Singapore Maths by Judy Hornigold

Singapore consistently ranks at the top of the international assessment of student maths achievement called the Trends in International Mathematics and Science Study (TIMSS). Consequently, many countries are now looking to Singapore to find out about their approach to maths and why it is so successful.

For some people, it appears that Singapore Maths is the ‘new kid on the block’ and may be wary of yet another new initiative. However, nothing could be further from the truth. The approach to teaching maths in Singapore centres around problem solving and draws on research from very familiar names in educational theory.

The five main players in the approach are, Piaget, Dienes, Bruner, Skemp and Vygotsky. Their research spans four decades from the 1950s to the 1980s, so it is clear that Singapore Maths is nothing new.

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In the 1950s Piaget was advocating that if we teach less, the children will learn more as they will have more control over their learning and will be more involved in the exploration and discovery of new concepts. Bruner in the 1960s, introduced the concept of the spiral curriculum and the Concrete Pictorial Abstract approach which underpin the Singaporean method for teaching maths.

Zoltan Dienes taught us that children need to explore the maths informally before formal methods are introduced and then they should have the opportunity to stricture their thinking. It was Dienes who introduced the wooden blocks that we now call Base Ten blocks.

In the 1970s Skemp identified two types of learning in Maths; Instrumental and Relational. He emphasised that the ‘why’ in maths was just as important as the ‘how’.

Vygotsky in 1980s talked about constructivism and how children talking together will help to construct their understanding of a mathematical concept.

The work of these great theorists has been combined together to produce the approach that is now referred to as Singapore Maths.

Singapore Maths focuses on five core competencies in maths that children need to develop in order to be successful mathematicians. These are:

– Visualisation

– Generalisation

– Number Sense

– Metacognition

– Communication

These are areas that children with learning differences such as dyslexia and dyscalculia may struggle with, so the emphasis on these five competencies can support their understanding of maths, by helping them to strengthen these weaker areas.

Visualisation is a key skill and is the Pictorial element of the Concrete – Pictorial- Abstract approach that was championed by Jerome Bruner in the 1960’s. All too often maths teaching jumps from the concrete straight to the abstract and this leaves the children with an incomplete understanding of the concept and an inability to ‘see’ the maths.

Generalisation encourages the children to use what they already know to find out what they don’t know. For example, using the fact that 5 + 5 = 10 to help them to state that 5 + 6 must be 11.

Number sense is all about how we understand the relationships between numbers and how our number system works generally and enables children to find the most elegant and simplest solution to a problem. All too often our struggling children are actually relying on procedures that may be inefficient and long winded, making maths inaccessible and over complicated.

Metacognition is how we ‘think about our thinking’ and is a way for children to reflect on the strategies that they use and to consider the best approach to solving a problem. Children with learning differences are not afraid of effort, they just don’t always know what type effort or approach they need. Metacognitive awareness will help them to develop that skill.

Communication is key in this approach with the children spending that majority of a lesson working collaboratively. This can be very supportive for the child who is struggling, as they are not working in isolation and can harness the support and explanations of their peers to further their understanding.

I have no doubt from my experience with the children that I work with, that Singapore Maths is one of the most effective ways of teaching maths and will be beneficial to all children, whether they have specific learning differences or not.

Judy Hornigold