Maths, mistakes and memory
I found that this week’s task linked back to several ideas from previous tasks. Matthew Syed’s video reminded me of Jo Boaler’s “An Elephant in the classroom” about growth mindsets and fixed mindsets and how this influences maths learning. The fixed mindset says: ‘I can’t do maths’ while in a growth mindset everyone can learn maths (but not without effort). How can we change this and help more students succeed in maths instead of assuming failure is inevitable? Thinking success is only based on talent is like a trap holding back whoever does not show an obvious talent from an early age.
I think part of our teaching job will be to make the learning experience effective as Matthew suggests. Students should be stretched, lessons a bit hard, not too easy but also not too difficult and creating a lesson which can do that for a large group will be challenging. I do agree that they will need to practice. Not endless repetition but effective practice moving on to more complicated and hopefully more interesting problems and problem solving. From all our previous tasks, I think they will need a mix of conceptual and instrumental learning, not just one or the other. And I think Matthew makes an extremely important point about feedback and we should aim to pass on meaningful and useful feedback to every single student. Willingham had quite a few very practical tips for helping students retain their learning. We were never taught any study skills at school but I see my children now use mind maps, revision tables and other techniques. And advising them to spread out their revision is sensible but I bet there will always be lots of last-minute cramming. I found out that for me, writing things down helps them stay in my memory and for maths: practising a lot of different sums and past papers! How do you know if you’ve done enough? We all seem to underestimate and forget that we will forget.
But these lessons will be useless if we can not somehow motivate the ones labelled as ‘low ability’ that they ARE able to learn maths. And teach high ability students resilience so that they don’t give up when something becomes difficult after years of sailing through school. Matthews talks about high quality self-motivated practice will enable you to learn a skill. But how does a student become self-motivated if they have felt bad at maths from an early age? They want to give up from the start. First, we somehow need to build up confidence. Then, lessons must be interesting, varied and creative and captivate and keep their attention. But I think one of the most important ideas I have learnt is that the brain uses mistakes to learn, that the brain is flexible and adaptable. But that the brain also warns us when something is hard and discourages us to keep going! Remember the bonus video in task 3 about the Lizard brain? That makes us avoid risks, failure and change? To learn something hard, we need to repress that instinct. Somehow we need start giving students the confidence to keep learning, to go against their instincts to stop when it’s hard, to feel happy about making mistakes and to use their mistakes to deepen their knowledge. Given that they often come from primary school convinced they are no good at maths, this is not going to be easy. But I will try.