In the United States

United States

The United States of America is a federal constitutional republic comprising fifty states and a federal district...

, Singapore Math is a teaching method based on the primary textbooks and syllabus from the national curriculum of Singapore

Singapore

Singapore , officially the Republic of Singapore, is a Southeast Asian city-state off the southern tip of the Malay Peninsula, north of the equator. An island country made up of 63 islands, it is separated from Malaysia by the Straits of Johor to its north and from Indonesia's Riau Islands by the...

. These textbooks have a consistent and strong emphasis on problem solving and model drawing, with a focus on in-depth understanding of 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.

Explanations of math concepts are exceptionally clear and simple (often just a few words in a cartoon balloon), so that students (Singapore is a cosmopolitan nation) can read it easily. The method has become more popular since the release of scores from the Trends in International Mathematics and Science Study in 2003 showed Singapore at the top of the world in 4th and 8th grade mathematics. This was the third study by the NCES, and the 2007 TIMSS was released in December 2008.

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

1. Each semester-level Singapore Math textbook builds upon preceding levels, and assumes that what was taught need not be taught again. Consequently, it is necessary to assign Singapore Math students to a textbook that matches what they are ready to learn next. (Placement exams are available online.) By contrast, the typical US classroom offers the same grade-level math instruction to all students, reviews previously taught math skills before teaching new skills, and gives more emphasis to topics that don’t build on previously taught math skills (bar graphs, geometric shapes, measurement units).
2. A great deal of instructional time is saved by focusing on essential math skills, and by not reteaching what has been taught before. In fact, some teachers report that Singapore Math feels slower paced than what they’re used to. However, the result is that students master essential math skills at a more rapid pace. By the end of sixth grade, Singapore Math students have mastered multiplication and division of fractions, and they are comfortable doing difficult multi-step word problems. With that foundation, they are well prepared to complete Algebra 1 in middle school.
3. Singapore Math students begin solving simple multi-step word problems in third grade, using a technique called the “bar model” method. Later grades apply this same method to more and more difficult problems, so that by sixth grade they are solving very difficult 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?” Consequently, when a school first adopts Singapore Math, the upper elementary grades will need to catch up on what they missed. This can be done by going through the problem-solving chapters in the preceding grade levels, or by using a Singapore Math Model Method supplemental textbook.
4. The principle of teaching mathematical concepts from concrete through pictorial to abstract. For example, introduction of abstract decimal fractions (in Grade 4) is preceded by their pictorial model of centimeters and millimeters on a metric ruler, but even earlier (in Grades 2 and 3) addition and subtraction of decimals is studied in the concrete form of dollars and cents.
5. Systematic use of word problems as the way of building the semantics of mathematical operations. Simply put, 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 any redundancies, and challenge students' understanding of mathematics only. This is different from many U.S. curricula, where word problems are to show "applications" of math and are spiced with immaterial details intended to obscure the mathematical content of the problem.
6. The need for repetitive drill is minimized by clever sequencing of the 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.
7. The use of bar-models in teaching problem solving (a form of pre-algebra). This device is as old as Book V of Euclid's Elements
   Euclid's Elements
   Euclid's Elements is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria c. 300 BC. It is a collection of definitions, postulates , propositions , and mathematical proofs of the propositions...
   
   , written in the 4th century BC, and consists simply in representing (mentally or graphically) arithmetical quantities by line segments. In SM books, such line segments are regularly used to show and teach one's thinking process in solving an arithmetical problem. For aesthetic reasons, the segments are typeset as colorful "bars" of a fixed width (hence bar-models). In this form, they fascinated many educators as being a miraculous "novel method" (hence Singapore Math Method) of problem solving. While mathematicians endorsing Singapore Math see the use of bar-models at best as one of many attractive features of the curriculum, the focus of the U.S. media and of education experts has been almost entirely on this feature.
8. The hallmark of the curriculum is the careful guidance of students, done in a child-friendly pictorial language, not only to technical mastery, but to complete understanding of all the "whys" (see an example). This differs from typical U.S. curricula, which either aim for dogmatic memorization of "rules," or expect students to reconstruct mathematical ideas from hands-on activities without much guidance (see Math Wars
   Math wars
   Math wars is the debate over modern mathematics education, textbooks and curricula in the United States that was triggered by the publication in 1989 of the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics and subsequent development and...
   
   ).

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. 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.

Other issues and observations

Alignment with state standards. 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. The US-adapted versions also include extra math topics that are currently popular in state math standards, but the textbooks try to use even these topics as a vehicle for teaching essential/core/focal math skills. By contrast, American textbooks often have state-specific versions or supplements that cover all of that state’s objectives, and they typically treat extra math topics as the primary focus of the chapters devoted to those topics.

Probability, Statistics, and Data Analysis. American textbooks and state standards currently give this much more emphasis than Singapore Math, the NCTM Curriculum Focal Points, the National Math Panel, and the proposed national Core Curriculum. The current American emphasis is on topics that don’t rely on prior math skills and are not developed further (defining probability, constructing tables and charts) rather than the core building blocks of statistical analysis (probability distributions, margin of error, hypothesis testing). Some analysts believe that even these non-core statistics topics offer real-world mathematical applications and 21st century skills, but the emerging consensus is that they should be almost entirely eliminated from the primary curriculum. Interim results of a comparative study of Singapore and US math education systems were released that show that Singapore students (who do not have a formal statistics strand in their curriculum) do better in the TIMSS tests involving statistics questions than do US students (who study statistics in each grade) in similar tests.

Teacher training. Teacher’s Guides are available for Singapore Math. Experienced trainers are also available, although schools may feel that teaching and learning from these books is so simple that teacher training is not needed.

Expense trade-offs. Paperbook Singapore Math textbooks are less durable but much cheaper than standard hardback textbooks. Also, unlike standard textbooks for which teachers create their own worksheets or the student copies a problem onto his or her own paper, Singapore Math textbooks have companion workbooks which are consumable (as is the entire kindergarten program). Potential adopters should compare the cost, quality, and convenience of consumable workbooks to the cost, quality, and burden of teacher-created worksheets and student-copied problems.

Cultural differences. Cultural differences between the US and Singapore, and among diverse cultures within the US, may be relevant. Cultural differences do have large impacts on student learning; however, that does not imply that students from different cultures respond differently to the distinctive features of Singapore Math – e.g., the focus on essential math skills, exceptionally simple explanations, and the bar model method of solving multi-step word problems.