Last weekend, I read an excellent blog by Nicola Clements (https://firestartingblog.wordpress.com/) in which she reminded me of some great advice: spend less time focusing on the final outcome produced by the children and more on the journey they go on in order to reach that outcome, as this is the point where learning really takes place.
It got me thinking about how this approach relates specifically to maths. Unlike a lot of other subjects, children usually produce several ‘outcomes’ in every lesson, with each answer they generate being an end product in its own right. Taking Nicola’s advice into account, it made me wonder whether too much importance is placed upon the answers that children give in maths. After all, the answer to question 3 will no doubt be instantly forgotten by little Freddie as soon as the lesson has finished, but the skills that were honed or the links that were made on the way to getting that answer could stay with him for a lifetime.
With this in mind, I decided to try something a little bit different with my class this week. As well as giving them a question, I also gave them the answer. They seemed a little confused for a few seconds, but I explained that I wanted them to find as many ways as they could to get to that answer and to discuss with their peers the methods they preferred and why. I suppose it’s a little bit like giving them all a map, telling them the final destination they need to get to and asking them to find the best route by looking at all the options available to them. The fact that I have told them where they need to get to makes the task no less challenging while the opportunities for learning are doubtless much greater than if I had given them all the same set of directions to follow and asked them to find out where it leads them to.
A number of things struck me as the class worked enthusiastically on the task they had been given:
- Those children who are usually in a race to be the first to get to the answer realised that the rules of the game had now changed. I like to think that this was a good thing because, while I do want to promote mathematical fluency, children can miss so many opportunities to develop their mathematical thinking due to being in a rush to get to the answer. Children who fall into this group are often very capable procedurally but is their conceptual understanding as secure as I would want it to be?
- From the feedback they gave me, it was clear that less confident children had just had a real weight taken off their shoulders. That pressure of needing to get the correct answer had been removed which can only have helped to increase their confidence and motivated them to get stuck into the task.
- By already knowing the answer, they had some instant feedback available to them. If they had made a mistake in their calculations, they knew about it straight away and wanted to identify and correct any errors. Far too many children, having generated an answer for a question, see it as a case of ‘job done’ and they move on. Knowing the answer actually encouraged children to grapple with the question more and this surely has to be a good thing.
- The different methods that were shared generated some excellent discussions and doubtless helped a number of children to make links that they hadn’t picked up on before.
Overall, I feel that it was a really worthwhile exercise and something which I will definitely look to repeat. Having said that, it is important to acknowledge that children need to generate their own answers on a regular basis. Producing accurate answers with good speed and efficiency is an extremely important skill that needs to be encouraged while a set of answers in a child’s maths book can provide a teacher with valuable feedback. Therefore, I am certainly not advocating giving out the answers all of the time but let’s not give too much status to them. We all want our children to be able to ‘do maths’ but the aim should surely be to turn them into mathematical thinkers who value what they can learn from the process much more than the final outcome.