What Is Singapore Math?

Student working on math problem with a teacher
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The Singapore Math method marked a change in how math was taught in many American classrooms and homeschool settings. The program uses a three-step learning model, moving from the concrete (such as showing something using manipulatives) to the pictorial (creating a visual representation on paper) to the abstract (solving problems).

Singapore Math closely aligns with the Common Core State Standards Initiative, which may be positive or negative, depending on your views about Common Core. The sequential learning allows students to grow without unnecessary busywork, which is great for many students but may be confusing for those who drop into the curriculum later because of a move or a change in schools.

What Is Singapore Math?

It’s not the content that makes Singapore Math different from other methods; it’s the philosophy. Rather than rote memorization, the framework of Singapore Math is developed around the idea that learning to problem-solve and develop mathematical thinking are the key factors to being successful in math. Without a solid foundational base, students won’t have anything to draw on when it comes to increasingly complicated math learning.

This doesn’t mean, however, that the skills elementary students learn are simplistic. Rather, the view is that when teaching a concept or a skill, it’s essential to spend as much time as needed for students to master the skill. That way, you’re not moving on to the next concept with the thought that earlier skills can always be retaught if necessary. Teachers can simply revisit instead, opening up more instructional time.

The CPA Approach

The method uses a three-step learning model, which consistently introduces concepts in a progression. It moves from the concrete to pictorial representation and then on to the more abstract (Concrete, Pictorial, Abstract or CPA). Students learn not only to know how to do something but also why it works.

History of Singapore Math 

What is referred to as Singapore Math in other countries is, for Singapore, simply math. The program, developed under the supervision of the Singaporean Minister of Education, was introduced as the Primary Mathematics Series in 1982.

In 1998, Jeff and Dawn Thomas realized that the math program they brought back from Singapore and used to supplement their own child’s schoolwork could be helpful to schools and homeschoolers across the nation. As the program began garnering attention, the couple incorporated under the name Singaporemath.com Inc. and marketed their books under Singapore Math, a registered trademark.

In the U.S., Singapore Math first gained popularity among homeschoolers and small private schools. Singapore is consistently a top country in Trends in International Mathematics and Science Study (TIMSS), revealing Singapore’s fourth-graders and eighth-graders as the leading math performers in the world. Of note, Singapore remains the top-performing country as of the 2019 TIMSS.

Singapore Math Curriculum 

With so much interest in the method, in 2007, U.S. educational publisher Houghton-Mifflin Harcourt teamed up with the leading academic publisher in Singapore to publish and distribute a math series called "Math in Focus: The Singapore Approach." This series and the Thomas' "Dimensions Math" and "Primary Mathematics" are the only curriculum packages available to United States educators and parents for teaching the Singapore math method.

The Singapore curriculum comes with a textbook, workbook, and teacher’s or home instructor’s guides. The textbooks present new concepts, the workbooks offer practice to solidify the concepts, and the guides provide lesson plans and instructions for using the books.

Singapore Math in Action 

A typical third-grade math instruction might go something like this: "Today we’re going to learn about long division." Students watch while the teacher demonstrates the steps and actions necessary to solve a long division problem.

Singapore Math instruction looks different. Instead of watching a demonstration of a new math concept and then doing similar problems to reinforce the idea, students are tasked with mastering the theory at the onset.

For instance, with the long division example, a parent or teacher might say, "I have some pennies I want to put in some jars." The instructor then places baggies of pennies and jars on the table. They then clarify, "I have 17 pennies I want to share equally in 5 jars." First, students must figure out how that might work and then share their ideas about what sharing equally means and how they approached the problem.

Singapore Math Pros and Cons

Singapore Math’s unique focus on building problem-solving skills aligns with the Common Core State Standards. While some people see this as a benefit, others find it more detrimental.

Some find Singapore Math confusing for children to learn as part of a Common Core Standards framework and find that it unnecessarily complicates the teaching of mathematical principles to young children.

Pros 

Singapore Math is popular with homeschoolers, private schools, and public schools alike—and for good reason. Research into the pedagogy of countries whose students excel in math, like Singapore and Japan, has found these countries’ use of diagrams in teaching math can provide a valuable bridge between early and advanced learning stages and encourage intuitive problem-solving skills.

Some benefits of Singapore Math include the following:

  • It asks for students to build meaning to learn concepts and skills instead of rote memorization of rules and formulas.
  • It aligns with the Common Core State Standards Initiative.
  • It covers fewer topics in a year but in an in-depth way that ensures students have a foundation to move forward without needing to relearn concepts.
  • Textbooks and workbooks are simple to read with clear and concise graphics.
  • Textbooks are sequential, building on previously learned concepts and skills, which offers learning acceleration without additional work.

Cons 

Despite the number of pros to Singapore Math and some research suggesting that it is superior to traditional U.S. textbooks, some schools find that the method is not easy to implement. 

Some drawbacks of Singapore Math include the following:

  • It aligns with the Common Core State Standards (yes, this can be a pro and a con, depending on whom you ask).
  • It may not work well for a nomadic student population. Many students move in and out of school districts, which isn’t a big problem when the math programs are similar. However, since Singapore Math is sequential and doesn’t re-teach concepts or skills, using the program could potentially set these students up for failure whether they’re moving into or out of a district using it.
  • It has less of a focus on applied mathematics than traditional U.S. math textbooks. For instance, Everyday Mathematics, a curriculum developed by the University of Chicago, which came out around the same time as Singapore Math, emphasizes data analysis using real-life, multiple-step math problems. On the other hand, Singapore Math’s approach is more conceptual and ideological.
  • It requires extensive and ongoing teacher training, which is neither financially nor practically feasible in some school districts and not always practical for homeschooled children.
  • Supplies are consumable and must be re-ordered for every classroom every year, which can put a financial burden on already strained school budgets and homeschoolers alike.

Frequently Asked Questions

How do you teach Singapore Math?

Teaching Singapore Math follows a Concrete, Pictorial, Abstract (CPA) approach that helps students understand math by building on existing knowledge. In the concrete phase, you will encourage students to interact with physical objects to work out problems. In the pictorial step, you will help students mentally connect their objects and visual representation. In the abstract phase, you will guide students to use numbers and math symbols.

How is Singapore Math different?

Singapore Math differs from other math curriculums in its approach. Instead of rote memorization and drilling concepts through similar problems, Singapore Math teaches students how to mathematically think so that they can rely on the theory and build on concepts.

How can I help my child with Singapore Math?

Remember that Singapore Math utilizes a progressive learning process that includes helping kids understand the concrete, the pictorial, and the abstract. If you are your child’s teacher, be sure to utilize the teacher’s guides, which offer lesson plans and instructions. Whether you are homeschooling or supporting a child who attends public or private school from home, you may find online communities, like Singapore Math’s Facebook group, helpful.

How do I know what level to start at in Singapore Math?

Singapore Math’s grades align with U.S. schools. Even so, it may be helpful to have your child take Singapore Math’s placement test.

What grades does Singapore Math cover?

Singapore Math is for students in Pre-K through 8th grade.

What comes after Singapore Math?

Since Singapore Math teaches students critical mathematical thinking skills, students can transition to nearly any math curriculum after Singapore Math.

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8 Sources
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