Singapore Math refers to the mathematics curriculum in the country of Singapore, a tiny, 700-square mile island nation situated between Malaysia and Indonesia. A former British trading colony, Singapore lacks the natural resources that traditionally symbolize the wealth of a nation. Its greatest natural resource, according to the Ministry of Education, is its people. Singapore’s second-largest national expense is education, underscoring the wide-held belief in the value of its citizens.

In Singapore, all academic instruction is in English. The importance of developing a common language while maintaining the traditions and cultures of the indigenous people is clearly important. Singapore is a multiracial and multilingual nation. The four official languages of Singapore are Mandarin, Malay, Tamil and English.

Since all students are taught in a second language, they are considered, like many American students, to be English Language Learners. Teaching methodologies must reflect this issue by being very visual and very concrete. The development of language occurs as the children are mastering the concepts of mathematics. This means the language of math, through rich oral communication between teachers and students, is critically important.
 
In 2003, Singapore’s goal of improving mathematics education was realized when the nation’s 4th and 8th grade students scored the highest in the world. (Trends in International Mathematics and Science Study-TIMSS; www.nces.ed.gov). The latest TIMSS report (2007) shows Singapore in second place, topped by Hong Kong. (American students fall in the middle, out of 46 countries.)

In the United States, the Singapore Math generally refers to the Primary Mathematics Series, which is the textbook series for teaching math Grades 1-6.

Singapore Math is highly regarded because it is coherent, logical, and very concrete. It builds on students’ prior knowledge and experiences with numbers. The approach is very concrete-to pictorial-to abstract and based on the work of Jerome Bruner, one of the most influential and highly regarded learning theorists in the world. The goal of Singapore Math is conceptualization and mastery.

In the U.S., the mathematics curriculum is often described as a “mile wide and an inch deep.” There is exposure to much, but mastery of little. Typical reading programs tend to emphasize skills at the expense of comprehension and meaning. A love for reading and the printed word is rarely inculcated in the typical classroom of scripted and “teacher-proof” reading programs. Typical math instruction is heavily weighted by procedures – we teach HOW to solve particular problems but fail to address the foundational knowledge that makes solving those problems meaningful, relevant, and reasonable.

The core understandings in Singapore Math are essential for numeracy and later learning. They are number facts, number sense, patterns, visualization, and communication. Key instructional strategies relate to place value, computation, mental math, and model drawing. When you consider these core understandings and strategies, you realize they are, or should be, the logical foundation of any math program. But the U.S.’s poor showing on the international math tests (TIMMS) show that typical American math programs fall short of the mark.

Developing early number sense is the main focus of the K-1 curriculum. Experiences in rote counting, rational counting, cardinal numbers, ordinal numbers, measurement, subitizing, and nominal numbers are presented repeatedly in order to ensure mastery number concepts. The “spiraling” of the Singapore Math curriculum ensures that the concepts revisited will be instructed at subsequently higher levels of understanding. This contrasts with the typical American math textbooks that simply revisit the concept and introduce it all over again.

In early primary classrooms, children should constantly be “bumping into” centers – places in the classroom where math happens. They always have something to do. But don’t mistake this as a rigidly academic approach to learning math. It is disguised as play, which is the “work” of young children. Counting and sorting a variety of objects, counting on number lines, skip counting, counting sets, understanding “before” and “after,” and changing decades are good examples of math learning – but these tasks are disguised as games and fun activities. Building an understanding of our base ten system, using ten frames and other manipulatives, is also essential. Using number bonds and branching, without renaming at first, and then with renaming, will further strengthen the number concepts our students will master – in a developmentally appropriate way.

There are a wide variety of math manipulatives, or tools, which may be employed for the purposes of developing number sense, and not just in early primary classrooms. Older elementary students benefit too. Using place value charts, disks, playing cards, and drawings will solidify more complicated concepts like multiplication, division, calculating area, and adding and subtracting fractions. Introduction of abstract decimal fractions (in Grade 4) is preceded by their pictorial model of centimeters and millimeters on a metric ruler. The use of the ruler replaces the non-standard measurement tools (tiles, cubes, paper clips, etc.) from the earlier grades. But, even in Grades 2 and 3, addition and subtraction of decimals is studied in the concrete form of dollars and cents.

With Singapore Math, there is a clear sequencing of topics. This minimizes the need for repetitive drill. For example, 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.

Systematic use of word problems is used to build the semantics of mathematical operations. Simply put, students learn when to add and when to subtract, relying not on "clue words" (as it is often done in U.S. schools) but on the meaning of the situation. Formulations are free of any redundancies, and challenge the student's understanding of mathematics only. This is different from many American math programs, where word problems are used to show "applications" of math and are spiced with immaterial details intended to obscure the mathematical content of the problem. Singapore Math does not trick or confuse students.

Because the program is very pictorial, the use of bar-models in teaching problem solving (a form of pre-algebra) is prevalent. Many educators consider this approach novel, but in reality the device is as old as Book V of Euclid’s Elements, written in the 4th century BCE. It consists of representing arithmetical quantities by line segments. In Singapore Math books, such line segments are regularly used to show and teach one's thinking process in solving an arithmetical problem. For aesthetical reasons, the segments are typeset as colorful "bars" of a fixed width (hence bar-models).

The hallmark of the Singapore Math curriculum is careful guidance of students, with child-friendly pictorial language, not only to technical mastery, but to complete conceptual understanding. This differs from typical U.S. curricula, which aim for dogmatic memorization of "rules," or expect students to reconstruct mathematical ideas from hands-on activities without much guidance. Put simplistically, this emphasis on careful and systematic guided instruction is just good teaching!

Communication between the children, with the teacher, and as a classroom community helps students articulate their learning. Explaining their reasoning helps children to remember – but it also assists the teacher with assessing the child’s needs and strengths – in order to plan appropriate instruction. It is classroom SILENCE we need to justify, not talking, and certainly not movement.

Assessment drives instruction and is crucial for meeting the needs of each student within the Singapore Math curriculum. Students struggling with particular concepts are given more experiences, different experiences, and more opportunities to develop necessary skills before moving along. Conversely, students needing less time to master a concept are moved along at a more rapid pace – to ensure that learning is continuous and all members of the learning community are being challenged.

The adoption of Singapore Math by SCVi is unusual. It is a program that demands excellence from teachers in order for the curriculum to be taught with fidelity and complete understanding. For this reason, SCVi teachers attended intensive training in Singapore Math in July and will continue to receive training during the upcoming school year. It is a program that will help our students become competent in math – essential for citizenship in the future global economy.