Singapore math is a term assigned to the newly developed math curriculum in Singapore that stands out because of its distinct learning approaches that focus on understanding concepts and problem-solving.

These main approaches are Concrete Learning, Pictorial Learning, and Abstract Learning. It is different from general math curriculums that involve examples or formulas that the child often replicates when solving a question independently. In the Singapore Math method, the focus is more on learning skills to solve any kind of problem instead of rote learning formulas restricted to the syllabi.

Even though all methods and approaches have both benefits and shortcomings, teachers^{[1]} have supported this approach to learning. Singapore math is also adopted by schools outside Singapore because of its learning philosophy.

**Singapore Math: What is it, and what makes it different from usual Math?**

Singapore math is an approach to teaching mathematics in a way that is focused on learning to solve problems and develop mathematical thinking. Basically, in this approach, the idea is to build a foundation and aptitude for mathematical skills rather than teaching how to solve a question on the topics given in their textbooks.

Singapore Math is different from usual math in both its goals and approach to learning. Unlike usual math, Singapore math does not focus on rote learning or memorization of concepts through similar problems. In usual math, often, children are taught through solved examples and then asked to apply the same concept in the questions they are presented with by using similar steps on different numbers.

On the other hand, the Singapore Math approach would aim at getting the child to think from a mathematical perspective and explore the problems on their own without a proxy answer. This promotes creative thinking and greater mental engagement. Students^{[2]} who are taught Singapore Math have been found to demonstrate more knowledge of mathematics than students taught traditional approaches.

**Characteristics**

Singapore math is based on an objective learning method. The major characteristics of this method are centered around the CPA (Concrete Pictorial Abstract) approach. These steps or stages are discussed in detail below.

**1. Concrete Learning**

This approach to learning ensures that children learn through experiences that enable them to develop a good understanding of concepts such as numerical, algebraic, statistical, and analytical concepts. For the same, concrete materials like cubes, blocks, place value mats, and base blocks, and geometric figures are used. Learning in a concrete manner also involves practical work as a part of the process. This stage is the “doing” stage.

**2. Pictorial Learning**

In this “seeing” stage of learning, the concrete learning model is converted into a pictorial form. This involves model drawing, circles or number dots, and visual representations of concrete objects. Building or drawing a model makes the learning process engaging as well as enjoyable for children, further making it easier for children to grasp the concepts.

**3. Abstract Learning**

Abstract learning is the ‘symbolic’ stage of the CPA approach. To reach this stage of learning children must have a solid understanding of the concrete and pictorial stages. In this learning stage, the teacher introduces abstract concepts to children such as numerical symbols and lets them reflect upon the same. These symbols can be notations or mathematical symbols such as +, -, or x, to indicate the process of addition, subtraction, or multiplication.

**Examples**

**1. Teaching Addition**

In a Singapore math method, if the teacher wants to teach the method of addition using an example of fruits, like apples, she might set up a classroom in which children have several apples in their own baskets. Now, she may ask children in pairs to give a specific number of apples to their partner and then count the total number of apples with their partner. This way they will learn the concept of addition.

**2. Teaching Long Division**

For this, the teacher might show a number of candies to the children and tell them that she wants to put them in some jars. Now, she can place the candies and some jars on the table and say that she wants to have 21 candies that she wants to put in 4 jars equally. The children can be asked to think about how that can happen and then share their insights.

**Pros and cons of Singapore math**

Although the Singapore Math method promotes creativity and makes children learn from a more objective perspective, all methods have their own benefits and shortcomings. These are discussed below.

**Pros**

- The Singapore Math method facilitates children to follow a way of semantic learning in which they learn the meaning of the concepts rather than just memorizing them.
- This approach to learning stands parallel with the Common Core State Standards Initiative
- It ensures students build a solid foundation and meaningful learning of concepts which leaves fewer opportunities to go back to concepts and relearn them as would be required in usual curricular learnings.
- The textbooks and workbooks are simple, visually stimulating, and enjoyable. They are also developed in a sequential manner where knowledge and skills are put across on the basis of previously learned concepts which further accelerates learning.

**Cons**

- The Singapore Math method may not work well for children who keep moving in and out of schools due to their parents’ jobs or any other reason. Adapting to an education program that is different from those in all other schools they have been to can be challenging.
- It is not cost-effective. It requires extensive training for school staff and especially teachers and educators on a regular basis which makes it expensive and nearly impractical.
- Singapore math focuses less on applied mathematical concepts such as data analysis than the U.S. math textbooks in curricula like Everyday Mathematics common there.

**Is Singapore math too hard?**

Although Singapore Math can seem tough to adapt to initially as students may require to unlearn the concepts of math that they have learned previously, when the learning in the method is embraced and children ease into it, math, in general, seems like an easier subject to learn.

Singapore math flows very well over the years due to its sequential method of learning. This helps children reinforce the concepts learned earlier on every step that they take next. It can be said that relative to usual math, Singapore Math is not harder but it requires more effort from the children to be actively present in the learning process. The course is demanding because it involves children, not because it is complex, it is deceptively simple^{[3]}.

**Conclusion**

Singapore Math is a methodological approach to math that was developed in schools to change the way math was being taught. This approach directs learning in a more objective and semantic way where the focus is on the meaning of concepts and the development of skills for students to think mathematically instead of learning formulas or theories.

It involves concrete learning, pictorial learning, and abstract learning where all three are centered around the idea of engagement, participation, creativity, and skill enhancement. Each child is left to their own thinking and reflection and is free to explore their own methods of problem-solving. Although Singapore math is expensive and extensive, it is now widely used by many schools even outside Singapore and has turned out to be quite successful^{[4]} in the field of education.

**References**

*Mastery mathematics: Changing teacher beliefs around in-class grouping and mindset*. (2018). Pete Boyd.*The impact of Singapore Math on student knowledge and enjoyment in mathematics*. (2011). Blalock, Jenny Taliaferro.*Singapore Math: Simple or Complex?*(2007, November). John Hoven and Barry Garelick.- Hoover Institution Press. (2006).
*Miracle math: a successful program from Singapore tests the limits of school reform in the suburbs*. Barry Garelick.