Mastering Maths means pupils acquiring a deep, long-term, secure and adaptable understanding of the subject.The phrase ‘teaching for mastery’ describes the elements of classroom practice and school organisation that combine to give pupils the best chances of mastering Maths. Achieving mastery means acquiring a solid enough understanding of the Maths that’s been taught to enable pupils to move on to more advanced material.
Concrete, Pictorial, Abstract
The Concrete, Pictorial, Abstract approach (known as CPA) is a crucial element of mastery.
The CPA method involves using actual objects for children to add, subtract, multiply or divide. They then progress to using pictorial representations of the object, and ultimately, abstract symbols. Children often find maths difficult because it is abstract. The CPA approach helps children learn new ideas and build on their existing knowledge by introducing abstract concepts in a more familiar and tangible way.
The theory behind this approach is that pupils are taught through whole-class interactive teaching, where the focus is on all pupils working together on the same lesson content at the same time, as happens in Shanghai and several other regions that teach Maths successfully. This ensures that all can master concepts before moving to the next part of the curriculum sequence, allowing no pupil to be left behind. If a pupil fails to grasp a concept or procedure, this is identified quickly and early intervention ensures the pupil is ready to move forward with the whole class in the next lesson. More able pupils are challenged through carefully planned reasoning and problem-solving questions. The aim here is for breadth of understanding; they do not access content from the year group above.
At Mabe School, we started our journey towards mastery in Spring 2018 when Maths lead Julia Pearce witnessed features of mastery in action at St. Merryn School. Since then, we have worked hard to develop our own practice, which has been greatly assisted by our partnership with the Maths Hub. Since September 2019, we have attended sessions to develop our thinking, observed mastery expert Ross Barnes in action in his own classroom and formed valuable links with Mylor School. The Maths lead has held meetings with staff to ensure that they are up to date with mastery thinking. We are now in the second year of our partnership with the Maths Hub. The aim of this year is for mastery to be embedded across the whole school.
It is important to note that the development of Maths mastery does not happen overnight; it is a process that takes many years and one that is in need of regular refinement. All good teachers should be reflective of their practice; always seeking new ways to make experiences even better for the children and Maths mastery is certainly no exception!
At Mabe School, our mission is to give your children the very best Maths experiences possible!
*Daily rapid recall - Children answer a series of calculations at speed at the start of each lesson.
*Vocabulary check - The children discuss key Maths terminology that will be used in the lesson. This links to our wider school aim of developing vocabulary across the curriculum.
*Stem sentences - These provide a scaffold to help children communicate their understanding with precision and clarity. For example: There are two equal groups of 4. There are 4 in each group. There are two 4s.
*Manipulatives - Each class is well stocked with a range of manipulatives to help children get to grips with a concrete understanding.
*Visuals - Pictures help children see mathematical ideas, which aids understanding. For example, the following cupcake image is an array. Children can see 4 x 4 = 16.
Along with other schools in our Trust, we assess pupils using PUMA materials at the end of each term. PUMA tests assess pupil understanding across the Maths spectrum. In order for us to get a sense of children's understanding within each specific topic, such as Addition and Subtraction or Fractions, we use White Rose end of block assessments. We also formatively assess pupils on a daily basis, which is an essential feature of our practice across the entire curriculum. If pupils are not meeting objectives within a lesson, they will take part in interventions/pre-teach activities that afternoon.
Maths in Action at Mabe
Below you can see Maths displays from across the school. Each class has a wipeable gridded board, so that the display is interactive. At Mabe School, we believe that our displays should not simply become 'wallpaper' but rather be a workable document that is ever changing as the learning progresses. There are opportunities for children to write on the board, answering a range of fluency, reasoning and problem-solving questions. Key vocabulary and stem sentences will also feature, acting as useful prompts for the children. We are aware of the importance of making cross curricular links, so our displays show how Maths is not taught in complete isolation.
In our Choughs and Chicks Nursery Class and our Kittiwakes Reception Class, Maths is everywhere! There are always opportunities for childen to explore mathemactical concepts through play. We have taken this first class early years practice of using manipulatives to develop understanding right up through the school. Tens frames, beadstrings, Cuisenaire rods, Numicon, place value counters and Base 10 materials are all over the school. Using concrete materials helps lay the foundations for a deepened understanding. This quote from Hoong et al summarises why manipulatives are so important and why they should not be neglected in any year group:
"Neglecting manipulatives and moving straight to the abstract often means that children have not had the opportunity to make sense of a concept for themselves, and therefore the child has not developed a deep and structural understanding of the mathematics."
Maths lead Julia Pearce and Year 6 teacher Steve Cruse have been working with the Maths Hub in order to develop mastery across the school. They have attended training, observed lessons and gained expert support from Maths specialist Ross Barnes. Parents were treated to lessons which included the use of practical resources (such as counters, Numicon and cubes), visual representations, key vocabulary chat, the use of stem sentences and careful questioning.
Parents were pleased to have the opportunity to come into school and see ‘Maths in action’. One parent commented that ‘It felt positive to come in and make a learning connection between home and school’ whilst another said, ‘I feel much less intimated by it all!’
The children were very pleased to spend the day being mathematical! Across the school, a broad spectrum of activities could be seen from finding lines of symmetry, measuring lengths around the school grounds, playing with our Mathletics online resources and number hunting in the playground. There was an overwhelming sense of enjoyment regarding Maths amongst the children. They demonstrated great positivity throughout the assembly and in their lessons. Many of the adults commented that they wished they learned Maths using the mastery approach!