The Singapore method

It's a fact that French pupils are having more and more difficulty at school, particularly in math. Gaps appear right from the start of learning, in primary school. By the time they reach middle school, some are already overwhelmed and drop out fast. It's a downward spiral, and it's hard to get them interested in studying again. That's why they need an effective method in primary school to ensure that they have a good foundation and that each stage is acquired definitively.

In mathematics, the Singapore method was created to give these young students the opportunity to better understand and learn.

What does it involve? What are its advantages? Is it really effective?
Here are the answers to your questions about this method from elsewhere.

How does the Singapore Method work?

The Singapore method consists in giving a picture to mathematical problems to better understand the usefulness and functioning of this subject. Students first visualize a diagram or object, then gradually replace it with a number. Addition, subtraction, multiplication or division - children learn all this right from the start of primary school, down to the smallest detail, so that they don't have to go back to it in secondary school. They progress slowly but surely. Pupils invent stories around calculations.

The importance of modeling
To solve a problem, students draw a diagram, often with bars of different lengths. In this way, a situation that might seem complicated, even for older children, becomes very easy thanks to this method. This will make things much easier for them in later years, when they study algebra.

The "concrete-imagined-abstract" principle
The principle is to move from a concrete to an abstract situation. This is done in three stages:

1. concreteness: children in particular retain much more through the visual. To understand, they need to touch, manipulate and see the object. To do this, the teacher needs to replace the data in a math problem with an object: cubes, sticks, tokens, etc. The students can then manipulate them as they wish. Pupils can then manipulate them as they wish.
2. pictorial: the object is replaced by a picture or diagram.
3. abstract: once children have understood the principle, the mathematical situation can be solved using numbers, symbols and formulas.

The benefits of verbalization
Students ask questions of the teacher and exchange ideas with their classmates. Why? How? etc. The answers they give are simple and make it easier for them to remember the work they've just done.

Understanding this learning method

Where does this method come from?
The Singapore Method was created around the 1980s by a team of mathematics educators commissioned by the Singapore Ministry of Education. Reasoning was tested and developed there to raise students' academic level in mathematics. Thanks to this approach, students have become the best in the world in this subject according to TIMSS(Trends In International Mathematics And Science Study) assessments.

However, we can't say that it's revolutionary, because it's actually based on research from all over the world, and particularly from Western countries. Maria Montessori, Georges Polya, Jerome Bruner and Célestin Freinet are all familiar names. The Singaporeans have synthesized this research into an effective method. In 1998 manuals arrived in the U.S. and then around the world (nearly 60 countries).

In France, they arrived in 2007. Mathematician and Member of Parliament Cédric Villani presented a report based on the Singapore method, hoping to raise children's level in this subject. Today, over 2,000 classes have switched to this method.

Significant advantages
The method is a success in many countries because it offers a number of advantages:

• acquisition of a solid foundation: the various situations are solved in depth, and students begin mathematics in good conditions.
• fun and attractive: manipulating objects gives rhythm to the lesson, making children more attentive.
• understanding of all pupils: there's no comparison of levels, they can all do it. They better assimilate the relationship between addition and subtraction, then multiplication and division.
• improved self-confidence : the principle is to encourage the pupil in difficulty and not to label him or her.

What are the limits?
Although the method seems ideal, there are a few limitations:

• teaching can seem long. In first grade, it takes a long time for pupils to tackle simple subjects without talking about arithmetic. So you have to manage your time well.
• the method has to be adapted to France. We can't just copy and paste; the exercises and explanations have to be done in the French style.
• French education is not the same. In Singapore, the quest for success is very real. Children are tutored from an early age, and the spirit of competition has nothing to do with France.
• teachers need training. The method is new, and training is essential if we are to achieve a high success rate.

About teacher training
To put this recent method into practice, training is essential. Teachers need to be able to ask children the right questions and answer them as simply as possible.

In Singapore, students have ranked top in world assessments in recent years, thanks in part to teacher training. There, they have nearly 400 hours of initial training in the subject, as well as 100 hours of ongoing training per year. In France, we're a long way off, with just 80 hours of initial training and 18 hours of continuing education. In the recently published Villani report, the MP and mathematician recommends more intensive teacher training. The investment is greater, but well worth it for the future of education in France.

A multitude of tools for the Singapore method

To use this new method, tools are mandatory for the long modeling stage. Games and kits are available to allow children to manipulate them as they wish, and to add a touch of fun. Teachers usually use cubes or tokens.

A more original approach is to use pizza-shaped toys, for example. A slice of pizza represents a number, ideal for the notions of fraction, quarter or half. Rulers are perfect for explaining the principle of adding and subtracting. They better understand what a unit and a dozen mean. Everyday objects can be used: cups, magnets, dice, stickers, etc., as long as they are easy to handle and not dangerous. Cards and pictures are useful for the pictorial stage. They can be used to replace objects with images.

All geometric shapes are suitable for this apprenticeship. Pupils need colored pencils and drawing paper. Stickers are also a good idea. Their textbooks and workbooks are full of colorful drawings and attractive math problems.

The similarities between the Singapore and Montessori methods

The Singapore method is reminiscent of Montessori pedagogy. The principle of object manipulation is the same. To better understand, children must touch and move cubes, beads and other shapes. The emphasis is on play, with workshops replacing long lectures by teachers. Montessori classrooms have been set up all over the world, and the materials used in schools are a great success.

Based on the same principle as the abacus

Finally, the abacus and the Singapore method are similar in spirit. These instruments, dating from the 13th century, are used to calculate the 4 arithmetic operations: addition, subtraction, multiplication and division. In a rectangular frame, balls are hung on rods, which can be slid around.

We're all familiar with the Chinese abacus (Suan pan), but there's also the Japanese abacus (Soroban) and the Russian abacus (Stchoty). The Greeks, Indians, Egyptians and Mexicans all used the same method.

The notion of manipulating objects to calculate is identical.

A few tips for getting started with the Singapore Method

A teacher who wants to try out the Singapore Method in the classroom needs, first and foremost, to know the rules and follow a few tips to ensure that everything goes as smoothly as possible.

Focus on object handling
The object handling stage is crucial for students, as this is when they understand the principle of the 4 operations, fractions and the different terms (tens, hundreds, etc.). It's important to give them time to get the basics right.

Time management
With this approach, the teacher may have the impression that the work is not progressing. However, once the children have assimilated the material, the work can progress very quickly. The teacher must therefore be careful not to be too fast or too long, as the program may not be completed and the children may become bored.

Letting students fend for themselves
Leaving children to their own devices allows them to follow their reasoning through to the end. They discover that the solution to the problem is not the right one and start again. The teacher can then explain why it doesn't work that way, and they learn faster.

Enjoy working in a group
There's a lot of group work involved. Students get together and discuss possible solutions. The shyest and those with the most difficulties can participate, as everyone helps each other out.

Being patient
Not being afraid of repetitive work is one of the keys to successfully teaching the Singapore Method. You may think that the exercises are the same every week, but it's worth being patient.

Good training
The Singapore Method can't be improvised. It's important to have the right training to be able to teach it properly. The better trained the teacher, the better he or she will be able to explain to young students. In Singapore, teachers have succeeded in raising math standards thanks in part to their solid training.

Long-term vision
To see the results of this method on children, they need to follow this learning method for several school years and, if possible, not just in elementary school. It's over the long term that results can be seen.

Our conclusions on the Singapore Method

The Singapore method has been very successful in recent years, just about everywhere in the world. The principle is to explain mathematical problems to primary school pupils in a playful way. They move from the concrete to the abstract without realizing it. Some see it as the miracle solution to the shortcomings of the French in this subject, while others say it's almost a "copy-paste" of the Montessori pedagogy founded over 100 years ago.

Even if, thanks to this method, Singaporeans are the best in the world in mathematics, can France expect a success rate similar to that of the city-state? Aren't there limits? Are the recommendations of the Villani report useful and applicable in the classroom?