In the 1980s, the island nation of Singapore decided to reform their math curriculum. The country's Ministry of Education brought together the best teachers to developed its own mathematics textbooks that focused on problem solving and heuristic (investigative) model drawing.
Singapore looked at how best to teach math, not necessarily focusing on the topics. Over the past few decades, Singapore has placed at the top every year on international tests such as Trends in International Mathematics and Science Study (TIMSS, grades 4 and 8).
- View classrooms as mathematical communities, not collections of individuals
- Use logic and mathematical evidence to verify results rather than relying on the teacher as authority
- Emphasize mathematical reasoning rather than memorizing procedures
- Focus on conjecture, inventing, and problem solving instead of mechanical answer finding
- Make connections among the ideas and applications of mathematics, rather than seeing them in isolated concepts and procedures
The Concrete, Pictorial, Abstract Approach
The Singapore Math approach embraces these elements, building from the Concrete (hands-on) to the Pictorial (bar modeling) to the Abstract, or CPA. This highly effective approach to teaching, first developed by American psychologist Jerome Bruner, develops a deep and sustainable understanding of mathematics.
The CPA approach brings concepts to life by allowing children to experience and handle physical (concrete) objects. In the CPA framework, every abstract concept is first introduced using interactive physical materials. Children often find math difficult because it is abstract, so the CPA approach helps children learn new ideas and build on their existing knowledge by introducing those abstract concepts in a more familiar and tangible way.
For example, if a problem involves adding pieces of fruit, children can first handle actual fruit (the concrete stage).
Pictorial is the “seeing” stage. In it, 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.
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.
Singapore Math at TASIS Portugal
Singapore Math is based on international standards and research for teaching and learning in math. Lessons are filled with visual models, concrete hands-on activities, and a consistent format through 8th Grade. TASIS Portugal is using Singapore Math because the lessons empower students to develop critical thinking skills, positive attitudes, and confidence. We want students to be high achieving mathematicians and we want them to love math!
Eighty minutes are dedicated to math every day to allow teachers to meet the needs of all our incoming students. For some students and parents, the rigor of Singapore Math will not be obvious at the outset. In the lower grades, the content might seem easier than expected. It is important to understand that Singapore Math is designed to build strong number sense requiring mastery of, not just exposure to, concepts and content. By 5th Grade, Singapore Math textbooks are clearly accelerated.
Problem-solving strategies are developed gradually across the grades. Lessons are organized to allow opportunities for direct instruction and modeling, small group practice, and independent work.
Parent Resource Videos
These Parent Resource Videos (while not created for the 2020 edition) are meant to provide a framework for understanding the approach of Singapore Math as you support your child’s development as a mathematical thinker: