In the United States, Singapore math is a teaching method based on the national math curriculum used for kindergarten through sixth grade in Singapore. It involves teaching students to learn and master fewer mathematical concepts at greater detail as well as having them learn these concepts using a three-step learning process. The three steps are concrete, pictorial, and abstract. In the concrete step, students engage in hands-on learning experiences using concrete objects such as chips, dice, or paper clips. This is followed by drawing pictorial representations of mathematical concepts. Students then solve mathematical problems in an abstract way by using numbers and symbols.
The development of Singapore math began in the 1980s when the country's Ministry of Education developed its own mathematics textbooks that focused on problem solving and heuristic model drawing. Early adopters of these textbooks in the United States included parents interested in homeschooling as well as a limited number of schools. These textbooks became more popular since the release of scores from the Trends in International Mathematics and Science Study (TIMSS), which showed Singapore at the top of the world three times in 4th and 8th grade mathematics. US editions of these textbooks have been adopted by a large number of school districts as well as charter and private schools.
Before the 1980s, Singapore imported all of its mathematics textbooks from other nations. In 1981, the Curriculum Development Institute of Singapore (CDIS) (currently the Curriculum Planning and Development Division) of Singapore began to develop its own mathematics textbooks and curriculum. The CDIS developed a textbook series called Primary Mathematics, which was first published in 1982 and subsequently revised in 1992 to emphasize problem solving. The texts were later distributed in the United States by Singapore Math, Inc., a private venture based in Oregon. Starting in 2002, the Singapore math textbooks have also been translated into Hebrew and implemented in Israeli schools.
Following Singapore’s curricular and instructional initiatives, dramatic improvements in math proficiency for Singapore students on international assessments were seen. In 1984, Singapore’s students were placed 16th out of 26 nations in the Second International Science Study (SISS). By 1995, the Trends in International Mathematics and Science Study (TIMSS) ranked Singapore’s students first among participating nations. The 2007 results also showed Singapore as a top-performing nation.
Covers fewer topics in greater depth
In contrast to a traditional US math curriculum, Singapore math focuses students to learn fewer topics but at greater detail. Each semester-level Singapore math textbook builds upon preceding levels, and assumes that what was taught need not be taught again. A great deal of instructional time is saved by focusing on essential math skills, and by not reteaching what has been taught before. Careful guidance of students is done in a child-friendly pictorial language, not only to technical mastery, but to complete understanding of all the "whys" (see an example). The need for repetitive drill is minimized by sequencing of topics. For instance, the introduction of multiplication facts by 2, 3, 4 and 5 in the middle of Grade 2 is followed by a seemingly unrelated section on reading statistical data from a graph. In fact, the latter task reinforces the learning of multiplication facts when the scale begins to vary from 2 to 5 objects per graphical unit. The result is that students master essential math skills at a more rapid pace. By the end of sixth grade, Singapore math students would have mastered multiplication and division of fractions and are comfortable doing difficult multi-step word problems.
Singapore math emphasizes the essential math skills recommended in the NCTM Curriculum Focal Points (National Council of Teachers of Mathematics), the National Mathematics Advisory Panel, and the proposed Common Core State Standards, though it generally progresses to topics at an earlier grade level than indicated by those US standards.
Three-step learning process
Singapore math teaches students mathematical concepts in a three-step learning process: concrete, pictorial, and abstract. During the concrete step, students engage in hands-on learning experiences using concrete or real-world objects such as chips, dice, or paper clips. The students then draw pictorial diagrams called "bar-models" to solve mathematical problems involving addition, subtraction, multiplication, and division. Students then transition to solving mathematical problems in an abstract way using numbers and symbols.
There is also systematic use of word problems as a way of building the semantics of mathematical operations. Students learn when to add and when to subtract, relying on the meaning of the situation (rather than "clue-words," as often done in the US schools). Formulations are free of redundancies and challenge students' understanding of mathematics only. Students begin solving simple multi-step word problems in third grade, using the bar model method. Later grades apply this same method to more and more difficult problems, so that by sixth grade they are solving harder problems. An example would be: “Lauren spent 20 percent of her money on a dress. She spent 2/5 of the remainder on a book. She had $72 left. How much money did she have at first?”
- Brown, Laura L. "What’s Singapore Math?", PBS. Retrieved on September 19, 2013.
- Hu, Winnie. "Making Math Lessons as Easy as 1, Pause, 2, Pause ...", The New York Times, New York, September 30, 2010. Retrieved on September 19, 2013.
- Knake, Lindsay. "Saginaw Township elementary schools implement hands-on Singapore math program", MLive. Grand Rapids, MI, December, 2011. Retrieved on September 19, 2013.
- Jackson, Bill. "My view: America's students can benefit from Singapore math", CNN, Atlanta, October 10, 2012. Retrieved on September 19, 2013.
- Wright, Gerard. "Mathematics Mighty Ducks", The Age, Australia, Mat 12, 2008. Retrieved on September 20, 2013.
- Garelick, Barry (Fall 2006). "Miracle math: A successful program from Singapore tests the limits of school reform in the suburbs.". Educational Next 6.
- Garelick, Barry (2006). "A tale of two countries and one school district.". Nonpartisan Education Review 6 (8).
- Hoven, John; Garelick, Barry (November 2007). "Singapore Math: Using the bar model approach, Singapore textbooks enable students to solve difficult math problems--and learn how to think symbolically.". Educational Leadership 65: 38–21.
- National Council of Teachers of Mathematics. Curriculum Focal Points for Prekindergarten Through Grade 8 Mathematics: A Quest for Coherence. (2006)
- Edinformatics, “NCTM Focal Points and Singapore Math Syllabus”
- National Mathematics Advisory Panel. Foundations for Success: The Final Report of the National Mathematics Advisory Panel, U.S. Department of Education: Washington, DC. (2008) p. 20
- Common Core State Standards Initiative. Common Core State Standards for Mathematics (2010).
- Jackson, B. "Singapore Math Demystified!". The Daily Riff. Retrieved September 20, 2013.