Following their poor performance in international league tables in the early 1980s, the Singapore Ministry of Education drew on the best practice research findings from the West and applied them in their classrooms. Now, Singapore is consistently at the top of the international benchmarking studies for mathematics and also scores well in science and reading. Countries all over the world, including the UK, is drawing on Singapore’s Mathematics teaching to improve children understanding. For me, one of the key benefits of this approach is that pupils learn to think mathematically. In other words, they understand what they are doing, they are not just using a method blindly.
Some of the learning theories Singapore maths draws on include:
1. The CPA approach – C for Concrete, P for Pictorial and A for Abstract, based on Jerome Bruner’s theory of representation. The idea is that abstract ideas are introduced firstly by concrete resources (such as dienes blocks) and then by visual means. It is one of the fundamental theories used in Singapore mathematics through strategies such as the bar model. Read the example Year 6 question below and see how it has been broken down visually.
To start with, the blocks show that Sam has 5 times as many marbles as Tom (before). We know that Sam and Tom end up with the same amount. If we look at the picture, it becomes clear that Sam gives away two blocks (after). We know those two blocks are worth 26 because the question tells us that Sam gives away 26 marbles. What we then need to find out is how much is 1 block worth, then, how much is there altogether.
2. Relational and Instrumental Understanding: conventional understanding, conceptual understanding (relational) and procedural understanding (instrumental). In Singapore maths, all procedural understanding (how you do something) is supported by conceptual understanding (understanding how and why you do something). In other words, students should be able to explain whatever they do. This approach is based on Richard Skemp’s idea of relational understanding. Have a look at the Year 6 question below.
3. The Spiral Approach: based on Jerome Bruner’s idea that children revisit the core areas they have learnt but at a higher level each time. Eventually, the abstract representation is acquired by revisiting the same concept.