PHILOSOPHY BEHIND SINGAPORE MATHS
We believe that every child can master an understanding and love of maths with the right kind of teaching and support.
Maths No Problem
Maths — No Problem! is a comprehensive series that adopts a spiral design with carefully built-up mathematical concepts and processes adapted from the maths mastery approaches used in Singapore. The Concrete-Pictorial-Abstract (C-P-A) approach forms an integral part of the learning process through the materials developed for this series.
Maths — No Problem! incorporates the use of concrete aids and manipulatives, problem-solving and group work.
Singapore Maths Overview
Singapore has become a “laboratory of maths teaching” by incorporating established international research into a highly effective teaching approach. With its emphasis on teaching pupils to solve problems, Singapore Maths teaching is the envy of the world.
The whole class works through the programme of study at the same pace with ample time on each topic before moving on. Ideas are revisited at higher levels as the curriculum spirals through the years.
Tasks and activities are designed to be easy for pupils to enter while still containing challenging components. For advanced learners, the textbooks also contain non-routine questions for pupils to develop their higher-order thinking skills.
Lessons and activities are designed to be taught using problem-solving approaches to encourage pupils’ higher-level thinking. The focus is on working with pupils’ core competencies, building on what they know to develop their relational understanding, based on Richard Skemp’s work.
Concrete Pictorial Abstract (CPA) Approach
Based on Jerome Bruner’s work, pupils learn new concepts initially using concrete examples, such as counters, then progress to drawing pictorial representations before finally using more abstract symbols, such as the equals sign.
The questions and examples are carefully varied by expert authors to encourage pupils to think about the maths. Rather than provide mechanical repetition, the examples are designed to deepen pupils’ understanding and reveal misconceptions.
What Is CPA?
The concrete, pictorial and abstract approach allows for children to gain conceptual understanding in a gradual systematic approach.
Using concrete resources allows the opportunity for informal play, which is supported by the theory Zoltan Dienes. This should take place at the beginning of all learning as it gives pupils the opportunity to investigate a concept first and then make connections when formal methods are introduced through teaching. It also allows the pupil to become familiar with the resources and what they are representing.
This stage is vital for allowing children to show their understanding of a concept taught, for example in bar modelling when given the statement 23+21 and draws one bar much greater than the other, it highlights how the pupils hasn’t sufficiently understood that there is not much difference between the two numbers and therefore he bars will be similar in length, with one being only slightly shorter. It also continues to support children in sufficiently understanding process they need to go through in order to solve mathematical statements, for example when regrouping, the pupil will need to draw dienes or place value counters and then show the regrouping of a number through crossing out and re-drawing, reinforcing the concept.
The abstract stage often runs alongside the concrete, pictorial stage as children need to read mathematical statements and use the concrete resources or pictorial representations to show their understanding of the mathematical statement. So when teaching addition, for example, using dienes or drawing dienes the children do this alongside the formal written column method, which is abstract.