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204 CHAPTER 8characterize each stage determine the child’s performance in
a wide range of situations. There are four such general
stages, or periods, in Piaget’s theory.
The sensorimotor period represents the first 2 years of
life. The infant’s initial schemes are simple reflexes. Gradu-
ally, these reflexes are combined into larger, more flexible
units of action. Knowledge of the world is limited to phys-
ical interactions with people and objects. Most of the exam-
ples of schemes given earlier—grasping, sucking, and so
on—occur during infancy.
During the preoperational period, from roughly 2 to 6 years,
the child begins to use symbols to represent the world cogni-
tively. Words and numbers can take the place of objects and
events, and actions that formerly had to be carried out overtly
can now be performed mentally through the use of internal
symbols. The preoperational child is not yet skilled at symbolic
problem solving, however, and various gaps and confusions are
evident in the child’s attempts to understand the world.
Many of these limitations are overcome when the child
reaches the period of concrete operations, which lasts approx-
imately from ages 6 to 11. Concrete operational children are
able to perform mental operations on the bits of knowledge
that they possess. They can add them, subtract them, put
them in order, reverse them, and so on. These mental opera-
tions permit a kind of logical problem solving that was not
possible during the preoperational period.
The final stage is the period of formal operations, which
extends from about age 11 through adulthood. This period
includes all of the higher level abstract operations that do
not require concrete objects or materials. The clearest exam-
ple of such operations is the ability to deal with events or
relationships that are only possible, as opposed to those that
actually exist. Mentally considering all of the ways certain
objects could be combined, or attempting to solve a prob-
lem by cognitively examining all of the ways it could be
approached, are two operations that typically cannot be per-
formed until this final stage.Sequences. Sequences order ideas chronologically by illustrating the
ordering of steps, events, stages, or phases. Sequences usually appear
in a left-to-right pattern, with arrows between steps. Figure 8.2 pro-
vides an example of the stages of cognitive development described in
the preceding excerpt. Timelines in history also can be used to visu-
alize the sequence of events by drawing a horizontal line and mark-
ing it off in intervals. The times when different events in history