Singapore Math Method - Features

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 avalable 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 utilizes pictorial models to bridge the gap between concrete mathematical experiences (e.g., using objects to act out what math concepts mean) and abstract representation (using symbols like numbers to convey mathematical ideas). These pictorial models include, but are not limited to, bar models, number bonds, ten frames, arrays and place value charts.
4. 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 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?” 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.
5. The principle of teaching mathematical concepts range 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.
6. 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.
7. 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.
8. 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, 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.
9. 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).