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CHAPTER 14: MODELS OF COGNITIVE DEVELOPMENT: PIAGET AND PERRY

TEACHING ENGINEERING

CHAPTER

14

MODELS OF COGNITIVE

DEVELOPMENT: PIAGET AND PERRY

We will focus on the two theories of development which have been the most influential in

the education of scientists and engineers: Piaget¡¯s theories of childhood development and

Perry¡¯s theory of development of college students. To some extent they are complementary

as both focus on different aspects of development, and since both Piaget and Perry discuss

how students learn, this material ties in with Chapter 15.

These theories are important since they speak to what we can teach students and to where

we want students to be when they graduate. Both theories postulate that students cannot learn

material if they have not reached a particular level of development. Attempts to teach them

material which they are unable to learn leads to frustration and memorization. As engineering

students become more heterogeneous, the levels of student development in classrooms will

also become more heterogeneous. Thus, it is becoming increasingly important to understand

the levels at which different students function.

14.1. PIAGET¡¯S THEORY

Jean Piaget was a Swiss psychologist whose research on the development of children has

profoundly affected psychological theories of development and of the teaching of children.

His theory has also been widely studied for its application to the teaching of science in grade

school, high school, and college. Unfortunately, Piaget¡¯s writings tend to be somewhat

obscure. We will present a significantly edited version focusing on those aspects of his theory

which affect engineering education. Further information is available in Flavell (1963), Gage

and Berliner (1984), Goodson (1981), Inhelder and Piaget (1958), Phillips (1981), Piaget

(1950, 1957), and Pavelich (1984).

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14.1.1. Intellectual Development

Piaget¡¯s theory conceives of intellectual development as occurring in four distinct periods

or stages. Intellectual development is continuous, but the intellectual operations in the

different periods are distinctly different. Children progress through the four periods in the

same order, but at very different rates. The stages do not end abruptly but tend to trail off. A

child may be in two different stages in different areas.

The sensorimotor period, which is only of indirect interest to our concerns, extends from

birth to about two years of age. In this period a child learns about his or her relationship to

various objects. This period includes learning a variety of fundamental movements and

perceptual activities. Knowledge involves the ability to manipulate objects such as holding

a bottle. In the later part of this period the child starts to think about events which are not

immediately present. In Piaget¡¯s terms the child is developing meaning for symbols.

The preoperational period lasts from roughly two to seven years of age. Piaget has divided

this stage into the preoperational phase and the intuitive phase. In the preoperational phase

children use language and try to make sense of the world but have a much less sophisticated

mode of thought than adults. They need to test thoughts with reality on a daily basis and do

not appear to be able to learn from generalizations made by adults. For example, to a child

riding a tricycle the admonition ¡°Slow down, you are going too fast¡± probably has no effect

until the child falls over. This continual testing with reality helps the child to understand the

meaning of ¡°too fast.¡± Compared to adults, the thinking of a child in the preoperational phase

is very concrete and self-centered. The child¡¯s reasoning is often very crude, and he or she is

unable to make very simple logical extensions. For example, the son of one of the authors was

astounded when he heard that his baby sister would be a girl when she got older!

In the intuitive phase the child slowly moves away from drawing conclusions based solely

on concrete experiences with objects. However, the conclusions drawn are based on rather

vague impressions and perceptual judgments. At first, the conclusions are not put into words

and are often erroneous (and amusing to adults). Children are perception-bound and often very

rigid in their conclusions. Rational explanations have no effect on them because they are

unable to think in a cause-and-effect manner. During this phase children start to respond to

verbal commands and to override what they see. It becomes possible to carry on a conversation

with a child. Children develop the ability to classify objects on the basis of different criteria,

learn to count and use the concept of numbers (and may be fascinated by counting), and start

to see relationships if they have extensive experience with the world. Unaware of the processes

and categories that they are using, children are still preoperational. Introspection and

metathought are still impossible.

At around age seven (or later if the environment has been limited) the child starts to enter

the concrete operational stage. In this stage a person can do mental operations but only with

real (concrete) objects, events, or situations. He or she can do mental experiments and can

correctly classify different objects (apples and sticks, for example) by some category such as

size. The child understands conservation of amounts. This can be illustrated with the results

of one of Piaget¡¯s experiments (Pavelich, 1984). Two identical balls of clay are shown to a

child who agrees they have the same amount of clay. While the child watches, one ball is

flattened. When asked which ball has less clay, the preoperational child answers that the

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flattened ball has less clay. The concrete operational child is able to correctly answer this

question. He or she becomes adept at addition and subtraction but can do other mathematics

only by rote. In the concrete operational stage children also become less self-centered in their

perceptions of the universe. Logical reasons are understood. For example, a concrete

operational person can understand the need to go to bed early when it is necessary to rise early

the next morning. A preoperational child, on the other hand, does not understand this logic and

substitutes the psychological reason, ¡°I want to stay up.¡±

Piaget thought that the concrete operational stage ended at age eleven or twelve. There is

now considerable evidence that these ages are the earliest that this stage ends and that many

adults remain in this stage throughout their lives. Most current estimates are that from 30 to

60 percent of adults are in the concrete operational stage (Pintrich, 1990). Thus, many college

freshmen are concrete operational thinkers; however, the number in engineering is small and

is probably less than 10 percent (Pavelich, 1984). For reasons which will become clear shortly,

concrete operational thinkers will have difficulty in an engineering curriculum. However,

these people can be fully functioning adults. Piaget¡¯s theories at the concrete and formal

operational stages measure abilities only in a very limited scientific, logical, algebraic sense.

His theories do not address ethical or moral development. Thus a person may be a successful

hard worker, a good, loving parent and spouse, and a good citizen, but be limited to concrete

operational thought.

The final stage in Piaget¡¯s theory is the formal operational stage, which may start as early

as age eleven or twelve, but often later. A formal operational thinker can do abstract thinking

and starts to enjoy abstract thought. This person becomes inventive with ideas and starts to

delight in such thinking. He or she can formulate hypotheses without actually manipulating

concrete objects, and when more adept can test the hypotheses mentally (Phillips, 1981). This

testing of logical alternatives does not require recourse to real objects. The formal operational

thinker can generalize from one kind of real object to another and to an abstract notion. In the

experiment with the balls of clay, for example, the formal thinker can generalize this to sand

or water and then to a general statement of conservation of matter. This person is capable of

learning higher mathematics and then applying this mathematics to solve new problems.

When faced with college algebra or calculus the concrete operational thinker is forced to learn

the material by memorization but then is unable to use this material to solve unusual problems.

The formal operational thinker is able to think ahead to plan the solution path (see Chapter 5

for a further discussion of problem solving) and do combinatorial thinking and generate many

possibilities. Finally, the formal operational person is capable of metacognition, that is,

thinking about thinking.

14.1.2. Application of Piaget¡¯s Model to Engineering Education

The importance of the formal operational stage to engineering education is that engineering

education requires formal operational thought. Many of the 30 to 60 percent of the adult

population who have some trouble with formal operational thought appear to be in a

transitional phase where they can correctly use formal operational thought some of the time

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but not all of the time. Engineering students in transition appear to be able to master

engineering material (Pavelich, 1984). This probably occurs because they have learned that

formal operational thought processes must be used in their engineering courses, but they have

not generalized these processes to all areas of their life. This domain specificity of many

students is one of the major criticisms of Piaget¡¯s theory (Pintrich, 1990).

The relatively small number of engineering students who are in the concrete operational

stage will have difficulties in engineering. These students may make it through the curriculum

by rote learning, partial credit, doing well in lab, repeating courses, and so forth. Concrete

operational students can be identified by repeated administration of tests with novel problems

on the same material (Wankat, 1983). On the first few tests students may be unable to work

the problem either because of lack of knowledge or because of an inability to solve abstract

problems. On the basis of a single test it is difficult to tell if lack of knowledge or poor problemsolving ability has caused the difficulties. Students who can use formal operational thinking

learn from their mistakes, learn the missing knowledge, and fairly rapidly become able to solve

difficult new problems. Students who are in the concrete operational stage do not appear to be

able to learn from their mistakes on problems requiring formal operations. Thus, they make

the same mistakes over and over. The solutions of these students do not appear to follow any

logical pattern since they often just try something (anything) to see if it works and to see if they

get any partial credit. These students have great difficulty in evaluating their solutions. In

engineering, concrete operational students are likely to be quite frustrated and frustrating to

work with.

The suggestion has been made repeatedly that freshmen-sophomore courses in engineering

should be made available for nonengineering students (e.g., Bordogna, 1989). If this were

done, the much higher percentage of concrete operational students in the general student

population would likely cause problems in the course unless some type of screening or selfselection takes place.

14.1.3. Piaget¡¯s Theory of Learning

The presence of some concrete operational students in engineering leads us naturally to the

question of how a student moves from one stage to another. This is another aspect of Piaget¡¯s

theories. Piaget postulates that there are mental structures that determine how data and new

information are perceived. If the new data make sense to the existing mental structure, then

the new information is incorporated into the structure (accommodation in Piaget¡¯s terms).

Note that the new data do not have to exactly match the existing structure to be incorporated

into the structure. The process of accommodation allows for minor changes (figuratively,

stretching, bending and twisting, but not breaking) in the structure to incorporate the new data.

If the data are very different from the existing mental structure, it does not make any sense to

incorporate them into the structure. The new information is either rejected or the information

is assimilated or transformed so that it will fit into the structure. A concrete person will

probably reject a concept requiring formal thought. If forced to do something with the data

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he or she will memorize even though the meaning is not understood. This is similar to

memorizing a passage in a foreign language that one cannot speak. An example of

transformation is a person¡¯s response to seeing a pink stoplight. Everyone ¡°knows¡± that

stoplights are red, and thus the pink stoplight will probably be registered as being red since red

stoplights fit one¡¯s mental structure.

How does one develop mentally? How does one make the quantum leap from concrete to

formal thinking? Mental development occurs because the organism has a natural desire to

operate in a state of equilibrium. When information is received from the outside world which

is too far away from the mental structure to be accommodated but makes enough sense that

rejecting it is difficult, then the person is in a state of disequilibrium. The desire for

equilibration is a very strong motivator to either change the structure or reject the data. If the

new information requires formal thinking and the person is otherwise ready, then a first formal

operational structure may be formed. This formal operational structure is at first specific for

learning in one area and is slowly generalized (the person is in a transitional phase). The more

often the person receives input which requires some formal logic, the more likely he or she is

to make the jump to formal operational thought. Since this input takes place in a specific area,

the transition to formal operations often occurs first in this one area. Also, a person with a less

rigid personality structure and tolerance for ambiguity is probably more likely to make the

transition. We emphasize that the transition to formal operations may not be easy.

Piaget developed a variety of experiments to test what stage children were in and to help

them learn to make the transition to the next stage. Unfortunately, the experiments work well

for testing the stage but not for moving people to the next stage. A method called the scientific

learning cycle has been developed to help students in their mental development (Renner and

Lawson, 1973; Lawson et al., 1989). In the scientific learning cycle the students are given firsthand experience, such as in a laboratory with an attempt to cause some disequilibration. The

instructor then leads discussions either with individuals or in groups to introduce terms and

to help accommodate the data and thus aid equilibration. Finally, students make further

investigations or calculations to help the changed mental structure fit in with the other mental

structures (organization). The scientific learning cycle is successful at helping people move

to higher stages, but progress is very slow. Since concrete operational students may try hard

but still have great difficulty in understanding abstract logic, the use of words like ¡°obviously,¡±

¡°clearly,¡± or ¡°it is easy to show¡± by the professor is frustrating and demotivating to them. The

scientific learning cycle is also useful for working with students who are already in the formal

operational stage since these students also learn by being in a state of disequilibrium and using

accommodation. The scientific learning cycle is discussed in more detail in Chapter 15.

Piaget¡¯s theory has partially withstood the test of time and partially been modified (Kurfiss,

1988). It is now generally agreed that individuals actively construct meaning. This has led

to a theory called constructivism, which is discussed in more detail in Chapter 15. Piaget¡¯s

general outline of how people learn and the need for disequilibrium has been validated.

Disagreements with Piaget focus on the role of knowledge in learning. More recent

researchers have found that both specific knowledge and general problem-solving skills are

required to solve problems, while Piaget did not recognize the importance of specific

knowledge.

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