Understanding before method

Published: February 26th, 2019

I often wish that schools would not teach children how to solve problems simply by method, often without the understanding upon which method must be based. This is an odd thing to say so let’s explore what I mean. The reason why children in Key Stage 1 do not set out sums in a formal way is because they need to explore and come to understand numbers (up to 100) in an informal way first. In other words, they must understand numbers thoroughly before they are given a formal method for solving number problems.

Unfortunately, some children need more time to thoroughly understand the ‘inner workings’ of the numbers and often move into Key Stage 2 without having mastered the required level of understanding. James is one such child who, in Year 4, tries valiantly to remember the method shown by his teacher for subtracting numbers such as 73 – 38. The ‘decomposition’ (changing a ten into units) method of subtraction means little because he has not spent enough time counting forwards and backwards along numberlines to perceive the problem visually. James separates the tens and units – ending up with 73 – 38 = 45 instead of 35. He has taken the 3 units from the 8 units because they are less, clearly not recognising the two digit numbers as values that cannot be separated in such a way. This is a common problem. If James had come to understand two digit numbers thoroughly as whole values, he would not be making such mistakes.

My plea therefore is for all schools and parents to ensure that children master two digit numbers before they are given formal methods for problem solving. In my view, the best way is for children to devise their own methods rather than being given one. Many children are put off maths quite early on because they struggle to understand what they are doing. Maths is fabulous and fascinating and deserves to be explored. Once children explore numbers thoroughly and come to understand how they work – most are capable of devising their own methods, all of which leads to more effective and efficient mathematical problem solving.

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