Development across the Life Span 329“conserve” (save) the volume of liquid as it takes on a different shape in the
tall, thin glass is not only caused by the child’s centration on the height of
the liquid in the second glass but also by the inability of the child to imagine
pouring the liquid back into the first glass and having it be the same amount
again. Similar “reasoning” causes children of this age to assume that a ball
of clay, when rolled out into a “rope” of clay, is now greater in mass.
CONCRETE OPERATIONS In the concrete operations stage (ages 7–12), chil-
dren finally become capable of conservation and reversible thinking. Cen-
tration no longer occurs as children become capable of considering all the
relevant features of any given object. They begin to think more logically about
beliefs such as Santa Claus or the Tooth Fairy and to ask questions, eventually
coming to their own more rational conclusions about these fantasies of early
childhood. They are in school, learning all sorts of science and math, and are
convinced that they know more than their parents at this point.
The major limitation of this stage is the inability to deal effectively with
abstract concepts. Abstract concepts are those that do not have some physical,
concrete, touchable reality. For example, “freedom” is an abstract concept. People can define
it, they can get a good sense of what it means, but there is no “thing” that they can point to
and say, “This is freedom.” Concrete concepts, which are the kind of concepts understood by
children of this age, are about objects, written rules, and real things. Children need to be able
to see it, touch it, or at least “see” it in their heads to be able to understand it.
FORMAL OPERATIONS In the last of Piaget’s stages, formal operations (age 12 to adult-
hood), abstract thinking becomes possible. Teenagers not only understand concepts that
have no physical reality, but also they get deeply involved in hypothetical thinking, or
thinking about possibilities and even impossibilities. “What if everyone just got along?”
“If women were in charge of countries, would there be fewer wars?”
Piaget did not believe that everyone would necessarily reach formal operations,
and studies show that only about half of all adults in the United States reach this stage
(Sutherland, 1992). Adults who do not achieve formal operations tend to use a more
practical, down-to-earth kind of intelligence that suits their particular lifestyle. Success-
ful college students, however, need formal-operational thinking to succeed in their col-
lege careers, as most college classes require critical thinking, problem-solving abilities,
and abstract thinking based on formal-operational skills (Powers, 1984).
Others have proposed another stage beyond formal operations, a relativistic think-
ing stage found in young adults, particularly those who have found their old ways of
thinking in “black and white” terms challenged by the diversity they encounter in the
college environment (LaBouvie-Vief, 1980, 1992; Perry, 1970). In this kind of thinking,
young adults recognize that all problems cannot be solved with pure logic, and there can
be multiple points of view for a single problem.
EVALUATING PIAGET’S THEORY Piaget saw children as active explorers of their surroundings,
engaged in the discovery of the properties of objects and organisms within those surround-
ings. Educators have put Piaget’s ideas into practice by allowing children to learn at their own
pace, by “hands-on” experience with objects, and by teaching concepts that are at the appro-
priate cognitive level for those children (Brooks & Brooks, 1993). But Piaget’s theory has also
been criticized on several points. Some researchers believe that the idea of distinct stages of
cognitive development is not completely correct and that changes in thought are more contin-
uous and gradual rather than abruptly jumping from one stage to another (Courage & Howe,
2002; Feldman, 2003; Schwitzgebel, 1999; Siegler, 1996). Others point out that preschoolers are
not as egocentric as Piaget seemed to believe (Flavell, 1999) and that object permanence exists
much earlier than Piaget thought ( Aguiar & Baillargeon, 2003; Baillargeon, 1986).
VYGOTSKY’S THEORY: THE IMPORTANCE OF BEING THERE Russian psychologist Lev
Vygotsky’s pioneering work in developmental psychology has had a profound influence
concrete operations stage
2iagetos third stage of cognitive devel-
oRment in which the school-age child
Decomes caRaDle of logical thought
Rrocesses Dut is not yet caRaDle of
aDstract thinMing.formal operations stage
2iagetos last stage of cognitive devel-
oRment in which the adolescent
Decomes caRaDle of aDstract thinMing.These concrete operational children, seen in a science class,
have begun to think logically and are able to solve many kinds
of problems that were not possible for them to solve while in
the preoperational stage.This girl is helping her younger brother
learn to read a book. Vygotsky’s view
of cognitive development states that
the help of skilled others aids in making
cognitive advances such as this one.