FIGURE 8CLASSIFICATION: AN IMPORTANTABILITY IN CONCRETE OPERATIONAL THOUGHT.A family tree of fourgenerations (I to IV): The preoperational child has trouble classifying the membersof the four generations; the concrete operational child can classify the membersvertically, horizontally, and obliquely (up and down and across). For example, theconcrete operational child understands that a family member can be a son, abrother, and a father, all at the same time.Children who have reached the concrete operational stage are also capableofseriation,which is the ability to order stimuli along a quantitativedimension (such as length).To see if students can serialize, a teacher mighthaphazardly place eight sticks of different lengths on a table. The teacherthen asks the students to order the sticks by length. Many young childrenend up with two or three small groups of “big” sticks or “little” sticks,rather than a correct ordering of all eight sticks. Another mistaken strategythey use is to evenly line up the tops of the sticks but ignore the bottoms.The concrete operational thinker who is capable Page 194of seriationsimultaneously understands that each stick must be longer than the onethat precedes it and shorter than the one that follows it.
FORMAL OPERATIONAL STAGESo far we have studied the first three of Piaget’s stages of cognitivedevelopment: sensorimotor, preoperational, and concrete operational. Whatare the characteristics of the fourth and final stage?