144 Intelligence
McNemar, 1951). Second, factor analyses have sometimes
been not so much misintepreted as overinterpreted. What one
gets out of a factor analysis is simply a psychometric trans-
formation of what one puts in. It is possible to support many
different possible theories by choosing one’s tests with a cer-
tain goal in mind. The resulting factors simply reflect the
choice of tests and their interrelationships. Third, in ex-
ploratory factor analysis, the rotation issue has proven to be a
thorny one. Any rotation is mathematically correct and equiv-
alent in Euclidean space. Arguments over which theory is
correct often have boiled down to little more than arguments
over which rotation is psychologically more justified. But no
adequate basis has been found for supporting one rotation as
psychologically preferred over all others. Fifth and finally,
the whole issue of deriving a theory of intelligence from
patterns of individual differences has never received fully
adequate examination by differential psychologists. Evolu-
tionary theorists (e.g., Pinker, 1997; see R. J. Sternberg &
Kaufman, 2001) would argue that intelligence needs to be
understood in terms of commonalities, not differences. Of
course, experimental psychologists have made the same
claim for many decades, preferring to view individual differ-
ences as noise in their data. Perhaps the best solution is some
kind of synthesis, as recommended by Cronbach (1957). Jean
Piaget, disheartened with his observations from work in
Binet’s laboratory, provided a synthesis of sorts. He com-
bined measurement with a more cognitive framework for
understanding intelligence.
INTELLIGENCE AS ARISING FROM COGNITIVE
STRUCTURES AND PROCESSES
Cognitive Structures
Piaget (1952, 1972), among others, has staked out an alterna-
tive position to the differential one. Piaget, who was never
very interested in individual differences, viewed intelli-
gence as arising from cognitive schemas, or structures that
mature as a function of the interaction of the organism with
the environment.
Equilibration
Piaget (1926, 1928, 1952, 1972), like many other theorists of
intelligence, recognized the importance of adaptation to in-
telligence. Indeed, he believed adaptation to be its most im-
portant principle. In adaptation, individuals learn from the
environment and learn to address changes in the environ-
ment. Adjustment consists of two complementary processes:
assimilation and accommodation. Assimilationis the process
of absorbing new information and fitting it into an already
existing cognitive structure about what the world is like. The
complementary process, accommodation,involves forming a
new cognitive structure in order to understand information.
In other words, if no existing cognitive structure seems ade-
quate to understand new information, a new cognitive struc-
ture must be formed through the accommodation process.
The complementary processes of assimilation and accom-
modation, taken together in an interaction, constitute what
Piaget referred to as equilibration. Equilibrationis the bal-
ancing of the two, and it is through this balance that people
either add to old schemas or form new ones. Aschema,for
Piaget, is a mental image or action pattern. It is essentially a
way of organizing sensory information. For example, we
have schemas for going to the bank, riding a bicycle, eating a
meal, visiting a doctor’s office, and the like.Stages of Intellectual DevelopmentPiaget (1972) suggested that the intelligence of children ma-
tures through four discrete stages, or periods of development.
Each of these periods builds upon the preceding one, so that
development is essentially cumulative.
The first period is the sensorimotor period,which occu-
pies birth through roughly 2 years of age. By the end of the
sensorimotor period, the infant has started to acquire object
permanence, or the realization that objects can exist apart
from him or herself. In early infancy, the infant does not as-
cribe a separate reality to objects. Thus, if a toy is hidden
under a pillow or behind a barrier, the infant will not search
for the toy because as far as he or she is concerned, it no
longer exists when it goes out of sight. By the end of the pe-
riod, the infant knows that a search will lead to finding the
object.
The second period is the preoperational period,which
emerges roughly between ages 2 and 7. The child is now be-
ginning to represent the world through symbols and images,
but the symbols and images are directly dependent upon the
immediate perception of the child. The child is still essen-
tially egocentric: He or she sees objects and people only from
his or her own point of view. Thus, to the extent that thinking
takes place, it is egocentric thinking.
The third period is the concrete-operational period,which
occupies roughly ages 7 through 11. In this period, the child
is able to perform concrete mental operations. Thus, the child
now can think through sequences of actions or events that
previously had to be enacted physically. The hallmark of
concrete-operational thought is reversibility. It now is possi-
ble for the child to reverse the direction of thought. The child
comes to understand, for example, that subtraction is the