I’ve found getting some pupils to understand the concept of equality to be surprisingly difficult. The problem seems to limit pupils’ ability in many other topics such as equivalent fractions, solving equations and changing the subject of a formula. I stumbled upon an article the other day that gave me some insight into why pupils struggle with it. When you do a calculation on a calculator, what button do you press to get the answer? The equals button. The article argued that kids think of the equals sign as an operator. Kids see the equals sign as something you press to get an answer.
Enlightened with this possible explanation for kids’ misconceptions, by fortune I then came across an interesting blog post by the excellent Keeping Mathematics Simple blog called “How to teach the properties of equality through problems solving“. The author puts forward a way of teaching the topic of solving linear equations. Her method, of focussing on developing the concept of equality first, before moving on to solving the equations later is logical and well thought through, ensuring there is no misconception about the properties of equality before teaching how to solve the equations.
When teaching solving linear equations (or similar) in the future I think I’ll experiment first with giving them something like 2x = 10 and ask them to come up with 5 equations based manipulating the first one (do the same to both sides etc…) e.g. 4x = 20, 2x + 2 = 12 and so on. They could produce a spider diagram with the starting equation in the middle and alternatives off on legs. Once they solve for x they can then subsitute it back into all of their equations and they’ll see that the statements of equality still hold true. Hopefully this will help develop an understanding of the properties of equality which is so important if their learning of solving equations is going to be anything less than procedural.