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In the United States, Singapore Math is a teaching method based on the national math curriculum used for kindergarten through sixth grade in Singapore.[1][2] It involves teaching students to learn and master fewer concepts at greater detail each year.[2] The method exposes students to mathematical concepts in a three-step learning process: 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.[3] This is followed by drawing pictorial representations of mathematical concepts. Students then solve mathematical problems in an abstract way by using numbers and symbols.[4]

The development of Singapore Math began in 1980 when the country's Ministry of Education developed its own mathematics textbooks that focused on problem solving and heuristic model drawing.[1] These textbooks were later adopted by parents and a limited number of school districts across the United States. These books became more popular since the release of scores from the Trends in International Mathematics and Science Study (TIMSS) [5] in 2003, which showed Singapore at the top of the world in 4th and 8th grade mathematics.

History

Prior to 1980, Singapore imported all of its mathematics textbooks from other nations. Beginning in 1980, however, Singapore began to take a new approach to mathematics instruction. Instead of importing its mathematics textbooks, the Curriculum Development Institute of Singapore (CDIS) was established. One charge of CDIS was to develop primary and secondary textbooks. At the same time, the Ministry of Education, the centralized education authority in the country, set new goals for mathematics education. These goals emphasized a focus on problem solving and on heuristic model drawing. The CDIS incorporated these goals into the textbooks, and in 1982 the first Singapore math program, Primary Mathematics 1-6, was published. In 1992, a second edition was made available. The second edition revisions included an even stronger focus on problem solving and on using model drawing as a strategy to problem solve.

The country continued to develop its mathematics program. Further revisions included:

  • Creating a tighter content focus of the mathematics curricula following a study to review the scope and sequence in 1998
  • Privatizing the production of the primary level mathematics textbooks in 2001, with the hope that collaboration among textbook publishers would lead to quality textbooks at more affordable prices
  • Placing an even greater focus on developing mathematical concepts and fostering mathematical problem solving in 2006 revisions

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.

Features

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.[1] 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.[6]

Singapore Math emphasizes the essential math skills recommended in the NCTM Curriculum Focal Points (National Council of Teachers of Mathematics),[7][8] the National Mathematics Advisory Panel,[9] and the proposed Common Core State Standards,[10] though it generally progresses to topics at an earlier grade level than indicated by those US standards.[11]

A bar model used to solve an addition problem. This pictorial approach is typically used as a problem-solving tool in Singapore Math.

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.[3] The students then draw pictorial devices called "bar-models (a form of pre-algebra)" to represent arithmetical quantities as line or bar segments.[12] They can use these 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.

Word problems

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 like this: “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?”

Israeli experience

Starting in 2002, the Singapore math textbooks have been translated into Hebrew and implemented in schools. The translations are now approved from grade 1 to grade 6. The books are used in about 150 schools (8% of the Hebrew speaking schools in Israel). National tests have shown success.[citation needed] Ten schools participated in the tests, and their average was about 8 points above the national average. There are complaints about the books as from 4th grade, concerning difficulty and "jumpiness", lacking in systematic structuring of the material. On the other hand, middle schools report that the students who studied with the books arrive better prepared.[citation needed]

References

  1. ^ a b c 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.
  2. ^ a b Brown, Laura L. "What’s Singapore Math?", PBS. Retrieved on September 19, 2013.
  3. ^ a b Knake, Lindsay. "Saginaw Township elementary schools implement hands-on Singapore math program", MLive. Grand Rapids, MI, December, 2011. Retrieved on September 19, 2013.
  4. ^ Jackson, Bill. "My view: America's students can benefit from Singapore math", CNN, Atlanta, October 10, 2012. Retrieved on September 19, 2013.
  5. ^ TIMSS
  6. ^ 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" (PDF). Educational Leadership. 65: 38–21.
  7. ^ National Council of Teachers of Mathematics. Curriculum Focal Points for Prekindergarten Through Grade 8 Mathematics: A Quest for Coherence. (2006)
  8. ^ Edinformatics, “NCTM Focal Points and Singapore Math Syllabus”
  9. ^ 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
  10. ^ Common Core State Standards Initiative. Common Core State Standards for Mathematics (2010).
  11. ^ Math in Focus and the Common Core Standards Draft Alignment Guide
  12. ^ An A-Maze-ing Approach to Math by Barry Garelick


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