Mathematical understanding is a journey... not a destination"
- Dr Yeap Ban Haar (Math Consultant)
Mathematics underpins our daily lives. It is a subject of vital importance as with the speed and scale of technological change, it makes mathematics increasingly essential. The Singapore method of teaching mathematics develops pupils' mathematical ability and confidence, making mathematics more engaging and interesting.
The aim of the ‘Singapore Maths’ is to raise standards of attainment and progress, and ensure every child achieves above national expectations. A study, by UCL Institute of Education and Cambridge University, shows that children who were taught through the Singaporean “maths mastery” approach learn faster than their classmates - making on average, an extra month of progress in a calendar year. The approach has led to world-leading results in Singapore. It uses a rigorous, coherent syllabus which integrates concepts and skills in a concrete to pictorial to abstract way. The Singapore method of teaching mathematics develops pupils' mathematical ability and confidence without having to resort to memorising procedures to pass tests.
Maths Mastery concentrates on problem solving skills - using equipment like building blocks to find answers. Under the Singapore system, teachers generally do not split their pupils into different ability groups. Instead, they wait for academically weaker pupils to reach a basic standard in each topic before the class moves on to the next concept. The able pupils study the topic in greater depth gaining greater depth of knowledge. In addition, the Singapore system concentrates more on developing problem solving skills rather than mental arithmetic.
Theory behind Singapore Maths
The teaching of Singapore Maths focuses on the use of three core competencies: Visualisation, Finding Patterns, and Mental Strategies. The Singapore method of teaching mathematics is based on research from a variety of sources. The work of educational psychologist Jerome Bruner, Richard Skemp's work on relational and instrumental understanding, and the work of Zoltan Dienes on systematic variation.
• Jerome Bruner
Bruner studied how children learned: he coined the term "scaffolding" to describe how children often build on the information they have already mastered. Bruner proposed three modes of representation: enactive representation (concrete or action-based), iconic representation (pictorial or image-based), and symbolic representation (abstract or language-based). This learning theory is the basis for the Concrete -> Pictorial -> Abstract approach.
• Richard Skemp
Skemp distinguishes between the ability to perform a procedure (instrumental) and the ability to explain the procedure (relational). He argues that these are two different methods of learning - relational and instrumental. In reading Skemp's article it is clear that relational understanding is necessary if children are to progress beyond seeing mathematics as a set of arbitrary rules.
• Zoltan Dienes
Based on Dienes' ideas (Dienes, 1960), systematic variation is used throughout this method of teaching. The idea is that you vary the lesson through a series of examples that deal with the same problem/topic. It is employed in several ways, including mathematical variability - where the learning of one particular mathematical concept is varied and perceptual variability -where the mathematical concept is the same, but the students are presented with different ways to perceive a problem. The idea of multiple embodiments is to use different ways to to represent the same concept. The Singapore maths books present this in a systematic way to ensure students comprehend what they are learning.
Transferring Pedagogy into Classroom Practice
Singapore Maths’ prescriptive approach to teaching ensures that all concepts and skills are taught following the same format. Lessons follow the concrete–pictorial–abstract pedagogy. Clear and engaging visuals are used to present concepts, and to model solutions that allow all pupils, regardless of language skills, to focus on the mathematics. The concrete–pictorial–abstract sequence helps students build understanding of mathematical processes.
Singapore Maths Textbooks and Workbooks
The textbooks allow teachers and pupils to explore each topic in real depth. The colourful textbooks include anchor tasks, guided practice examples and group activities for use in the classroom.
The workbooks allow pupils to work independently, demonstrate their understanding and assess their own learning.
The varied examples have been specifically chosen to stretch pupils into harder concepts, create depth and generate dialogue providing teachers with better expert resources than if they were developing materials on their own.
“Parental involvement in the form of ‘at-home good parenting’ has a significant positive effect on children’s achievement and adjustment even after all other factors shaping attainment have been taken out of the equation. In the primary age range the impact caused by different levels of parental involvement is much bigger than differences associated with variations in the quality of schools. The scale of the impact is evident across all social classes and all ethnic groups.”