Math in Singapore
“Teacher, you have an obsession with drawing,” a cheeky student said to me a while ago. She had a point: I often try to get students to visualize math problems, first on paper and later in their heads.Later, I found out that with this approach, I am in the good company of teachers in Singapore, where students rank among the top 4 in the world in math. Countries like England and the US have adopted this approach and are now working hard to surpass the Netherlands on this list. By the way, this approach is not entirely new or unique: many elements of it can be found in our own ‘realistic math education,’ which has been criticized a lot lately. I do not share this criticism: in my opinion, the stagnation in math levels recently is not due to realistic math education, but because of education budget cuts and other societal developments in recent years. I think of class sizes, resources for special needs children, the level of teacher training, computing instead of reading, etc.
To be clear: realistic math education does not mean neglecting mental arithmetic and calculation or letting weak math students drown in a multitude of solution strategies. It is a balanced combination of routine and insight, where you mainly develop that insight by teaching students to imagine something when faced with a math problem, in their heads or through a drawing.
Some children can effortlessly convert cubic decimeters to other volume units using the ‘ladder’ method (a way to shift decimal points), but they have no spatial representation of a cubic decimeter. They can blindly do a series of calculations but fail the Cito tests because those require real spatial insight. Also, with fractions and all those other tricky topics in higher grades, it’s important to imagine them using pizzas, chocolate bars, etc. The ability to visualize something is not only important in math but also in language. Reading comprehension is essentially making a movie in your head of what you read: the clearer the movie, the better you understand the text.
My student had therefore accurately expressed my main didactic principle. The math didactics from Singapore greatly contribute to my teaching in the upper grades because they provide a system for how you can visualize different math problems.