The new National Curriculum, together with the tests that are planned to accompany it from next year, places a much greater emphasis on pure number skills than has been seen for many years. The tests for Key Stages 1 and 2 will both include a test paper on the subject of ‘arithmetic’, a term that is not used in the National Curriculum itself and that hasn’t been much in evidence since the nineteen sixties. I keep having to remind myself that it is concerned purely with non-contextual number calculations.
For the last fifty years we have been urged to help children to learn number facts and number skills within the context of realistic mathematical problems – problems that can be related to the pupils’ everyday lives; problems that mean something to the children; problems that can be solved because there’s a desire to solve them.
There is no doubt that contextually based learning is an educational utopia. But concerns have been growing – what if the problems we set don’t encourage the children to learn all the number facts they may ever need? What if the problems are actually too difficult for the pupils simply because the number facts they have practised are not easily retrievable from the depths of their minds?
Surely then, an ideal recipe for mathematical success has to be the solid acquisition of number skills coupled with the application of these skills in context-based, interesting and challenging problems. Is that what the new curriculum is designed to achieve? Will it achieve it?
I have been fortunate enough to be able to produce a wide range of educational books over the past twenty years, including many on problem solving. But the opportunities and demands of the new curriculum and the tests that derive from it have encouraged me to return to looking at pure number skills, an area that is of great interest to me.
When not writing, I spend a considerable amount of term working with students aged between four and twenty-two. Many of the pupils with whom I work are of above average intelligence yet still experience some difficulties with mathematics.
The difficulties encountered by some of the secondary school pupils and university students can be traced back to an inadequate grasp of fundamental skills, which could have been gained at the primary level. It is interesting to observe that these students lack confidence in their own abilities and are likely to make comments such as ‘I hate fractions’ or ‘I can’t do algebra’. When discussed closely, however, the reason why the student can’t find, say, the value of x when 3x = 24 is simply because he/she can’t remember how to divide 24 by 3 and can’t find a strategy for doing so!
In my view, the vast majority of children need to learn a wealth of number facts with some contextual clues to start them off. They need to recognize that 3 + 2 = 5 is a representation of a reality, such as three pencils together with two more make a total of five pencils, or that 3 x 2 = 6 could be a representation of three sets of two pencils making a total of six. But once shown the reality there is no reason why they shouldn’t learn all the facts that follow the same pattern. Once learnt these can be applied to a countless number of realistic problems and, ultimately, the fairly abstract concepts represented by algebra. If not learnt, however, the whole of maths is likely to become a mystery.
Andrew Brodie was a head teacher for twelve years after many successful years in the classroom. He began writing his best-selling educational workbooks in 1992 and since then has established himself as an author that parents and teachers have come to trust. Follow him on Twitter @AbrodieWriter
The most recent titles in his Andrew Brodie Basics series are Let’s Do Times Tables, covering ages 5-11. They are designed to improve children’s confidence with 100s of questions and reward stickers and also match the requirements of the National Curriculum.