Singapore Math K-6

Our Singapore Math program for primary school students is intended to supplement and enhance the math programs found in the region’s public and private schools.  Singapore Math utilizes the Concrete – Pictorial – Abstract, or CPA, Approach to instill in children the fundamentals of mathematics.  The CPA instructional approach encourages active thinking, communication of mathematical ideas, and problem solving by gradually introducing students to different ways of thinking about the mathematical process.  The first stage is concrete or ‘doing’ stage.  Students are introduced to mathematical topics by acting them out using real objects.  For example, division might be introduced by separating objects such as apples into two groups of red and green.  This hands-on component of the program, in which students physically manipulate real objects, is the foundation for conceptual understanding.  In the pictorial, or ‘seeing’, stage, students relate their hands-on experiences from the concrete stage to representations, such as diagrams or picture problems.  In the case of division, this could mean circling 5 of 10 objects pictured and visually comprehending that half of the objects have been circled.  The final stage is the abstract or ‘symbolic’ stage.  By this stage, students have gained an understanding of mathematical concepts through objects and pictures and are able to translate that knowledge into mathematical notation.  In other words, students come to know that 10÷2 = 5 is the correct representation of circling 5 of 10 objects in the pictorial stage or dividing 10 apples into 2 groups of 5 during the concrete stage.  In this way, each stage builds on the previous, allowing students to reinforce key skills and achieve a multi-dimensional understanding of mathematics.