Singapore Math

Singapore Math has gained in popularity in the United States in recent years.  Numerous schools, both private and public, have adopted it with varying degrees of intensity and success. But where did Singapore Math come from, and what makes it different?

Ironically, Singapore Math has its roots in the United States. Born October 1, 1915, American psychologist Jerome Bruner has spent a lifetime dedicated to understanding how humans perceive and learn. He graduated from Duke University in 1937, and obtained a PhD in pyschology from Harvard in 1941.

A pioneer of modern psychology, his work on human perception and sensation was important in establishing the concepts of cognitive psychology. Following his work on perception and sensation, he turned his attention to learning and developmental psychology. His work there led to a framework of how learning takes place that can be applied to various situations. The framework is broken down into 3 stages, also known as the 3-step learning process.

Enactive – Sometimes called the ‘concrete’ stage, the enactive stage involves interactions with the physical world and objects — how they fit together or come apart, how they can be grouped, etc.

Iconic – The iconic or pictorial stage is when learning occurs by looking at pictures or models.

Symbolic – The symbolic or abstract stage is where learning can take place in abstract terms.

Singapore Math aims to utilize these three stages, progressing deliberately through each. In the enactive stage, students are taught by using physical objects in the classroom — paper clips, crayons, or other objects that they can pick up, pile up, and shift around.  Subtraction, then, would be taking a few crayons from a pile, and figuring out how many are left.  This isn’t described as subtraction, so much as it is a demonstration of play.

In the iconic stage, Singapore Math has students drawing pictures — usually bar models — to describe ratios and simple equations.  The emphasis is on visualizing what happens


during the mathematical exercise. At this point students still aren’t thinking in terms of algorithms, equations, or even numbers.

In the symbolic stage, students start using numbers and equations. With concrete and iconic bases, the idea is that the symbolic stage will be more easily understood.

The application of Singapore Math in the United States has mad mixed results. Unless schools utilize the curriculum completely, it can fail. Also, since most Americans learned math a different way, parents may have difficulty helping their children with Singapore Math homework, instinctively teaching algorithms (stage 3) when the children are counting paperclips (stage 1).  Still, the concrete applications like this of cognitive psychology to learning are exciting steps toward improving education.


Hu, Winnie. “Making math as easy as 1, pause, 2, pause, 3.” Sept 2010, The New York Times, retrieved from

Macleod, Saul. “Bruner.” 2008, retrieved from


2 thoughts on “Singapore Math

  1. Stacey Dian Brantley

    Singapore Math – A Reply
    By Stacey Brantley

    As a parent of a Singapore math learner, your blog post struck a chord with me.
    My son has attended a charter school for the past six years that follows the philosophy of mastery learning in all subjects. In his fourth grade year, the school began using the Singapore curriculum as their standard method for math instruction. As it’s basis, Singapore math uses mastery learning and not memorization or “teaching to the test”, to provide children with a deeper understanding of the material. The curriculum, which sequences its topics based upon child development theory, also allows for students to learn at different paces thereby meeting each child where they are and permits for advancement at any time the student is capable of proving mastery. Singapore math also extensively employs visualization as a teaching tool – unlike the standard concrete abstract American approach of trying to use visual imagery; model and diagram drawing are used to assist in teaching word problems and multiplication respectively. Ultimately the method teaches children both the how and why of math and with mastery, a solid foundation is laid so that the need to reteach skills as the student moves to the next grade (summer learning loss) is eliminated.

    For more on Singapore math:


    Brown, Laura Lewis. What’s Singapore Math? N.d. Web. 27 Apr. 2014

  2. Jeffery Thomas Kerr

    This is an extremely interesting article. I am very interested in both math and hands-on learning, and this article explores both of these options. This article was especially interesting to me because it describes some of the cognitive processes involved in math.
    Lots of research has shown a strong connection between hands-on learning and mathematics and science. It has been shown that music can also increase knowledge through math because of the tactile response associated with music, and the counting that is involved. Applying the use of tactile elements helps engage certain cognitive functions, and boosts the way the mind works.
    Mathe is an extremely interesting subject to me and it is very impressive to see how they can compare aspects of it to psychology. I thoroughly enjoyed reading this article as it brought together both of my favorite subjects and helped me in relating them to one another.

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