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Learning the facts about maths

    Early in 2005 Nick Gibb asked to see me after reading my CPS publications advocating synthetic phonics. At the time he was serving on the Commons Education Committee, and he understood that our primary schools were sending vast numbers of pupils to secondary school with literacy skills that would be an embarrassment in a third-world country. The rest is history: the following year, synthetic phonics replaced the National Literacy Strategy, just as we had been advocating since 1996.

    At this meeting, Nick also expressed his concern about the failure of primary schools to teach the multiplication tables. This was a more difficult proposition; being innumerate is no disgrace in Hampstead. Yet maths skills are critical, especially for children from Haringey and Halifax. The National Child Development study found that poor maths skills have “a devastating effect on people’s chances of well-paid and stable employment”. Even after controlling for the number of formal qualifications, the effects are “major and evident”.  

    And even more to the point, knowing one’s tables is a critical component of maths skills.  To previous generations, this was self-evident; now we need research to refute the myths generated in our education colleges. A study by Bull, Johnston and Roy found that

    "Children with poor arithmetical skills show a lack of automaticity in retrieving numbers and number combinations from long-term memory, evidenced through slow item identification and through the use of slow, inefficient counting strategies rather than direct memory retrieval." 

    Significantly, one of the authors is none other than Rhona Johnston, the co-author of the Clackmannanshire study that established that synthetic phonics was vastly more effective than the ‘mixed methods’ recommended in the National Literacy Strategy. There is a close parallel between the two subjects: just as children who have difficulty decoding words have much less attention left for understanding and recalling what they’ve read, children who struggle to find the product of 9 x 12 will lack the mental resources for higher-order tasks.

    At last, Nick Gibb’s views on learning the multiplication tables have been translated to policy. Next year, all children leaving primary school will take an on-screen test to demonstrate their knowledge of the tables up to 12 x 12. They will have 10 seconds to come up with the right answer for each item.  Ten seconds is actually quite generous: anyone who actually knows their tables should be able to answer in under two seconds.  Primary school heads will face the sack if any of their pupils fail the test.

    Needless to say, these plans have drawn intemperate criticism not only from teaching unions and Labour, but also from David Laws - who replaced Nick Gibb as Schools Minister in Cameron’s 2012 re-shuffle. Nick was returned to office in 2014, and is now Schools Minister again.

    However, these critics do have a point: no one really knows how to teach pupils their tables. With synthetic phonics, there were any number of good synthetic phonics programmes on the market when New Labour made the change in 2006. Now, all we have is educational software, which is difficult to deploy effectively in a primary school setting. The traditional method of chanting tables is no doubt better than doing nothing, but it is not the same as “direct memory retrieval”.  Without a lot of further practice with random retrieval, most pupils will need to recite the entire 7-times series just to find the answer to 7 x 8. 

    Unfortunately, the problem is probably much worse than is generally understood. At one school—a comprehensive where about 80% of the pupils are of Pakistani origin—pupils have recently been tested for reading, spelling and maths. Results for reading and spelling were exceptional, especially compared to the results I routinely obtained in secondary schools before the introduction of synthetic phonics. Clearly, their feeder schools are as good as any in this respect. Yet with maths, they found that pupils still have to count even to do simple sums like 5 + 3.  It will be perverse in the extreme if the result of next year’s tests is to produce pupils who can multiply, but not add.

    Sadly, many if not most teachers—even science and maths teachers—lack the “direct memory retrieval” that enabled earlier generations of workmen to chalk instantly and accurately at the dartboard. They are hardly alone: when introducing the new tests, Education Secretary Nicky Morgan declined to answer when a reporter asked her “What’s seven times eight?”

    We are now devising a remedial package to teach number bonds for addition as well as multiplication.  Pupils are paired off with another pupil who is at the same level, and they drill each other with flashcards and time each other on worksheets. Progress will be reported and posted at fortnightly intervals, and pupils will be encouraged to work in their own time. 

    This is only the first step in the re-introduction of arithmetic to the maths curriculum and the reform of primary mathematics. Above all, we need to train specialist maths teachers for primary schools—a question I will consider in another post.

    Tom Burkard is a Visiting Professor of Education Policy at the University of Derby. He is the co-author of the Sound Foundations reading and spelling programmes, which are rapidly gaining recognition as the most cost-effective means of preventing reading failure. In June 2015 he was awarded a DPhil by Published Works by the University of Buckingham.

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    Comments

    Douglas Hainline - About 646 days ago

    Learning the times tables is absolutely critical -- it is a tragedy that there are people who train teachers -- I talked to one at the ACME conference this week -- who are opposed to teaching children their times tables.

    Professor Ruth Merttens has a lot of good ideas here. One point she makes is that chanting the times tables should be done every day, not in Maths class, but in 'home room'.

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