While it might seem obvious that living in a three-dimensional world would require a certain amount of innate spatial abilities, it is less obvious in how this spatial ability informs science and math learning. Current research in visuospatial ability does show that children who have an understanding of how shapes fit together, and can see an object from a perspective other than their own, also have a significant advantage when it comes to problem solving in science and mathematics. Even something as important for small children as learning the number line or stacking blocks can be improved by spatial understanding.

Piaget and Inhelder worked with young children to try and understand their development of spatial reasoning and they found that young children do have a limited concept of space. For a young child, all objects exist in a fixed location relative to their own position and it is very difficult to represent in their mind’s eye the same scene from a different position, often referred to as perspective taking. As a child grows older they begin to construct their own conceptual model of space representing our three-dimensional world as a Euclidean space (horizontal, vertical, and depth axis). Piaget and Inhelder used the “water level task” as a procedure to test children’s spatial ability. In this task, a child is shown a container half full of water. Then an image of an outline of the same container which has been “tipped” at various angles is given to the child who is then asked to draw in the line representing the water level in the tipped container. Their research showed a definite age progression in the completion of this spatial task. Before the age of nine, children typically cannot consistently produce the correct answer. But much to everyone’s surprise many older students, both high school and university students, have significant difficulty with this task. Since that time numerous studies have explored spatial reasoning with university level students and have found that only about half could correctly draw in the correct water level on a consistent basis.

I find these results regarding spatial learning fascinating. Piaget’s water level task is an event that everyone experiences multiple times a day in the real world, yet is difficult for a significant number of people to represent on paper. We certainly all have experiences representing this task, so wherein lies the difficulty? Clearly there are gaps in our understanding of space, perspective, and frame of reference that spatial learning could help address in the classroom. How do you think you would do on Piaget’s water level task? Why don’t you give it a try.