Singapore math

[2][3] In the concrete step, students engage in hands-on learning experiences using physical objects which can be everyday items such as paper clips, toy blocks or math manipulates such as counting bears, link cubes and fraction discs.

The CDIS developed and distributed a textbook series for elementary schools in Singapore called Primary Mathematics, which was first published in 1982 and subsequently revised in 1992 to emphasize problem solving.

[1][15][16] Following Singapore's curricular and instructional initiatives, dramatic improvements in math proficiency among Singaporean students on international assessments were observed.

[4] In 2005, the American Institutes for Research (AIR) published a study, which concluded that U.S. schools could benefit from adopting these textbooks.

[3] Each semester-level Singapore math textbook builds upon prior knowledge and skills, with students mastering them before moving on to the next grade.

[2] By the end of sixth grade, Singapore math students have mastered multiplication and division of fractions and can solve difficult multi-step word problems.

[21] In the U.S., it was found that Singapore math emphasizes the essential math skills recommended in the 2006 Focal Points publication by the National Council of Teachers of Mathematics (NCTM), the 2008 final report by the National Mathematics Advisory Panel, and the proposed Common Core State Standards, though it generally progresses to topics at an earlier grade level compared to U.S.

[22][23] Singapore math teaches students mathematical concepts in a three-step learning process: concrete, pictorial, and abstract.

In the 1960s, Bruner found that people learn in three stages by first handling real objects before transitioning to pictures and then to symbols.

They then learn basic arithmetic operations such as addition or subtraction by physically adding or removing the objects from each row.

[24] Students then transition to the pictorial step by drawing diagrams called "bar-models" to represent specific quantities of an object.

[11][21] Bar modeling is far more efficient than the "guess-and-check" approach, in which students simply guess combinations of numbers until they stumble onto the solution.