“Teacher, you have an obsession with drawing,” a sharp-witted student told me some time ago. She had a point: I often try to get students to visualize math problems, first on paper and later in their minds.
Later, I found out that this approach places me in good company with schoolteachers in Singapore, where students rank among the top four in the world for mathematics. Countries like England and the U.S. have adopted this method and are now working hard to surpass the Netherlands on this ranking.
However, I don’t think this approach is entirely new or unique. Many elements of it can be found in our own ‘realistic mathematics education,’ which has faced a lot of criticism recently. I don’t share that criticism: in my view, the stagnation in math proficiency isn’t due to realistic mathematics but rather to budget cuts in education and other societal developments in recent years. I’m thinking of class sizes, resources for special-needs students, teacher training levels, the shift from reading to computers, and so on.
To be clear: for me, realistic mathematics education does not mean neglecting mental arithmetic and calculations or overwhelming struggling students with too many solution strategies. It is a balanced combination of routine and understanding, where insight is developed by teaching students to imagine a math problem—either in their minds or through drawing.
Some children can effortlessly convert cubic decimeters to other volume units using the ‘ladder’ method (a way to shift decimal points), yet they have no spatial understanding of a cubic decimeter. They might blindly complete a series of numerical exercises, but they struggle with Cito exam questions, where spatial reasoning is crucial. The same applies to fractions and other complex topics in upper primary school: it’s essential that students can visualize concepts using examples like pizzas or chocolate bars.
This ability to visualize isn’t just important for math but also for language. Reading comprehension is essentially about creating a mental movie of what you’re reading: the clearer that movie is, the better you understand the text.
So, my student summed up my most important teaching principle quite well. The mathematics education approach from Singapore greatly enhances my lessons for upper primary school, as it introduces a structured way of visualizing different math problems.