At Parkway, we want our children to be confident, fluent mathematicians who have a positive attitude towards problem solving. We teach maths for mastery. This means that we are teaching children to have a deep conceptual understanding rather than teaching so that children can get a correct answer. Being able to explain how they got an answer, why that answer is correct, and what might happen if a particular variable was changed are the hallmarks of a mathematician – simply getting the answer right ought to be a given. We believe that all children can succeed mathematically, and that one of our primary tasks as teachers is to find ways of presenting, scaffolding, and teaching concepts in such a way that everyone will achieve.
Implementation: What does Maths look like at Parkway Primary?
At Parkway Primary, we teach maths in units following the Maths No-problem scheme. The units are ordered to build upon each other, usually spending a few weeks on each topic. We aim to develop children’s understanding using the CPA approach which builds on children;s existing knowledge by introducing abstract concepts in a concrete and tangible way. The CPA approach moves from the Concrete (actual physical manifestation of the maths), on to the Pictorial (being able to approach the maths using pictures rather than physical resources), and finally onto the Abstract (being able to approach mathematics without physical or pictorial resources).
- Concrete step of CPA - Concrete is the “doing” stage. During this stage, students use concrete objects to model problems. Unlike traditional maths teaching methods where teachers demonstrate how to solve a problem, the CPA approach brings concepts to life by allowing children to experience and handle physical (concrete) objects. With the CPA framework, every abstract concept is first introduced using physical, interactive concrete materials. For example, if a problem involves adding pieces of fruit, children can first handle actual fruit. From there, they can progress to handling abstract counters or cubes which represent the fruit
- Pictorial step of CPA - Pictorial is the “seeing” stage. Here, visual representations of concrete objects are used to model problems. This stage encourages children to make a mental connection between the physical object they just handled and the abstract pictures, diagrams or models that represent the objects from the problem. Building or drawing a model makes it easier for children to grasp difficult abstract concepts (for example, fractions). Simply put, it helps students visualise abstract problems and make them more accessible.
- Abstract step of CPA - Abstract is the “symbolic” stage, where children use abstract symbols to model problems. Students will not progress to this stage until they have demonstrated that they have a solid understanding of the concrete and pictorial stages of the problem. The abstract stage involves the teacher introducing abstract concepts (for example, mathematical symbols). Children are introduced to the concept at a symbolic level, using only numbers, notation, and mathematical symbols (for example, +, –, x, /) to indicate addition, multiplication or division.
Typical Daily Lesson
Individual teachers have individual styles, different classes have different needs. At the start of the year, Year 1 teachers will find that they need more time for the task, however, a typical Maths No-problem lesson at Parkway should consist of these elements:
- In focus: (5 minutes) – Includes questions related to various lesson objectives as an introductory activity for children.
- Let’s Learn: (10 minutes) – Here the teacher gives a whole-class input, with lots of opportunities for children to talk to their partner or table about particular questions, apply their learning to mini-tasks, and clarify misconceptions (The teacher isn’t talking for 10 minutes).
- Guided practise: Here the children discuss and attempt the new learning. This may be in the form of a game, a sheet with the same layout as your teaching, however, with different numbers or some form of physical resource that they will use to solve a problem. At this point, the teacher can move around the room, and assess how well children have understood the learning.
- Independent task: Children then are provided with an opportunity to practise their new knowledge using fluency, reasoning, problem solving and word problems.
Assessment
In lessons we use formative assessment to help decide on what we should do next with the children and the progress they are making. This allows us to understand how to support and extend our children appropriately. Teachers recognise the difference between performance and learning and understand that pupil performance in the lesson today does not necessarily translate into the type of learning that will be evident tomorrow. As a result, PiXL assessments are used to enable all staff (both Teachers and ISA) to regularly assess what learning has been retained by the children over longer periods of time. This also provides children with the regular opportunity of retrieving information from memory. Alongside, our daily ‘Maths meeting’ which allows the children to apply retrieved information from previous units.
Please click to the link below to see how our Mathematics teaching progresses throughout each year group.