Thinking at Piaget's Stage of Formal Operations

P iaget's theory of cognitive de velopment changed the way psy chologists and educators view children's intellectual development. However, with the widespread ac ceptance of Piaget's insight and theory has also come research that modifies and refines his contribution. According to Piaget, there are four major stages of development: the sensory-motor, the pre-operational, the concrete operational, and the formal operational. Children within each of these stages think about the world and attempt to solve problems in similar ways. Piaget characterized these stages in children's thought using "logico-mathematical models." Children enter the stage of formal operations at 11 or 12 years of age when their thinking about the world changes (Inhelder and Piaget, 1958). Consider the following task, which has often been used to study formal operational thought. An individual is presented with a set of rods made of different materials (plexiglass, wood, steel). They also differ in diameter (thin, medium, and thick) and length (short, medium, long). On a table is a stand in which two rods may be placed beside each other, parallel to the table and about 24 inches above it. There are two equal weights that may be hung from the ends of the rods. The individual is given the following instructions: