Mathematics at Rushmore
Mathematics Lead: Hannah Herlihy
At Rushmore, we follow the National Curriculum for Mathematics. We believe it is an essential life skill and our wish is that all children enjoy maths and become confident mathematicians who thrive on challenge.
The main areas in the program of study for mathematics are number, measure, geometry and statistics. There is a strong emphasis at Rushmore on number and using and applying new skills. We use the Maths No Problem! program and White Rose program to drive our teaching and learning, focusing on the these key principles: to be fluent in the fundamentals of mathematics (i.e. quick recall number facts and application of knowledge, to reason mathematically (i.e. justify, generalise and explain why), and to problem solve.
In doing this, we deepen pupil’s knowledge and understanding of mathematics. Our teaching and learning strategies are underpinned by the concrete pictorial and abstract teaching approach as seen in both the Maths No Problem! Program and the White Rose Program.
Maths No Problem Program (Years 1 - 3)
Maths No Problem uses the maths mastery approach to maths. This involves employing approaches that help pupils to develop a deep and secure knowledge and understanding of mathematics at each stage of their learning, so that by the end of every school year or Key Stage, pupils will have acquired mastery of the mathematical facts and concepts they’ve been exposed to, equipping them to move on confidently and securely to more advanced material. When taught to master maths, children develop their mathematical fluency without resorting to rote learning and are able to solve non-routine maths problems without having to memorise procedures.
Each class moves through the content at the same pace, each topic is studied in depth until the children demonstrate that they have a secure understanding of mathematical concepts. This allows children time to think deeply about the maths and really understand concepts at a relational level rather than a set of rules or procedures. This inclusive approach allows all children to build self-confidence in maths, and its emphasis on promoting multiple methods of solving a problem builds resilience in pupils.
Though the whole class goes through the same content at the same pace, there is still plenty of opportunity for differentiation. Unlike the old model, where advanced learners are accelerated through new content, those pupils who grasp concepts quickly are challenged with rich and sophisticated problems within the topic. Those children who are not sufficiently fluent are provided additional support to consolidate their understanding before moving on.
White Rose Program (Years 4 - 6)
The White Rose schemes of learning are designed to support a mastery approach to teaching and learning and are in line with the aims and objectives of the National Curriculum. They have number at their heart and a large proportion of time is spent reinforcing number to build competency. It allows teachers to stay the required key stage and support the ideal of depth before breadth of understanding. It also ensures students have the opportunity to stay together as they work through the schemes as a whole group and provides plenty of opportunities to build reasoning and problem solving elements into the curriculum.
The White Rose program allows children to make small steps to move through the following aspects of mathematical thinking:
Fluency - having number sense, understanding how numbers relate to each other, seeing how numbers can be split and put together in different ways and having knowledge of number facts and efficient methods to calculate.
Reasoning - thinking through mathematical problems logically and systematically and involves using and applying their mathematical knowledge to explain or justify a solution.
Problem Solving - drawing on problem solving skills such as working systematically, trial and improvement, logical reasoning and spotting and exploring patterns. Problems often have multiple solutions.
Concrete Pictorial Abstract (CPA)
Concrete, Pictorial, Abstract (CPA) is a highly effective approach to teaching that develops a deep and sustainable understanding of maths in pupils. Often referred to as the concrete, representational, abstract framework, CPA was developed by American psychologist Jerome Bruner. It is an essential technique within the Singapore method of teaching maths for mastery.
- Concrete – students should have the opportunity to use concrete objects and manipulatives to help them understand what they are doing.
- Pictorial – students should then build on this concrete approach by using pictorial representations. These representations can then be used to reason and solve problems.
- Abstract – with the foundations firmly laid, students should be able to move to an abstract approach using numbers and key concepts with confidence.
Concrete is the “doing” stage.
During this stage, students use concrete objects to model problems. This 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 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. Bar modelling is an essential maths mastery pictorial strategy. A Singapore-style of maths model, bar modelling allows pupils to draw and visualize mathematical concepts to solve problems.
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.
Every child from Reception to Year 6 is given a login (username and password) with which they can enter their account from any computer which has access to the internet.
One of the best things about IXL is that your child can access it from home, so you have a chance to see your child’s progress.
We hope you will encourage your child to use IXL daily. Click here to be redirected to the IXL home page.