Automatic recall of number bonds:
The essential first step in becoming numerate
What is ‘automatic recall’ of number bonds?
6 x 7 = _____
If it took you more than 1 ½ seconds to come up with the right answer to 6 x 7—or if you weren’t sure your answer was correct—you don’t have automatic recall of number bonds (often called ‘number facts’). When answers are predominantly recalled from memory, the student should be able to answer approximately 40 basic mathematics questions correctly in one minute. 1 Our initial screening tests can be downloaded free here.
Are number bonds really that important?
Over the last generation, research in the cognitive sciences has proved beyond doubt that it is all but impossible to become good at maths if you don't have automatic recall of number bonds. A recent Canadian study summed up the evidence:
...studies consistently find that students who have difficulty with mathematics by the end of their primary school years have not memorized basic number facts, making further math learning difficult and resulting in feelings of helplessness and a lack of confidence and enjoyment. 2
Why is automatic recall so important?
Cognitive Load theory explains the problem: when working memory is largely occupied with lower-order tasks, there is insufficient attention left for problem solving. 3 The calculating strategies taught in primary school are a very useful induction to the concept of number, but it does not appear that many children progress to automatic recall without specific practice.
Our initial tests indicate that the problem is worse than the Government suspects—relatively few pupils have anything approaching automatic recall of number bonds for addition, let alone for multiplication. With Fast Maths, schools can attack this problem without placing undue burdens upon staff and without distracting from other curricular priorities.
Why don’t most schools teach automatic recall?
Unfortunately, the above evidence is generally ignored by educators. On 3 January, 2016 the NUT General Secretary Christine Blower told Sky News that
Looking up your times tables is very easy to do. So the other thing we have to do is to make sure that children and young people use the computing ability on their mobile phones so they can get that at their finger tips. Recall is not the only way to make sure you understand mathematical concepts.
Unfortunately, Ms Blower is only reflecting the consensus in teacher training courses, and in all probability, in many of our primary schools. Many of our children pay a heavy price this mistaken belief. The National Child Development study found that
Poor literacy and poor numeracy—especially the latter—have a devastating effect on people’s chances of well-paid and stable employment. Moreover, this is not just because people with poor skills tend to have few GCSEs or other formal qualifications. Even after controlling for these, the effects of low skill levels are major and evident. 4
Comments by two of the UK’s top education bloggers:
I support the introduction of times tables tests at the end of Key Stage 2. The main reason is that I am a secondary maths teacher and I see so many students arrive at secondary school not knowing their times tables. The complacency of those who say “primary schools already do this” amazes me. . .If you don’t get how fundamental times tables are to learning maths, I am prepared to argue that you don’t understand how to learn maths. Maths is cumulative and fluency at one level leads to understanding (and more fluency) at the next.” 5
Heather Fearn [on teaching maths to her own children]:
. . .the progress of my children has stunned even me. How is it they missed out on SO much work on understanding while accelerating far ahead of their peers? . . .I’ve realised the reason I’ve never had to invest significant time in exercises to build understanding. It is because when my children are given a new sort of problem they can already calculate the separate parts of that problem automatically. All their working memory is focused on the only novel element of a procedure and so it is very quickly understood. Understanding is just not a biggy. Identify the knowledge necessary to calculate the component parts of a problem and get fluency in those and generally activities for understanding become a (crucial but) small part the maths diet.
My children learnt all possible addition and subtraction facts between one and twenty until they were known so well that recall was like remembering your own name. I did the same with multiplication and division facts. There were hours and hours and hours and hours of quite low level recall work.
. . .Generally the the focus in schools is the opposite and this creates a vicious cycle. Children are taught more complex problems when they are not fluent in the constituent parts of the problem. Therefore they struggle to complete calculations because their working memory breaks down. The diagnosis is made that children don’t ‘understand’ the problem posed. The cure is yet more work focused on allowing children to understand how the problem should be solved and why. . .By comparison my children seem to have a ‘gift that keeps on giving’. Their acceleration isn’t just in the level of maths proficiency they have reached it is in the capacity they have to learn new maths so much more easily. 6
1 Wong, M, & Evans, D (2007) Improving basic multiplication fact recall for primary school students Mathematics Education Research Journal, 19(1), 89-106.
2 Stokke, A (2015) What to Do About Canada's Declining Math Scores?
3 Ball, D. L., Ferrini-Mundy, J., Kilpatrick, J., Milgram, R. J., Schmid, W., & Schaar, R. (2005). Reaching for common ground in K-12 mathematics education. Notices of the AMS, 52(9), 1055-1058.
4Wolf, A., (2002) Does Education Matter? myths about education and economic growth, Penguin Books, London, p.34