Fractions

Last night I was visiting a friend. His son is 14 and just starting to study for his GCSE additional maths. He had forgotten to bring his Additional Maths folder home from school and as a result he didn’t have his homework. He spent about 45 minutes trying to get his friend to text him the questions, and eventually, after the intervention of his father, he phoned and spoke to his friend and got him to read the questions out so that he could write them down. Having thus acquired the questions he needed, he set to work to solve them. The problems were solving simultaneous equations in 3 variables. The first question produced results such as x = 2, y=3, z=1; as did the third and forth questions. However, the second problem produced the answers x = -174/39, y = 75/39, z = 17/39. Given the solutions to the other questions were integer numbers it seemed strange that the author of the maths book should include a question with such a bizarre set of numbers for the solution. Having checked the working, I concluded that the boy had written down a wrong digit or sign when copying the question over the phone. But that is not my cause for concern. What concerns me is that this boy, who attends a grammar school and is towards the top of his class in Maths, was unsure when working in fractions. He was put off by having to work in thirty nineths. Why? There is no difference in maths in working in thirds, or working in fifths, or working in thirty nineths or eight sevenths. He was unsure what to do with the fractions he had, or how to manipulate them. He knew that the top was called the “numerator” and that the bottom was called the “denominator”, but he had no idea what they signified.

Fractions were a black art to him. For this I believe the electronic calculator is to blame. Today’s pupils do not work in fractions, they just divide one number by another using the electronic tool and write down the answer without thought as to where it has come from, or what meaning it might carry. A Puppet Maths, we believe that our pupils should have a thorough understanding of fractions, they should be able to do calculations with them without recourse to a calculator; and it should be easy and fun.