This article featured in the NCETM Primary magazine, issue 4.
It wasn’t just the children who felt their hearts sink when the time came to study division at Hexham Middle School in Northumberland; the teachers were just as unenthusiastic. In my role as subject coordinator, I had seen that staff avoided teaching it if they could, devoting the lesson to multiplication then running out of time before touching on division.
An analysis of the pupils’ SATs tests confirmed division as a general weakness in the school, so it was obvious the issue needed to be addressed. When we then received a grant from NCETM for professional development, the headteacher and I were in agreement that we should tie these two elements together.
First, I investigated the nature of the problem through interviewing the pupils and observing them in lessons, and we sampled work across the school. We gave pupils division calculations which varied in difficulty, ranging from straightforward number operations to addressing a problem.
I found that the lessons on division in the school varied enormously. Chunking and number lines were used most frequently, both based on an understanding of the concept of division as repeated subtraction. The actual process of carrying out these methods, though, varied from class to class and so did the terminology (particularly the terms ‘sharing’ and ‘grouping’). The more able children were able to adapt to the different approaches used by their teachers, but others became confused. And when a pupil was struggling, many of the teachers felt unsure about how to revisit teaching of the necessary skills.
Very few of the teachers specialised in mathematics and they needed more support and training in helping the pupils understand the concept of division and developing it. We needed consistency in their methods, particularly in terms of the terminology used throughout the school. This would help the children understand the subject and become more confident. I also wanted staff to make greater use of the school’s maths policy on methods of calculation. I had produced a document, with the help of a numeracy adviser, which outlined the progression in division skills both in complexity and in the methods to develop the skills.
In order to achieve all this I decided to use peer coaching. This was a tool I had first discovered about five or six years earlier when I had attended a course on thinking skills with a colleague. We had found it hugely beneficial and, in describing our own positive experience, we were able to reassure staff. They recognised that what we were suggesting wasn’t something that was unknown and untried; we had already done it.
I invited an LEA consultant to run a twilight INSET session on coaching techniques for the whole maths department. This explored interview procedure, collaborative planning, the importance of being supportive to colleagues, and how to focus on constructive comments about strengths and weaknesses and areas of development.
I paired teachers of different year groups or ability bands so that they would bring different perspectives. They would be able to identify where the lesson was coming from on one hand, and where it was going on the other. They had time together to talk about their experiences, their difficulties and the areas they wanted to develop. Each pair worked together for an hour at a time during the school day to plan a lesson which one teacher would lead and the other would observe. Then they would evaluate the lesson’s effectiveness together. In planning the lesson, they used the progression in division skills map to identify methods appropriate to the skill level of their pupils. This was an attempt at standardising the way teachers taught division.
The project has worked very well. Staff have welcomed the opportunity to observe the ways in which other people teach the subject. They have liked being able to share ideas together and to think through and renew their approach to teaching.
They have commented on the value of being able to sit and watch the children, identifying which techniques work and which don’t. They have been able to interact with small groups of children and tune in to their way of thinking. In receiving feedback, the teachers have acknowledged how they have been reminded of elements of the lesson they might otherwise have forgotten or overlooked. And in revisiting the session they have been able to consider what worked and what didn’t.
All of this just doesn’t occur in the mainstream of school life. Our hope is to develop a system of peer support where staff who have been through this project will be able to work with new staff coming into the school. We hope it will be embedded as good practice.