights he had been given as Gods messenger to mathematicians everywhere.

  • rate this

    Comment number 157.

    Another crackpot theory from an academic who lives in an ivory tower.

  • rate this

    Comment number 156.

    Please and thank you would be nice.


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