In my 12 year old son’s eyes I am a failing parent. Why? Because, despite spending many hours standing on the side of a football pitch, I still can’t explain the offside rule. I’ve had it explained to me on many an occasion, even once with the use of Lego figures for concrete modelling, but I still just don’t get it, let alone apply my understanding during a match!
How many times have you heard a pupil say, ‘I know what I mean but I don’t know how to explain it’? Using explanation and reasoning is an essential part of developing a greater understanding in mathematics; a pupil really understands a mathematical concept if they can explain it to someone else. However, it is important that we teach pupils the skills to do this.
I think it helps to start with giving children something very simple to explain; something that doesn’t challenge mathematical ability but initiates talk. This will start to build up confidence in children who find expressing their ideas more difficult. Then start to gradually raise the level of difficulty so that explanation is at more of an expected level of mathematics. It is important that we listen to the whole of an explanation without any interrupting. This is often difficult for us as teachers, as we are sometimes too quick to intervene or get frustrated by the length of time a child takes, but allowing time will again develop confidence.
Pupils then need to be encouraged to refine their explanations. Asking children to think of alternative mathematics words, practice mathematical vocabulary and also ensures careful listening. You can next ask them to repeat the explanation but make sure they include the words that you have listed on the board.
Opening prompts are also useful to give a child somewhere to start. I have on my classroom wall speech bubbles with prompts such as: ‘I have worked this out by…’, ‘I think this… because…’, ‘I have noticed…’ Encouraging learners to use pictures or diagrams is also a helpful tool for them.
We need to provide a range of opportunities for pupils to use their explanation skills as frequently as possible. I try to include explanation tasks in all of my mathematics lessons, even if it is just for a few minutes. Questioning children about how they have worked something out can help them to understand the order of calculation. It also encourages those who find showing all of their working out difficult within written calculations. Using known facts to find new ones embeds the links between concepts, so use questions like ‘How will 13 x 3 = 39 help you to find 14 x 3?’ or ‘If double 3 is 6, what is 3+4?’ Turning around word problems is another way to demonstrate understanding. ‘Sam says… is he right?’ immediately converts a word problem into a reasoning task which can be made more complex with ‘Sam says… Jess thinks… and Ellie says… Who is right?’
Finally, one of the benefits of developing explanation skills is that, as well as deepening understanding in mathematics, it is a transferable skill for explanations in other curriculum subjects. Science is an obvious one but there is no reason why children shouldn’t explain and reason in geography or history, art or even PE… just as long as it’s not me attempting that offside rule!