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If someone will ask, “Is Math difficult?” Some people will automatically answer, “Yes! Very hard!”

Mathematics is one of the difficult subject a student may encounter. Many of them would say “I don’t like Math”, “Why we have to learn Math?” and “I don’t understand Math”. Mathematics is not difficult but it depends on how it is taught in school. Especially in some countries, where Math concepts are not taught very well.

Last 2015, Programme for International Student Assessment (PISA) organize by Organization for Economic Co-operation and Development (OECD) where 15-year-old school pupils around the world would take an exam on Mathematics, Science and Reading. When the result was released, Singapore came first especially in Mathematics.

Source: http://www.oecd.org/pisa/

Now, people would ask “How is Math taught in Singapore”, “What are their methods?” and lastly “What is the difference between Singapore Math and Abacus?”

In this Article, I would explain the difference between Singapore Math and Abacus and the method used in each concept. But first I’ll explain about Singapore Math.

## What is Singapore Math?

Singapore Math is a way to teach math to students in Singapore to help the students succeed. It also helps increase the level of proficiency of children.

It teaches students a systematic way of learning difficult math concepts using a child-friendly material. Singaporean Math uses *CPA Approach Method.*

Their curriculum focuses on

- Problem Solving
- Critical Thinking through mastery of foundation skills
- 21st-century competencies

**What is “CPA Approach” or Three Step Learning Process?**

Source: http://www.madisonpublicschools.org/

CPA Approach is all abstract ideas introduce by concrete materials which can be manipulated by using visual representation to represent the abstract concept.

It is developed by American psychologist, *Jerome Bruner*. It is a gradual and systematic approach to build child’s understanding. It also provides an effective way of teaching abstract~~s~~ concepts and as well as fractions.

There are three steps: *Concrete, Pictorial**, and Abstract*. CPA Approach is one of the fundamental theory used in the development of Singaporean Math.

*1.Concrete Approach*

Concrete is the “doing” stage where they use concrete objects as the model. In school, the teachers use the traditional way of teaching, where teachers demonstrate how to solve the problems but in CPA approach it brings math concepts into reality by allowing students to experience and use some concrete materials in solving by themselves.

For example:

Amber has 4 peso coins and her mother give another 2 peso coins. How much peso coins does she have?

In this step, there are no numbers only the materials needed. After this, they will proceed to the visual representation of the problem. It is called **Pictorial Approach.**

*2.Pictorial Approach*

The pictorial is the “seeing” stage where the children see the representations of the objects from the model problems. It encourages children to see a mental connection between the physical objects and abstract concepts by looking at the pictures, circles, or any model that represents the objects. Building or drawing a model makes it easier for children to visualize the problem, especially in fractions.

**Bar modeling** is a pictorial method used to solve word problems in arithmetic.

These bar models can come in multiple forms such as a whole-part or a comparison model.

For Example:

Amber has 4 peso coins and her mother give another 2 peso coins. How much peso coins do she have?

Concrete to Pictorial drawing

In this step, bar modeling is used to represent the peso coins. It is easier for students to see the difference because of the two colors used. After the pictorial drawing, this where *Abstract Approach*.

*3.Abstract Approach*

The abstract is the “symbolic” stage, where children can use abstract symbols to model problems.

Once a child already has a solid understanding of “*Concrete” *and *“Pictorial” *then the teacher can introduce the “*Abstract”. *Eventually in this stage, problems are represented using the symbolic concepts, such as numbers and mathematical symbols, for example the four basic arithmetic operations (+, -, x, /)

Concrete to Pictorial to Abstract

The children can answer the problem already. Thus, most children find it difficult to understand new concepts if they are directly introduced to the mathematical symbols and number. However, if that concept is introduced using some concrete materials like it is just a game. They find it much easier. As what *Benjamin Franklin* says, “*Tell me and I’ll forget. Show me and I may remember. Involve me and I learn”. * It tells that most children are visual learners.

So, what can you say about Singapore Math? Is their method easier than the usual method in school?

That sums up Singapore Math. Now, let’s discuss Abacus.

## What is an Abacus?

Abacus originated in Mesopotamia few thousand years ago, it is used as a calculating tool for trading well. And until now Abacus is still used in some countries and it is now included in their educational system.

It teaches students to activate the right brain usage through imagination. In Abacus education, the child has his own goals to achieve and works hard to accomplish them. Abacus teachers guides and supports the child to make these goals possible. This curriculum allows the child to concentrate more on achieving his goals.

**Abacus Education focuses on**

- Right Brain Activation
- Quick Calculation Skills
- High concentration Skills

~~【Abacus Education beyond the Border!】: http://ippo-abacus.com/abacus-beyond-border/~~

### What is the Method of the Abacus?

Learning Abacus is just the same as learning Singapore Math. It uses Abacus as the concrete materials. Abacus is not that hard to learn. It only requires your patience and hard work. In learning Abacus, the child’s right brain is used to picture out the image in the Abacus. It also tests student mental skills by doing mental exercise. Teachers do one on one teaching with students. Abacus function is to calculate the basic four operations (+, -, x, /). It is also used in calculating decimal and negative numbers.

**There are 3 benefits of learning Abacus;**

- Critical Analysis
- Problem Solving
- Thinking Skills

【Benefit of Learning Abacus】: http://ippo-abacus.com/whats-abacus/benefit/

Most children only use the left side of the brain which provides the ability to analyze information concerning languages and sound. However, the right side of the brain which is focused on thinking, creativity, and integration of information needs to be used and stimulated as well.

Scientific analysis indicates that abacus training in conjunction with mental math training can improve a child’s ability to concentrate, visualize, memorize, observe, and process information. Many children who are learning Abacus can also excel in other subjects.

【3 Reasons Why Leaning Abacus is Useful for Every Subject】: http://ippo-abacus.com/abacus-useful/

## Summary

- To sum up, Singapore Math and Abacus is almost the same in teaching math. They used visual representation in learning. These are the summary of attributes they have.

Singapore Math | Abacus | |

Method: | CPA Approach | Imagine the number then moving beads Concrete – Abstract |

Text and Materials: | Workbooks and Concrete Materials | Workbooks and Abacus |

Benefits: | Number Sense
Critical Analysis Problem Solving Concept Understanding |
Critical Analysis
Problem Solving Thinking Skills |

Age / Grade level: | Kindergarten to sixth grade | 3 years old and above |

Brain Usage: | Left and Right Brain | Left and Right Brain |

- Learning Abacus together with Singapore Math is also effective. It helps with all around brain development of children like concentration, listening, and creativity. Using both method, it will improve your child’s ability to calculate and analyze word problems.

What method do you like? Singapore Math or Abacus? Why not learn both?

Whatever you choose, the most important is that you understand the new concepts and analyze the problems.

Sources:

S.M.A India: http://www.seriouslyaddictivemaths.in/

Maths – No Problem: http://www.mathsnoproblem.co.uk/

Mastermind Abacus: http://www.mastermindabacus.com/

#### Richel

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