What’s the biggest mathematical favour we can do for our children? Teach them number facts so that they know them confidently. What’s the second biggest mathematical favour we can do for our children? Teach them how to use number facts confidently.
For decades we have been struggling with both these ideas. Back in the fifties and sixties, the tendency was to teach number bonds and multiplication tables so thoroughly that perhaps there wasn’t time to actually make use of them in real problem-solving. True, problems were set and children were taught techniques to deal with them but some teachers began to feel very concerned that the children were learning facts that they didn’t understand. So the educational pendulum began its swing towards ‘using and applying mathematics’ in context. What could be wrong with that?
The term ‘numeracy’ was invented in 1959 to represent the mathematical equivalent of ‘literacy’ in English. The aim, of course, was for all our children to be numerate and literate. ‘Literacy’ represented the ability to read effectively with comprehension and not just to ‘bark at print’, then to use this reading skill and to apply it to writing. In the same way, ‘numeracy’ came to mean ‘the ability to understand and work with numbers’ (Oxford Dictionaries). This was what we wanted then and that’s what we want now, isn’t it?
But some people misunderstood the message and decided that learning in context was the only way to gain effective knowledge in maths. Gone was any form of rote learning: number skills acquisition could only be achieved when the child was ready. What was the point in teaching multiplication tables, for example, if the child didn’t know how to use them?
The problem was that some children never did appear to be ready. Teachers, quite rightly, differentiated the curriculum to give greater access for pupils who were struggling but in some cases, there was a squeezing out of essential content. Children who could have learnt number facts at primary level moved on to secondary school ill-equipped and unready for the maths they were to face. They very quickly fell out of love with mathematics.
What should we be doing now? Exactly what good teachers have been doing throughout every decade and despite every swing of the educational fashion pendulum: teach a healthy balanced diet consisting of an effective mix of number knowledge and skills and of using maths in context. Every day, every child should enjoy the satisfaction of honing their mental maths skills through rapid recall as well as feeling the thrill of solving a problem in much the same way as working out the solution to a puzzle.
In much the same way as phonics may be seen as the building blocks of literacy and English as a whole, number skills are the building blocks of numeracy and mathematics as a whole. So what are those essential number skills?
Firstly, addition and subtraction bonds to 10, moving on to bonds to 20 then bonds to 100. In fact, if the child is confident with bonds to 10 the bonds to 20 or 100 will follow easily. (Here’s a quick test: ask a ten-year-old to subtract 64 from 100. Many children will produce the correct answer but many will say 46. They have ‘half-learnt’ the number facts: they know that 100 – 60 is 40 and that 10 – 4 is 6 but they haven’t learnt to combine the facts effectively. Using a number line is just one way to overcome this.)
Secondly, of course, multiplication tables! The new national curriculum spells out clearly at what age pupils should be learning their tables stating that ‘by the end of year 4, pupils should have memorised their multiplication tables up to and including the 12 multiplication table…’. So, do we stop practising after Year 4 because the pupils have ‘memorised’ their tables? Of course not – many pupils will need to revisit their tables time and time again until they really have memorised them to such an extent that their brain will automatically produce the answer 56 to the question seven times eight or can rapidly calculate the answer 138 when asked the question twenty-three times six.
But we won’t forget that alongside this we will be setting the children meaningful problems and providing them with number aids such as number lines, hundred squares, ‘base ten’ equipment and multiplication squares, so that they can access the number work in the problems before they have fully learnt every number fact.
What’s the biggest mathematical favour we can do for our children? Help them, guide them, nuture them, praise them and teach them to be truly numerate: It’s the best of both worlds.
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