As suggested by Albert Einstein, Piaget studied a child's conception of time, space, and motion. Piaget published his results in two volumes: TheChild's Conception of Time and The Childs Conception of Movement and Speed.Itshould be recognized that Piaget went beyond a child's conception ofconservation and studied the child's conception of dimension and number.
Before a child can develop a true conception of numbers the useage ofone-to-one correspondence must be recognized by the child. Piaget's conservationof number experiment displayed two rows of counters placed in one-to-onecorrespondence . Subjects admit their equality. One of the rows is thenelongated or contracted. The subjects are asked whether each row has the samenumber of counters. Numbers can be reversed (by subtraction) or combined (byaddition) and express characteristics of combinativity, association, identity,and reversibility. The ability of a subject to solve this conservation problemdepends upon subjects mastery of identity. The average age that a child canconserve number is approximately 6-7 years of age.
Conservation of substance demonstrates the principle that alteration ofan object (malleable clay) doesn't change the quantity or mass of an object.Before a child can conserve substance, which is achieved at the age of 7-8, thechild experiences "perception dominance" in which the appearance ofsomething dominates over logical thought progression. Conservation of length isa classic example of "perception dominance", a length of rope is notchanged by an alteration in configuration of the rope.
Piaget used a geometrical experiment called "cows on a farm"to test for conservation of area. To illustrate this, Piaget used greencardboard to represent farmland. Two identical green farms were established,each had a little wooden cow placed upon it, subjects were asked whether thecows had the same amount of grass to feed upon. Piaget would proceed to equallyadd little cubic farmhouses to the models. In one farmyard the houses where allarranged in a tidy row, on the other farmland the houses were all scatteredabout. Until the ages of 8-9, children are irresistibly inclined to think thereis less grazing land on the farmland which contains the scattered houses.
Conservation of volume is usually tested using a cylinder and a flatdish (see figure below). Children are inclined to think that a tall, erect,narrow dish contains more liquid than an equal amount in a flat dish. Mastery ofconservation of volume requires reverse thinking and is the last of thePiagetian conservation tests children grasp.