If you watch a young child at play you see that they are exploring all the time; balancing cubes, testing materials (often with their mouths!), rolling a ball or forming a sentence. It is as if they are driven by one question …. ‘what happens if….?’ What happens if I lean this way when I try to walk? What happens if I push this car into the next one? What happens if I move my mouth like this to make this sound?
Much research has been conducted in to the field of childhood development. The Swiss developmental psychologist, Jean Piaget in his theory of cognitive development considered the nature of knowledge and how it is acquired. Piaget showed in his studies that children think in very different ways to adults. He posseted that children first build an understanding, a mental model of the world which they then test out and adapt according to the information they subsequently collect.
Piaget’s work has had much influence of developing educational policy in early years; encouraging the facilitation of young children’s learning through active discovery. But for many educationalists, active learning, they believe, should not end at the doors of the primary school classroom. Mathematics, a subject rich in the potential for discovery learning, is too often taught as a set of rules to be followed. Take the learning of long multiplication. How often are our children shown an algorithm to be applied which, somehow, magically I’m sure for some, produces the answer (most of the time!). How much deeper would that child’s understanding be, if they could explore and develop ways to multiply numbers together. This process takes longer, but like many things in life, a slow gestation results in a stronger outcome.
Mastery of mathematics requires a deep understanding of the ways in which numbers, shapes, algebra and patterns behave and are connected. To develop this deep understanding, we must encourage our students to behave like the young child we met at the start, constantly asking ‘what happens if….?’ By encouraging our students to have mathematical curiosity, to ‘play’ with their maths, and to question ‘what happens if …?’, we allow them to subconsciously create their own mental model of the maths, a model which they can then test, correct and refine, to produce a deep and clear understanding of what is happening and why.
