How are maths lessons developed in any primary school classroom in the world? The teacher poses a problem. The students look at the question and then work on solving it in their exercise books. They are alone facing the mathematical world. Armed with a pencil and a rubber, they pose and try to solve the calculations. Then someone comes to the board to solve it with the teacher. If the result and the calculations match those on the board, they have done it correctly. And then they start all over again. Memory, procedures that are not understood and lots and lots of calculations.
How does a maths class which uses the Singapore method work? The teacher poses a problem, and the students discuss how they will solve it together. Here we already have two of the main characteristics of this pedagogy: exploration and the construction of one’s own knowledge. Students contribute their ideas and solutions to the problem. The idea is to find the result using different paths to get there. Guided by the teacher, the students explore and discuss the problem together and, after analysing and solving it, they present their conclusions to others and reflect on them. All of this without having yet moved on to the individual calculations. First, understanding and reflecting on the learning process itself. Reasoning before calculating. Involving students in the whole process and teaching them to think for themselves. That is the approach.
Telling a story
Traditionally, discussion and storytelling have been far removed from maths classes, but with the Singapore method this is not the case. As we will see, based on the three phases of the method, the pupils tell a mathematical story, starting from a specific situation inspired by their everyday life.
The method proposes a sequential acquisition of mathematical knowledge, known as the C-P-A approach:
- Concrete phase: the problem is presented in a concrete way, giving priority to manipulation and exploration. The students discover mathematical notions through the manipulation of concrete, real objects that they have to hand.
- Pictorial or visual phase: students create a graphical representation of the relationships between the quantities or the underlying mathematical processes that solve the challenge or problem. The objects are replaced by images, using bar models.
- Abstract phase: this third stage links these processes with the algorithms and formulations of more abstract mathematics. We find the corresponding mathematical calculation.
The Singapore Method website lists the main pedagogical rules of the method. These are:
- Spiral progression curriculum: as opposed to the traditional linear progression curriculum, this curriculum design involves the reinforcement of prior knowledge with the teaching of new knowledge, which reinforces learning and contextualises it as a whole. Reviewing what has already been learnt and making sense of it in a new context generates meaningful and comprehensive learning, as opposed to merely operational learning with a linear curriculum design.
- Thebar model: one of the most powerful and relevant of all modelling strategies (though not the only one), due to its versatility and application possibilities. The model helps students to have a greater understanding of concepts such as fractions, ratios or percentages; to establish a step-by-step plan for solving arithmetic problems; to make comparisons; and to engage in solving challenging problems. It also develops students’ lateral and creative thinking.
- Algebraic thinking: functional relationships, patterns and numerical relationships etc., always using the spiral curriculum and presenting each lesson on previously learnt concepts.
- The C-P-A approach: Concrete, Pictorial, Abstract. We have already discussed the three sequential phases of the method.
- Teaching model connected to learning objectives: teachers who use the Singapore method approach their teaching based on a variety of influences from psychologists, educators and mathematicians combining behavioural trends and cognitive psychology, among others.
Teachers using the Singapore method: drivers of change
What is the role of the teacher in this teaching method? What challenges do they face in applying this methodology, which is so different from more traditional ways of teaching?
As we have seen, in applying the Singapore method, the main role of the teacher is to encourage participation in discussion and collaboration among their students. They become a kind of facilitator who guides their students in the problem-solving process. We could also say that they become one of the learners themselves, by participating in the ideas and solutions proposed by their pupils. This can pose some challenges for teachers:
- High adaptability: in this regard, the teacher must make a 180-degree turn in their teaching methods. Class lectures in which the teacher does all the talking and the students just listen are no longer useful. The Singapore method works with students in a collaborative way.
- Understanding the students’ proposals: as a consequence of using this method, by letting the children think about the solution to the problem for themselves, the teacher who intends to apply this method must overcome the fear of not always understanding their students’ proposals and the way they think.
- The inertia of tradition: we teach as we were taught. That is a fact. A Singapore method teacher has to face the inertia of tradition, an endless loop of repetition of what they learnt from their teachers in the past.
- Deep conviction: in order to be able to apply this method, a deep understanding and conviction is required, the result of intense reflection on the very nature of teaching maths.
In short, this method teaches strategies that help students to visualise and conceptualise problems to gain greater control of “mental arithmetic”, as well as to strengthen their skills in problem-solving in a creative way, substantially improving their passion for mathematics, which is vital.
This method, part of a profound revolution in education and teaching, has led a small and poor country which had few prospects for the future only 50 years ago, to become one of the most prosperous states in the world. A small example of the transformative power of education.
If you would like to know more details about this method, visit the website in Spanish. You can also find out more about the method on the international website.