Singapore Math: New Trend?
The Singapore Math method is not new. Concepts and teaching styles that closely resemble Singapore Math are the preferred method of instruction in countries like Singapore and Japan, whose students have historically outranked their global counterparts in math performance. In 2018 Singapore students ranked highest by a landslide in the Pisa Global Competence Test, conducted every three years by the Organization for Economic Cooperation and Development (OECD) to test for math, science, and reading skills. About 46% of Singaporean students achieved the highest levels of competency--more than three times the global average by percentage. And Singapore was no stranger to the top of the pile, ranking 1st in the overall Pisa assessment program in both 2012 and 2015. That’s enough to make any instructor sit up and pay attention to exactly how math is being taught in Singapore and what principles can be drawn from it.
More than a curriculum or a set of performance standards, the Singapore Math method is a philosophy. Singapore Math focuses on helping students understand and then to master root concepts, and then builds from the conceptual to the practical. Singapore Math unapologetically starts out slow but boasts of great efficiencies as students progress. Students do not need to be retaught previous concepts and can advance to more difficult problems without hesitation. Moreover, students are subconsciously developing a profound intuitive understanding of the math concepts they are learning, setting them up to take leaps and bounds in complexity and mental modelling in more advanced stages of their learning career.
The Singapore Math Three-Dimensional Approach: CPA
Singapore Math teaching breaks down any mathematical concept into three dimensions, building the students’ understanding of the problem from something relatable to something more abstract. This is known as the CPA approach, and goes like this:
Work with Concrete objects and manipulatives** to model a simple problem.
Represent the model Pictorially, enabling students to connect their understanding of the physical problem to visual and mental representations.
Translate and apply these model-based concepts into the Abstract symbolic and numerical language we recognize as mathematics.
**What is meant by manipulatives are concrete objects that we can move around and “manipulate.” These might be blocks, playing cards, fingers, coins, or even little action figures that the children can move around to model addition, subtraction, multiplication, and division. In an online setting, it is typical to move around objects on a screen such as circles, squares, or little pictures.
Up Against Algebra
Where this differs from traditional Western mathematical teaching is in leaving the abstract symbolic and numerical representation of problems and answers until last. This difference unlocks the power of Singapore Math instruction, and is also sometimes a contention point for criticism.
Typical Western mathematics focuses on symbols and numbers. You won’t get through too many math classes without encountering a unit on algebra. This, unfortunately, is where some students get lost. Algebra, the language of math, is truly a separate and abstract language in the same way that musical notes differ from the sound we hear. Students found wanting for the abstract language skills to master it are left believing that they are equally unable to master the concepts behind the symbols.
Singapore Math instead teaches students using concrete, relatable objects, problems, scenarios, and visuals, and leaves the language of math as just that: a symbolic representation of a very real concept. That is, of course, how mathematics first emerged: mathematicians needed ways to efficiently and universally explain and extrapolate realities they were seeing around them.
“But,” one may argue, “when my future engineer is trying one day to calculate the forces of speed, inertia, and stability on an industrial crane picking up a precarious load, or when my future finance major is attempting to determine the historical statistical deviation of a group of stocks from index returns, do you really expect him or her to be counting out blocks? I mean, how many fingers do you think he has?”
A fair point. But it is a point that misses the power of Singapore Math completely. Singapore Math does not downplay the importance of mathematical language that has taken humanity’s most brilliant minds centuries to develop—and they continue to develop it today—but rather, it allows students to take their time in understanding the concepts that the symbols depict, empowering them to unlock the full power of the math language tool.
The Power of Intuitive Understanding
This hits on the crux of Singapore Math’s strength: the more intuitive and relatable the understanding is, the more flexible a student can be to manipulate variables to better reflect, model, hypothesize over, or predict real-life situations of vast complexity. Singapore Math’s focus on intuition not only enables the youngest students to understand how to apply the simple concepts they learn over and over again, but it empowers a generation with mathematical agility so that they can navigate the obstacle courses of today’s modern math problems.
Engineering. Computer science. Space exploration. Biological research. Economic management. Sports math. Agricultural innovation. Automation.
Today’s modern world is changing at a faster rate than we have ever seen before. It is crucial that the math specialists on the frontiers of new and exciting fields of study not only have a deep understanding of what math has already been shown to do, but can adapt and stretch that knowledge to dig into never-before-seen problems. Intuition is key to that kind of mathematical flexibility, and it all starts for your young child in a classroom setting where they can learn, for the first time, how they relate to the math problems they face.
Next week, we’ll start to explore exactly how the CPA method works and how it differs from other teaching methods, such as spoonfeeding and rote training.
Article Sources
Davie, S. (2020, October 22). Singapore's 15-year-olds top OECD's Pisa global competence test. The Straits Times. https://www.straitstimes.com/singapore/parenting-education/singapores-15-year-olds-top-oecd-global-competence-test.
Dean, M. E. (n.d.). Singapore Math vs. Common Core: What’s the Difference? Argo Prep. https://argoprep.com/blog/k8/singapore-math-vs-common-core-whats-the-difference/.
Morin, A. (2021, May 21). What Is Singapore Math? Very Well Family. https://www.verywellfamily.com/singapore-math-pros-and-cons-620953.
Teng, A. (2019, December 3). Pisa 2018: Singapore slips to second place behind China but still chalks up high scores. The Straits Times. https://www.straitstimes.com/singapore/education/pisa-2018-singapore-slips-to-second-place-behind-china-but-still-chalks-up-high.
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