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406 Chapter
12
Development
Thus, children’s stories and explanations to adults can be maddeningly uninformative
because they are delivered without any context. For example, a preoperational child
may start a story with, “He wouldn’t let me go,” neglecting to mention who “he” is or
where the storyteller wanted to go. We also see egocentric thinking when children at
the preoperational stage play hiding games. For instance, 3-year-olds frequently hide
with their faces against a wall and covering their eyes—although they are still in plain
view. It seems to them that if they cannot see, then no one else will be able to see them
because they assume that others share their view.
In addition, preoperational children have not yet developed the ability to under-
stand the principle of conservation, which is the knowledge that quantity is unre-
lated to the arrangement and physical appearance of objects. Children who have not
mastered this concept do not know that the amount, volume, or length of an object
does not change when its shape or confi guration changes. The question about the
two glasses—one short and broad and the other tall and thin—with which we began
our discussion of cognitive development illustrates this point clearly. Children who
do not understand the principle of conservation invariably state that the amount of
liquid changes as it is poured back and forth. They cannot comprehend that a trans-
formation in appearance does not imply a transformation in amount. Instead, it
seems as reasonable to the child that there is a change in quantity as it does to the
adult that there is no change.
In a number of other ways, some quite startling, the failure to understand the
principle of conservation affects children’s responses. Research demonstrates that chil-
dren during the preoperational period may completely misunderstand principles that
are obvious to and unquestioned by adults and that children do not grasp the concept
of conservation until the next stage of cognitive development (see Figure 10).
Concrete Operational Stage: 7 to 12 Years . Mastery of the principle of conservation
marks the beginning of the concrete operational stage. However, children do not
fully understand some aspects of conservation—such as conservation of weight and
volume—for a number of years.
During the concrete operational stage, children develop the ability to think in a
more logical manner and begin to overcome some of the egocentrism characteristic
of the preoperational period. One of the major principles children learn during this
stage is reversibility, the idea that some changes can be undone by reversing an
earlier action. For example, they can understand that when someone rolls a ball of
clay into a long sausage shape, that person can recreate the original ball by reversing
the action. Children can even conceptualize this principle in their heads without
having to see the action performed before them.
Although children make important advances in their logical capabilities during
the concrete operational stage, their thinking still displays one major limitation: They
are largely bound to the concrete, physical reality of the world. For the most part,
they have diffi culty understanding questions of an abstract or hypothetical nature.
Formal Operational Stage: 12 Years to Adulthood . The formal operational stage
produces a new kind of thinking that is abstract, formal, and logical. Thinking is no
longer tied to events that individuals observe in the environment but makes use of
logical techniques to resolve problems.
The way in which children approach the “pendulum problem” devised by Piaget
(Piaget & Inhelder, 1958) illustrates the emergence of formal operational thinking. The
problem solver is asked to fi gure out what determines how fast a pendulum swings.
Is it the length of the string, the weight of the pendulum, or the force with which the
pendulum is pushed? (For the record, the answer is the length of the string.)
Children in the concrete operational stage approach the problem haphazardly
without a logical or rational plan of action. For example, they may simultaneously
change the length of the string, the weight on the string, and the force with which
they push the pendulum. Because they are varying all the factors at once, they can-
not tell which factor is the critical one. In contrast, people in the formal operational
stage approach the problem systematically. Acting as if they were scientists conducting
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