Singapore math (an interactive instructional approach) emphasizes the development of strong number sense, excellent mental-math skills, and a deep understanding of place value. It is based on Bruner’s (1956) principles, a progression from concrete experience using manipulatives, to a pictorial stage, and finally to the abstract level or algorithm. This sequence gives students a solid understanding of basic mathematical concepts and relationships before they start working at the abstract level. Concepts are taught to mastery, then later revisited but not retaught. The Singapore approach focuses on the development of students’ problem-solving abilities. There is a strong emphasis on model drawing, a visual approach to solving word problems that helps students organize information and solve problems in a step-by-step manner.

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Bruner, Jerome, Jacqueline Jarrett Goodnow, and George Austin. 1956. A Study of Thinking.  New York: Wiley.