During the past week, Fran has taught many lessons across both of the Primary School campuses, which were observed by BIS teachers, but she also ran three workshops for teachers and two workshops for parents. Fran has been demonstrating to teachers how we can develop our maths teaching to further support and challenge all learners in developing their ‘mathematical muscles’. Here are some of the messages that teachers received from the training.
‘Low threshold, high ceiling’
The tasks that Fran used in classes were what NRICH call ‘low threshold, high ceiling’ with the aims that everyone will be able to get started, and everyone will get stuck at some points whilst working on the problem. One problem involved sorting nine houses: https://nrich.maths.org/5157
The task might start very simply:
- What is the same and different about the houses?
- Can you find a way to sort the houses?
But gradually can become more complex through questioning:
- Can you find another way to sort the houses?
- How many ways can you sort the houses?
- Have you found all of the ways?
- How can you be sure?
- What if you use more than one criteria?
- More than two groups?
- How could you remember what you have done?
- Can you guess how someone else has sorted the houses?
A simple starting point, with little mathematical knowledge requirement, means that all can access the task and reason, but also all will get stuck at some point. Some children will find more answers than others, but through the effort and thinking applied, they will all become a little ‘mathematically fitter.’
Exercise was a metaphor used throughout Fran’s explanations. During many of the lessons, Fran often started by picking a volunteer and moving their arms up and down like a jumping jack. The children were then asked: who is getting fitter? It was obvious to the children that it was Fran getting fitter and not the child. She was doing the work. Fran explained to the children that, if you give an answer to another person, they are not becoming fitter because you have done the work, not them.
In any case, answers were less important than the process of trying to find them. Fran explained that even if they were not able to find an answer to the problem or all the solutions to a problem, they would still get ‘mathematically fitter’ and this is more important. This is in the same way that I might not win in a 10k race, but I would definitely get fitter by doing it.
‘Question answers, not answer questions’
During Fran’s sessions in classes, it was a huge challenge for other teachers and me to avoid assisting and directing children too quickly when solving problems. Teachers often think we are helping, but Fran challenged us on this habit and asked us to avoid helping children a little too quickly before they have the chance to really think about how to go about solving a problem or not worry about being stuck. NRICH believe that it is a teacher’s role to ‘question answers, not to answer questions’. So instead of providing an answer when a child declared that they had ‘finished’, we might respond with ‘Are you finished or have you found an answer? Do you think you can find another answer?’ Then a little while later: ‘Can you find all of the answers?’ and maybe ‘How will you know that you have found all of the answers?' or ‘Is there another way to find the answers?’
Whether or not they got so far as to answer the problems completely, was less important than becoming a little ‘mathematically fitter’ each time.
Metacognition - ‘thinking about thinking’
When Michael Walsh, a trainer from ‘Let’s Think in English’, our English reasoning and thinking programme, visited in September, he spoke about the importance of developing children’s metacognition. Metacognition is, in very simple terms, the awareness of your own thought process or ‘thinking about thinking’. Developing metacognitive approaches have been shown to have a large impact on children’s progress. During the teacher feedback sessions, many teachers drew comparisons between ‘Let’s Think in English’ and the maths lessons that Fran was demonstrating. We want to develop children’s thought processes, so they ask themselves questions about their thinking. Some of the questions we want children to be asking might be:
- How do I know this? - Children like to know things, but do they know and can they explain how they know? What steps did they take to get there?
- Have I seen a problem like this before? - Can children draw upon their prior experience of other problems to help solve other problems like this one?
- Why am I using this strategy? - If children create a list of answers or a table or diagram, why are they doing this? They might tacitly know that it is a good idea, but do they fully understand why? Is it because it helps you remember the answers you have given? To help you to notice patterns? To check you do not repeat work you have done before? All could be valid responses and understanding why you are choosing to do something is a step that is often missed.
Fran ran two highly oversubscribed parent workshops where NRICH’s approach to problem-solving was outlined, and parents were challenged with some maths problems developed by NRICH. It is wonderful that so many parents are interested in developing their children’s Maths knowledge and skills. Due to the popularity, we will be offering further similar sessions run by our Primary Maths Leaders in the near future so we can share this approach to reasoning in Maths with a greater number of parents.
A huge thank you to John Handscombe, Andy James and Rob Wilson, the Primary Maths Leaders, for organising Fran’s visit and providing such a powerful learning opportunity for the children, parents and teachers.
Neil Gorton, Assistant Headteacher