The Mead Academy Trust
Mathematics Learning Sett 2013-2014
Case Study
Practitioner Research Undertaken by
Tracy Boulton (Facilitator)
Catherine Walker (Key Stage 1 Teacher)
Fay Cupis (Key Stage 2 Teacher)
Sophy Scruby (Key Stage 1 Teacher)
Alison Capstick (Key Stage 2 Teacher)
Research Question
How can the use of manipulatives support children to efficiently and accurately carry out, record and explain (division) calculations? Why did we decide to research this? At the initial session Mrs Boulton brought a think-­‐piece to stimulate discussion around why we teach Mathematics and why being numerate is important. We discussed some “big” questions: What is good Maths teaching? What makes a good Mathematician? The think-­‐piece was OFSTED’s report ‘Good practice in primary Mathematics’, ( 2011).Using the key findings contained in the report we reflected on our own practice and where we might make improvements. We also considered the OFSTED document ‘ Improving girls attainment in Mathematics: Westdene Primary School (2012) and this prompted us to think about what are doing to address underachievement in Maths not only for girls but for all learners, and to generate ideas about what we might go about it. We noted that many of the findings were already in place in the school. We all agreed that we needed to raise the profile of the teaching and learning of Maths and create a positive “buzz” around the subject. Additionally, Mrs Boulton is accredited by the NCETM (National Centre for Excellence in Teaching Mathematics) as a Primary CPD Leader. Through this role she was aware of a growing national agenda on improving children’s fluency in completing written calculations, a term referred to as procedural fluency. The team watched a video of a Maths AST from Oldway Primary in Devon. This showed a teacher using counters to “bridge the learning gap” for pupils encountering the bus stop method for division. The teacher modelled using manipulatives (counters) to explain the method, with the children exchanging amounts and recording what they had done. The team then agreed to focus on the use of manipulatives to support teaching of key Mathematical processes. Research: Refinement and enquiry In the following sessions all members of the research group undertook an online NCETM CPD unit on Models and Representations considering: This professional learning led us to reflect further on our practice: how much of our teaching used symbolic representations? How much was diagrammatic and how much involved use of concrete apparatus? We completed a recording sheet and realised that the majority of our teaching used symbolic representations and predominately at the beginning of the lesson. Following this analysis, we revised and refined our focus to the use of diagrammatic and concrete methods to support the teaching and learning of division.
Next we looked at planning and decided to carry out an action research study investigating the use of manipulatives to support division. All members of the research sett were responsible for adapting their teaching to include modelling the use of manipulatives to support Mathematical understanding as often as possible across the week. Fay and Cath volunteered to carry out a series of lessons in the following terms focussing on the use of manipulatives. This is the link to the online learning we undertook: https://www.ncetm.org.uk/online-­‐cpd-­‐modules/primary-­‐module Effect Validity and impact: From carrying out this study we found a number of outcomes: Outcome 1: There was increased use of diagrammatic representations throughout the school. Teachers modelled the use of drawings and diagrams to pupils to help them understand the concepts behind complex Mathematical procedures such as division. Outcome 2: There was an increased use of manipulatives (equipment) to help children to progress towards procedural fluency. More classrooms, especially in KS2, were using equipment to support children’s Mathematical understanding. Outcome 3: An unexpected outcome was the more thoughtful and accurate use of Mathematical language by teachers and children. This led to shared expectations of children and teachers to use the correct Mathematical terminology and language. Through the study we gathered evidence from: •
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taking photographs of the children working with manipulatives flipcharts used for teaching showing visual representations children recording written methods in their books teachers planning pupil interviews. Our findings were collated through learning walks, book scrutiny, pupils’ voice and lesson observations. Due to the nature of the research question our findings were more qualitative than quantitative. What difference has this made to teaching and learning in maths at The Mead? The most significant impact is that manipulatives are now considered non –negotiable resource for teaching and learning in Maths. All classes throughout the school have “Maths baskets” or Maths resource benches containing a selection of Mathematical equipment relevant to each year group to support. Another important change is that teachers are modelling the use of Mathematical equipment to support learning for all children not just children with SEN. Staff confidence has also heightened in using practical materials and the demand for resources has increased sue to usage. What difference has it made to children, staff, and parents? How do they know? The difference it has made for children is their increased confidence to tackle Mathematical problems independently and they are more likely to use the equipment to support them “ having a go” . We asked a group of pupils for their comments on the Maths baskets; these were some of the responses: I think the multiplication squares help me to mark the Murder Squares. My partner sometimes chooses tables I don’t know.” (Grace) • “It’s useful because the cubes help me to divide and the multiplication squares help me to multiply. The hundred squares help me to add.” (Evan) • “It’s useful for me – I use the cubes for dividing.” (Archie). •
Through sharing our findings at staff meetings and through the Learning Café we raised staff awareness of the importance of using equipment to support Mathematical understanding. To further build on this exciting research we are hoping to have another Maths Learning Sett focussing on the ambiguity of mathematical language, particularly how terms are interchangeable and often confusing. Reading OFSTED (2012) Good practice resource -­‐ Improving girls’ attainment in mathematics: Westdene Primary School [Online] available from: http://www.ofsted.gov.uk/resources/good-­‐practice-­‐
resource-­‐improving-­‐girls%E2%80%99-­‐attainment-­‐mathematics-­‐westdene-­‐primary-­‐school Ofsted (2011) Good practice in primary mathematics: evidence from 20 successful schools [Online] available from: http://www.ofsted.gov.uk/resources/good-­‐practice-­‐primary-­‐mathematics-­‐evidence-­‐
20-­‐successful-­‐schools NCETM Online CPD Modules: Primary Module[Online] available from https://www.ncetm.org.uk/online-­‐cpd-­‐modules/primary-­‐module