Piaget’s Theory of Intellectual Development Revisited

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					                                                                                          Research: Science and Education

                                                                                                                                   edited by
Piaget, Constructivism, and Beyond                                                                                     Stacey Lowery Bretz
                                                                                                                  Youngstown State University
                                                                                                                    Youngstown, OH 44555

Piaget’s Theory of Intellectual Development Revisited                                                                     Mary B. Nakhleh
                                                                                                                            Purdue University
                                                                                                                   West Lafayette, IN 47907
Susan C. Nurrenbern
Department of Chemistry, Purdue University, West Lafayette, IN 47907;

     Although I do not continually cite Piaget, I sincerely hope        participants in their intellectual development broadens our
     one realizes that almost everything I write herein can be writ-    knowledge base and perspective about the learning process
     ten only because Piaget spent some 69 years establishing the       and possible approaches to classroom teaching. The perspective
     basis for a dynamic constructivist theory of knowing.              that learners are active participants rather than passive receivers
     Constructivism arose for Piaget (as well as for Giambattista       of knowledge challenges the behavioristic, receptive, empty-
     Vico, the pioneer of constructivism at the beginning of the        vessel model of learners widely applied in many education
     18th century) out of a profound dissatisfaction with the theo-     situations.
     ries of knowledge in the tradition of Western philosophy.               The papers presented at the Piaget, Constructivism, and
                                                                        Beyond symposium held at the Spring 1998 ACS meeting in
                                         Ernst von Glasersfeld ( 1)
                                                                        Dallas, TX, and the 16th Biennial Conference on Chemical
     Piaget’s Theory of Intellectual Development claimed a              Education in Ann Arbor, MI, in 2000 illustrate the extensive,
significant and permanent presence in education during the              continuing influence of Piagetian theory in the field of cog-
last quarter of the 20th century as it ushered in the field of          nitive sciences and the overall understanding of intellectual
cognitive sciences. Piaget’s description of individuals as active       development and knowledge construction.

 Online Symposium

Piaget, Constructivism, and Beyond                                                                                                      W
The articles listed below are available in this issue of JCE Online as part of a featured Online Symposium. A link to the abstract and a pdf
file of each article can be found at The papers were originally presented at
the Piaget, Constructivism, and Beyond symposium held at the Spring 1998 ACS meeting in Dallas, TX, and the 16th Biennial Conference
on Chemical Education in Ann Arbor, MI, in 2000.

Does Piaget Still Have Anything to Say to Chemists?
Diane M. Bunce Department of Chemistry, The Catholic University of America, Washington, DC 20064

Implications of Cognitive Science Research for Models of the Science Learner
Ala Samarapungavan Department of Educational Studies, Purdue University, West Lafayette, IN 47907
William R. Robinson Department of Chemistry, Purdue University, West Lafayette, IN 47907

The Many Forms of Constructivism
George Bodner and Michael Klobuchar Department of Chemistry, Purdue University, West Lafayette, IN 47907
David Geelan Science and Mathematics Education Centre, Curtin University, Perth, Western Australia 6001, Australia

Theories or Fragments? The Debate Over Learners’ Naive Ideas About Science
Mary B. Nakhleh Department of Chemistry, Purdue University, West Lafayette, IN 47907

Novak’s Theory of Education: Human Constructivism and Meaningful Learning
Stacey Lowery Bretz Department of Chemistry, Youngstown State University, Youngstown, OH 44555

Kolb for Chemists: David A. Kolb and Experiential Learning Theory
Marcy Hamby Towns Department of Chemistry, Ball State University, Muncie, IN 47306

Reconstructing Student Meaning: A Theory of Perspective Transformation
Donald J. Wink Department of Chemistry, University of Illinois at Chicago, Chicago, IL 60607

                  • Vol. 78 No. 8 August 2001 • Journal of Chemical Education                         1107
 Research: Science and Education

Piagetian Theory: A Psychological Theory of Intellectual                                   2. Intellectual or cognitive growth is integrally linked to the
Development                                                                                   physical, social, and linguistic milieu of an individual.
                                                                                           3. Humans, being a biological species, are intrinsically
     Piagetian theory is a psychological theory of intellectual
                                                                                              motivated to grow intellectually or mentally by the
development focused on the process by which individuals
                                                                                              processes of organization and adaptation, processes
develop logical and viable (2) cognitive structures that support
                                                                                              common to all organisms.
logico-mathematical reasoning. Piaget drew on his background
in biology, philosophy, and logic to investigate human intel-                              Piagetian theory incorporates only two invariants: (i)
lectual growth and development. His ideas related to intel-                           organization and adaptation are the driving forces for human
lectual development were far-reaching, as evidenced by the                            intellectual development and (ii) intellectual development is
following passage from Flavell (3, p 84).                                             characterized by a hierarchical development of successively
                                                                                      more complex skills and operations. Consequently the keys
     He became particularly interested in the neural correlates
                                                                                      to understanding Piagetian theory involve understanding the
     of intellectual structures, and in one article in particular
                                                                                      nature of these invariants as well as the relationships between
     (1949) he made some guesses about brain mechanisms
     underlying the various structures which intellectual actions
                                                                                           Piaget’s findings and assertions are based on his obser-
     form in their progressive internalization. Thus, implicit
                                                                                      vations of children as they manipulated or interacted with
     motor responses seem to have been essentially by-passed
                                                                                      real objects or were faced with real tasks that involved trans-
     as an object of study in favor of action systems in the brain.
                                                                                      formation of an object or setting or correspondence between
     Much of the language Piaget used to describe his per-                            objects or object properties. Piaget would present the child
spective of intellectual development is rooted in the theories                        with a task to complete, then change some variable within a
of natural selection and evolution and at times is complicated                        task (e.g., hide objects; change the shape of pieces of clay,
by translation from French to English. Sometimes he uses                              then ask about the comparative masses of the differently
words and phrases that are similar to words and phrases in                            shaped pieces; determine the pivotal point for a balance beam
science but with a slightly different meaning. Box 1 is a                             with various masses) and observe how the child dealt with
glossary of Piagetian terms that will clarify the meaning of                          the task or questions under this new situation. The interview
terms as used in this theory.                                                         process did not include intervention or coaching the children
Basics of the Theory                                                                  into responses. Piaget’s findings led him to view intellectual
                                                                                      development as a progressive process that exhibits a high
    Piaget based his work on the following premises.                                  degree of variability among individuals. The identification and
   1. One can learn about another individual’s internal                               labeling of developmental periods was Piaget’s platform to
      mental structures, schemas, by direct observation of that                       present, discuss, and illustrate the basic principles of the con-
      individual’s behavior.                                                          tinuous, progressive development process.

                                                          Box 1. Glossary of Piagetian Terms

Adaptation and organization: Processes that account for and regulate human intellectual growth; these processes are intrinsic to all biological species (or
substrates) which in turn are fundamentally driven or motivated by the need to survive in a given environment.
Assimilation and accommodation: Interdependent adaptation processes that involve interactions with and responses to an individual’s environment;
these adaptation processes coincide with the formation of new schemas or modification of existing schemas (i.e., organization of knowledge).
Child/children: Persons from birth to approximately age 18.
Disequilibration: A mental state or condition of “imbalance” between the organization function and the adaptation functions of assimilation and
accommodation; this condition is necessary for intellectual development to occur.
Egocentrism: A state where the world is viewed only from the individual’s perspective; the environment outside an individual is seen to operate or behave in a
way that responds to or revolves around the individual; when asked to draw or describe what a person across the room sees, the individual can only draw or
describe from his/her perspective; cannot put himself or herself in another’s place.
Equilibration: A mental state or condition where the organization and adaptation (i.e, assimilation and accommodation) functions are in “balance”; existing
knowledge for an individual in this state is sufficient to explain what the individual needs to explain or understand; intellectual development does not occur for
an individual in this state.
Horizontal decalage: Differences in level of intellectual functioning exhibited by an individual in different situations or content areas; descriptor of an individual.
Idiosyncratic knowledge: Knowledge unique to an individual owing to unique intellectual processing.
Intellectual or cognitive growth: A process of constant addition to and adjustment of mental schemas; occurs as a response to interacting with and responding
to the individual’s total environment.
Invariants: Constants.
Logico-mathematical knowledge: Knowledge constructed from a child’s action on objects; that is, active experiences.
Physical knowledge: Knowledge derived from objects themselves.
Schemas: An individual’s self-constructed mental structures; these can be simple (e.g., the infant’s sucking schema) or complex (e.g., a physical chemist’s
thermodynamics schema), and can be related to other schemas (e.g., molecular structure schema to chemical properties schema).
Social-arbitrary knowledge: Knowledge that is tied to people and social interactions.
Variants: Variables.
Vertical decalage: Underlying differences in mental schemas at different points along the development continuum that can give rise to the appearance of
similar outward behavior; can lead to misinterpretation of actual level of intellectual functioning.

1108       Journal of Chemical Education • Vol. 78 No. 8 August 2001 •
                                                                                               Research: Science and Education

Organization and Adaptation Functions                                       brated state do not ensure that the intended restructuring of
in Cognitive Development                                                    knowledge will occur, because control of personal knowledge
                                                                            construction or reconstruction resides within each individual.
      The organization function in human intellectual devel-
opment involves the formation of schemas, mentally organized                Hierarchial Development of Skills and Operations:
sets of related knowledge, “within the knowing subject’s range              Periods of Development
of experience” (4 ). The adaptation function encompasses the
inseparable, synergistic, and slow processes of assimilation and                  Piaget initially identified three periods of intellectual
accommodation (3). Assimilation and accommodation are                       development as examples to illustrate the progressively chang-
entwined processes that moderate an individual’s response to                ing balance between organization and adaptation: the sensory-
the environment and any subsequent readjustment of existing                 motor period, the period of preparation for and organization of
schemas, or construction of new schemas, in a cyclic feedback               concrete operations, and the period of formal operations. As
manner. For example, an individual’s existing knowledge                     the theory developed with time, the second period was seen
schemas determine in large part what that individual thinks                 as encompassing two periods with distinctive characteristics
is important and worthy of attention. Yet the things to which a             worthy of separate discussion: the preoperational period and
person pays attention can bring about a change in knowledge                 the period of concrete operations. This series of hierarchial
schemas, which then affects what a person thinks is important               periods of development is best viewed as a continuum from
and worthy of attention. The process and quality of schema                  sensory-motor to formal operational thought, although the
organization is highly variable among individuals since each                hierarchial nature of the periods is invariant (Fig. 1). Chrono-
individual processes the same information or activities in                  logical age is merely a guideline used to identify the most
unique ways. For example, Piagetian theory would support the                frequently observed ages that children, observed by Piaget, made
conclusion that no two individuals have identical or super-                 transitions between periods using his logico-mathematical tasks.
imposable mental schemas for “titration” even after having                        Qualitative differences in mental schemas and an increas-
experienced the same physical, or concrete, activities related to           ing balance between organization and adaptation (assimila-
titrations in chemistry courses. Schemas are highly individualis-           tion and accommodation) form the basis for the progressive
tic, or idiosyncratic, owing to the unique personal experiences             intellectual development within a period and from one period
and mental processing of these experiences by each individual.              to another. Each higher level of intellectual operation requires
      Intellectual development is dependent on the equilibration            and is built on the foundation of mental schemas developed
(a changing balance) process between the organization and                   during previous periods. In other words, an individual can-
adaptation (i.e., assimilation and accommodation) functions that            not skip a period or jump from the phenomenological-based,
occur as personal experiences and chronological age increase                egocentric schemas of the preoperational period directly to
(3, 4 ). Intellectual functioning by infants is dominated by                the formal operational period in a given content area. The
assimilation. As a child matures, the influence of accommo-                 development from infants’ survival schema of sucking to
dation on intellectual development increases. At various                    children’s acquisition of object permanence schema (objects still
points in the developmental process, organization and adap-                 exist even when hidden) is easily observed and might account
tation reach equilibrated states. In an equilibrated state, the             for the fact that Piaget described this period in more detail
individual uses his or her existing knowledge as sufficient to              than the other periods. However, the role of and relationship
explain whatever he/she wants to explain. For example, many                 between some of the intellectual operations at higher levels
preschool-aged children are satisfied with “the sun follows me”             can be less obvious and intuitive. A broadening range of in-
as an explanation for the movement of the sun or shadows.                   terests and activities and an increasing influence of social-
      Potential for intellectual growth or reorganization of                arbitrary knowledge as well as language development play a
knowledge requires a disequilibration, or perturbation, of this             larger role in intellectual functioning as a child matures. The
balanced state. If a child’s existing, but limited, knowledge is            increasing number of progressively more complex schemas
acceptable or sufficient to him or her for understanding or                 and the interrelationships or connections among schemas
explaining some phenomenon (e.g., dissolving and evaporation                contribute to a situation where the separation between the
are processes where the dissolved or evaporated substance “just             concrete and formal operational periods is not as easily ob-
goes away”) then the child must experience some event that                  served as in the sensory-motor period. Piaget acknowledged
perturbs or disequilibrates this knowledge state before con-                that not all humans achieve the formal operational level of
sidering it worthwhile to restructure his or her knowledge                  logico-mathematical reasoning and suggested that testing for
schemas. This is reminiscent of an adage: “If it works, why                 developmental stage level should be done in an area of interest
fix it?” However, outside attempts to perturb another’s equili-             to the individual (4).

                                                              Chronological Age/years
                          0           2        4          6        8        10          12     14      16       18
                           Sensory-         Period of                Period of                      Period of
                            Motor         Preoperations         Concrete Operations             Formal Operations

                                      Increasing Balance between Organization and Adaptation

                          Figure 1. Qualitative representation of Piagetian cognitive developmental periods.

               • Vol. 78 No. 8 August 2001 • Journal of Chemical Education                             1109
 Research: Science and Education

      The first three Piagetian periods are characterized by the     schooling, although schooling and a supportive environment can
hierarchical development of cognitive structures within a            be facilitating factors in the growth of intellectual development.
given period. In the period of concrete operations, children               J. Dudley Herron introduced Piaget’s Theory of Intel-
acquire the conservation of number schema before conser-             lectual Development to the chemical education community
vation of mass, which precedes acquisition of conservation           in a 1975 Journal of Chemical Education article (7 ). The
of volume. The ability to serially order objects on the basis of     perceived correspondence between Piaget’s description of
some property such as length occurs with two objects before          intellectual growth from infancy through adolescence to
three objects. In contrast, the development of mental schemas        maturity and the challenges associated with classroom learning
characteristic of the formal operational period appears to occur     is a compelling relationship for educators.
almost simultaneously. Organization of formal operational                  The two Piagetian developmental periods most closely
mental schemas and capabilities is conceptualized as a lattice       aligned with school-age children, namely, the concrete and
rather than the hierarchical or ladder model of the previous         formal operational periods, formed the framework for much
periods (3). The mental schemas characteristic of the formal         discussion and interest among educators. Behaviors, abilities,
operational period are exhibited in an individual’s ability to       and characteristics commonly associated with these two periods
carry out combinatorial analysis (consider all possible per-         and with learning science were introduced to science educators.
turbations), propositional logic (“if …, then …” reasoning           Curriculum and learning tasks based on Piagetian tenets were
that combines propositions), proportional reasoning, and iso-        designed to improve the learning of science. Two different,
lating and controlling relevant variables from among the set of      but not mutually exclusive, strategies in curriculum devel-
identified possibilities the individual has generated. Formal and    opment were pursued. One focused on the nature of concrete
concrete operations are not mutually exclusive—abstract              activities needed to move students from the concrete period to
descriptions require supplementation with concrete examples (3).     the formal period and were often short-term-intervention
      Piaget addressed the wide range of mental operations           instructional techniques. The other, which has come to be
within and among individuals using the concepts of hori-             closely associated with the learning cycle and conceptual
zontal and vertical decalage. Horizontal decalage is the phrase      change teaching, emphasized the mental processes of learning
used to label the observation that any individual can operate        science concepts, although concrete activities were integral
at different developmental periods in different domains or           components of the these teaching strategies as well. The results
content areas, although the individual may be classified in          of these efforts revealed that learning science is a very complex
one specific stage using classic, logico-mathematical Piagetian      process for many reasons. Continuing efforts to identify and
tasks. To illustrate, just because a person is capable of formal     characterize the sources of learning difficulties in more detail
operational reasoning, for example, that person does not             reveal additional layers of difficulties. All of this brings us to
necessarily always operate at the formal level for all tasks. This   a position where the theories from the field of cognitive science
could be due to choice or to a true difference in intellectual       presented in this set of papers can be informative and useful
development in different areas.                                      pieces of information to help us understand the learning
      The concept of vertical decalage alludes to the hidden         process and the difficulties students have in learning science.
or perceived uniformity or structural similarities between                 Piagetian theory has had a profound effect on the way
schemas of one period and another. For example, a student at         we think about learners and learning as well as the methods
the concrete operational level in science may appear to be able      by which this dynamic development process is translated to
to solve a problem that is thought to require formal opera-          learning environments. Contemporary cognitive science
tional skills but might be doing so with rote memory language        theories such as those described in the papers presented at the
or computational skills instead of the interconnected formal         Piaget symposium refocus attention on the fundamental
operational skills (5). Or, while the imagination of youngsters      functions of organization and assimilation/accommodation
at the preoperational period may appear to an outside observer       in intellectual development.
to be “abstract” or unrelated to physical objects, there are
significant structural or organizational and adaptational dif-       Literature Cited
ferences between the egocentric, phenomenological-based
structures characteristic of the preoperational period and the        1. von Glasersfeld, E. In Constructivism in Education; Steffe, L.
self-generated abstract or reflective reasoning structures of the        P.; Gale, J., Eds.; Lawrence Erlbaum: Hillsdale, NJ, 1995;
formal operational period (6 ). An analogy might be the child            Chapter 1, p 6.
who appears to be reading a favorite book when, in fact, the          2. von Glasersfeld, E. In Constructivism in Science Education: A
child has memorized the book as a consequence of having                  Philosophical Examination; Matthews, M. R., Ed.; Kluwer:
heard it repeatedly read by adults. Instead of recognizing letters       Norwell, MA, 1998; Chapter 2.
and words, the child uses visual clues to retrieve and apply the      3. Flavell, J. H. The Developmental Psychology of Jean Piaget; Van
memorized sequence of words associated with the visual clues.            Nostrand: New York, 1963.
                                                                      4. Piaget, J. Hum. Devel. 1972, 15, 1–12.
Piagetian Theory and Learning Science                                 5. Greenbowe, T.; Herron, J. D.; Lucas, C.; Nurrenbern, S.
                                                                         C.; Staver, J. R.; Ward, C. R. J. Educ. Psychol. 1981, 73,
     Piagetian theory identifies chronological age, content              705–711.
knowledge, experience, interest, and social milieu as variables       6. Lawson, A. E. In Handbook of Research on Science Teaching &
that can account for observable differences in intellectual              Learning; Gabel, D., Ed.; National Science Teachers Associa-
functioning among individuals (3). From the Piagetian per-               tion; Macmillan: New York, 1994; Chapter 4.
spective, cognitive growth occurs independently of any formal         7. Herron, J. D. J. Chem. Educ. 1975, 53, 146.

1110      Journal of Chemical Education • Vol. 78 No. 8 August 2001 •

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