At Leopold, we have implemented the Singaporean mathematics mastery approach supported through the Math No Problem scheme of work. A fundamental aspect to this approach is applying the concrete, pictorial and abstact framework
Here is a further explanation from Maths No problem
Children (and adults!) can find maths difficult because it is abstract. The CPA approach builds on children’s existing knowledge by introducing abstract concepts in a concrete and tangible way. It involves moving from concrete materials, to pictorial representations, to abstract symbols and problems. The CPA framework is so established in Singapore maths teaching that the Ministry of Education will not approve any teaching materials that do not use the approach.
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.
Each year group In addition, from Reception to Year 6, there is a 15-minute Maths Meeting every day, during which the teacher focuses on basic maths skills.
The following PDFs contain examples of the activities children may participate in during a Maths Meeting.
All children, from Reception to Year 6, are given a personal login to access IXL online maths resources. The website complements all of the skills taught in class, and teachers are able to view reports showing children’s IXL usage and progress. The site can be found here.
Synthetic Phonics – Read Write Inc
Nursery, Reception, Year 1 and selected Year 2 pupils are working under the Read, Write, Inc scheme of learning. The programme guides children on their reading journey, and helps them to establish skills in writing, spelling and phonetic work.
By the end of Year 1, all children utilising the Read, Write, Inc framework have progressed into accurate and well-practiced readers.
Further information, and introductory videos for parents, can be found here.
The Power of Reading
In addition, we have adopted the approach developed and recommended by the Centre of Primary Literacy Education (CLPE). This approach is steeped in research of how to effectively teach reading and writing through high-quality texts. Selected texts are rich in vocabulary; reflect our pupils’ experiences and develop a love of reading. Pleasure for reading is a central driver of the approach along with developing pupils’ literacy skills.
The impact of this approach can be seen in this video:
All children, from Reception to Year 6, are given a personal login to access IXL online English resources. The website complements all of the skills taught in class, and teachers are able to view reports showing children’s IXL usage and progress. The site can be found here.