The school-age child develops the ability to recognize that if a block of clay is in a round ball and then is flattened, the shape changes but not the amount of clay. What understanding has this child developed?

The children have developed the understanding of conservation.

Explanation:

The conservation ability is the capacity of recognizing that a determined object can change its shape but this not means a change in its mass or weight. In this case, the school-age child recognizes that the same block of clay can have different shapes but this doesn't mean a change in its weight or mass.