Chapter 2: Embodied Knowledge in the Development of Conservation of Quantity: Evidence from Gesture

Understanding quantity is one of the foundations of mathematical thinking. Piaget (1941/1952) recognized this in his seminal work, The Child’s Conception of Number, in which he addresses conservation of quantity in the first two chapters. Conservation of quantity is the understanding that quantities remain invariant under certain sorts of transformations that alter perceptual appearance (see Figure 2.1). Consider, for example, transformations of discrete (countable) quantities, such as sets of checkers or blocks. In a classic Piagetian conservation task, the experimenter might alter the physical position of a row of checkers by spreading them out so that the row is longer and the spaces between checkers are larger, making the row appear more numerous. Similarly, consider transformations of continuous (noncountable) quantities, such as liquid or sand. An experimenter might pour a liquid into a container that is shorter and wider, making the amount of liquid appear less.