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 Susan C. Nurrenbern Department of Chemistry, Purdue University, West Lafayette, IN 47907;
[email protected] Although I do not continually cite Piaget, I sincerely hope one realizes that almost everything I write herein can be written only because Piaget spent some 69 years establishing the basis for a dynamic constructivist theory of knowing. Constructivism arose for Piaget (as well as for Giambattista Vico, the pioneer of constructivism at the beginning of the 18th century) out of a profound dissatisfaction with the theories of knowledge in the tradition of Western philosophy. Ernst von Glasersfeld ( 1)
Piaget’s Theory of Intellectual Development claimed a significant and permanent presence in education during the last quarter of the 20th century as it ushered in the field of cognitive sciences. Piaget’s description of individuals as active
Mary B. Nakhleh Purdue University West Lafayette, IN 47907
participants in their intellectual development broadens our knowledge base and perspective about the learning process and possible approaches to classroom teaching. The perspective that learners are active participants rather than passive receivers of knowledge challenges the behavioristic, receptive, emptyvessel model of learners widely applied in many education situations. The papers 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 illustrate the extensive, continuing influence of Piagetian theory in the field of cognitive sciences and the overall understanding of intellectual development and knowledge construction.
Online Symposium
Piaget, Constructivism, and Beyond
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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 http://jchemed.chem.wisc.edu/Journal/Issues/2001/Aug/. 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
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Piagetian Theory: A Psychological Theory of Intellectual Development Piagetian theory is a psychological theory of intellectual development focused on the process by which individuals develop logical and viable (2) cognitive structures that support logico-mathematical reasoning. Piaget drew on his background in biology, philosophy, and logic to investigate human intellectual growth and development. His ideas related to intellectual development were far-reaching, as evidenced by the following passage from Flavell (3, p 84). He became particularly interested in the neural correlates of intellectual structures, and in one article in particular (1949) he made some guesses about brain mechanisms underlying the various structures which intellectual actions form in their progressive internalization. Thus, implicit motor responses seem to have been essentially by-passed as an object of study in favor of action systems in the brain.
Much of the language Piaget used to describe his perspective of intellectual development is rooted in the theories of natural selection and evolution and at times is complicated by translation from French to English. Sometimes he uses words and phrases that are similar to words and phrases in science but with a slightly different meaning. Box 1 is a glossary of Piagetian terms that will clarify the meaning of terms as used in this theory. Basics of the Theory Piaget based his work on the following premises. 1. One can learn about another individual’s internal mental structures, schemas, by direct observation of that individual’s behavior.
2. Intellectual or cognitive growth is integrally linked to the physical, social, and linguistic milieu of an individual. 3. Humans, being a biological species, are intrinsically motivated to grow intellectually or mentally by the processes of organization and adaptation, processes common to all organisms.
Piagetian theory incorporates only two invariants: (i) organization and adaptation are the driving forces for human intellectual development and (ii) intellectual development is characterized by a hierarchical development of successively more complex skills and operations. Consequently the keys to understanding Piagetian theory involve understanding the nature of these invariants as well as the relationships between them. Piaget’s findings and assertions are based on his observations of children as they manipulated or interacted with real objects or were faced with real tasks that involved transformation of an object or setting or correspondence between objects or object properties. Piaget would present the child with a task to complete, then change some variable within a task (e.g., hide objects; change the shape of pieces of clay, then ask about the comparative masses of the differently shaped pieces; determine the pivotal point for a balance beam with various masses) and observe how the child dealt with the task or questions under this new situation. The interview process did not include intervention or coaching the children into responses. Piaget’s findings led him to view intellectual development as a progressive process that exhibits a high degree of variability among individuals. The identification and labeling of developmental periods was Piaget’s platform to present, discuss, and illustrate the basic principles of the continuous, 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.
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Organization and Adaptation Functions in Cognitive Development
brated state do not ensure that the intended restructuring of knowledge will occur, because control of personal knowledge construction or reconstruction resides within each individual.
The organization function in human intellectual development involves the formation of schemas, mentally organized sets of related knowledge, “within the knowing subject’s range of experience” (4 ). The adaptation function encompasses the inseparable, synergistic, and slow processes of assimilation and accommodation (3). Assimilation and accommodation are entwined processes that moderate an individual’s response to the environment and any subsequent readjustment of existing schemas, or construction of new schemas, in a cyclic feedback manner. For example, an individual’s existing knowledge schemas determine in large part what that individual thinks is important and worthy of attention. Yet the things to which a person pays attention can bring about a change in knowledge schemas, which then affects what a person thinks is important and worthy of attention. The process and quality of schema organization is highly variable among individuals since each individual processes the same information or activities in unique ways. For example, Piagetian theory would support the conclusion that no two individuals have identical or superimposable mental schemas for “titration” even after having experienced the same physical, or concrete, activities related to titrations in chemistry courses. Schemas are highly individualistic, or idiosyncratic, owing to the unique personal experiences and mental processing of these experiences by each individual. Intellectual development is dependent on the equilibration (a changing balance) process between the organization and adaptation (i.e., assimilation and accommodation) functions that occur as personal experiences and chronological age increase (3, 4 ). Intellectual functioning by infants is dominated by assimilation. As a child matures, the influence of accommodation on intellectual development increases. At various points in the developmental process, organization and adaptation reach equilibrated states. In an equilibrated state, the individual uses his or her existing knowledge as sufficient to explain whatever he/she wants to explain. For example, many preschool-aged children are satisfied with “the sun follows me” as an explanation for the movement of the sun or shadows. Potential for intellectual growth or reorganization of knowledge requires a disequilibration, or perturbation, of this balanced state. If a child’s existing, but limited, knowledge is acceptable or sufficient to him or her for understanding or explaining some phenomenon (e.g., dissolving and evaporation are processes where the dissolved or evaporated substance “just goes away”) then the child must experience some event that perturbs or disequilibrates this knowledge state before considering it worthwhile to restructure his or her knowledge schemas. This is reminiscent of an adage: “If it works, why fix it?” However, outside attempts to perturb another’s equili-
Hierarchial Development of Skills and Operations: Periods of Development Piaget initially identified three periods of intellectual development as examples to illustrate the progressively changing balance between organization and adaptation: the sensorymotor period, the period of preparation for and organization of concrete operations, and the period of formal operations. As the theory developed with time, the second period was seen as encompassing two periods with distinctive characteristics worthy of separate discussion: the preoperational period and the period of concrete operations. This series of hierarchial periods of development is best viewed as a continuum from sensory-motor to formal operational thought, although the hierarchial nature of the periods is invariant (Fig. 1). Chronological age is merely a guideline used to identify the most frequently observed ages that children, observed by Piaget, made transitions between periods using his logico-mathematical tasks. Qualitative differences in mental schemas and an increasing balance between organization and adaptation (assimilation and accommodation) form the basis for the progressive intellectual development within a period and from one period to another. Each higher level of intellectual operation requires and is built on the foundation of mental schemas developed during previous periods. In other words, an individual cannot skip a period or jump from the phenomenological-based, egocentric schemas of the preoperational period directly to the formal operational period in a given content area. The development from infants’ survival schema of sucking to children’s acquisition of object permanence schema (objects still exist even when hidden) is easily observed and might account for the fact that Piaget described this period in more detail than the other periods. However, the role of and relationship between some of the intellectual operations at higher levels can be less obvious and intuitive. A broadening range of interests and activities and an increasing influence of socialarbitrary knowledge as well as language development play a larger role in intellectual functioning as a child matures. The increasing number of progressively more complex schemas and the interrelationships or connections among schemas contribute to a situation where the separation between the concrete and formal operational periods is not as easily observed as in the sensory-motor period. Piaget acknowledged that not all humans achieve the formal operational level of logico-mathematical reasoning and suggested that testing for developmental stage level should be done in an area of interest to the individual (4).
Chronological Age/years 0 SensoryMotor
2
4 Period of Preoperations
6
8
10
12
Period of Concrete Operations
14
16
18
Period of ? Formal Operations
Increasing Balance between Organization and Adaptation
Figure 1. Qualitative representation of Piagetian cognitive developmental periods.
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The first three Piagetian periods are characterized by the hierarchical development of cognitive structures within a given period. In the period of concrete operations, children acquire the conservation of number schema before conservation of mass, which precedes acquisition of conservation of volume. The ability to serially order objects on the basis of some property such as length occurs with two objects before three objects. In contrast, the development of mental schemas characteristic of the formal operational period appears to occur almost simultaneously. Organization of formal operational mental schemas and capabilities is conceptualized as a lattice rather than the hierarchical or ladder model of the previous periods (3). The mental schemas characteristic of the formal operational period are exhibited in an individual’s ability to carry out combinatorial analysis (consider all possible perturbations), propositional logic (“if …, then …” reasoning that combines propositions), proportional reasoning, and isolating and controlling relevant variables from among the set of identified possibilities the individual has generated. Formal and concrete operations are not mutually exclusive—abstract descriptions require supplementation with concrete examples (3). Piaget addressed the wide range of mental operations within and among individuals using the concepts of horizontal and vertical decalage. Horizontal decalage is the phrase used to label the observation that any individual can operate at different developmental periods in different domains or content areas, although the individual may be classified in one specific stage using classic, logico-mathematical Piagetian tasks. To illustrate, just because a person is capable of formal operational reasoning, for example, that person does not necessarily always operate at the formal level for all tasks. This could be due to choice or to a true difference in intellectual development in different areas. The concept of vertical decalage alludes to the hidden or perceived uniformity or structural similarities between schemas of one period and another. For example, a student at the concrete operational level in science may appear to be able to solve a problem that is thought to require formal operational skills but might be doing so with rote memory language or computational skills instead of the interconnected formal operational skills (5). Or, while the imagination of youngsters at the preoperational period may appear to an outside observer to be “abstract” or unrelated to physical objects, there are significant structural or organizational and adaptational differences between the egocentric, phenomenological-based structures characteristic of the preoperational period and the self-generated abstract or reflective reasoning structures of the formal operational period (6 ). An analogy might be the child who appears to be reading a favorite book when, in fact, the child has memorized the book as a consequence of having heard it repeatedly read by adults. Instead of recognizing letters and words, the child uses visual clues to retrieve and apply the memorized sequence of words associated with the visual clues. Piagetian Theory and Learning Science Piagetian theory identifies chronological age, content knowledge, experience, interest, and social milieu as variables that can account for observable differences in intellectual functioning among individuals (3). From the Piagetian perspective, cognitive growth occurs independently of any formal 1110
schooling, although schooling and a supportive environment can be facilitating factors in the growth of intellectual development. J. Dudley Herron introduced Piaget’s Theory of Intellectual Development to the chemical education community in a 1975 Journal of Chemical Education article (7 ). The perceived correspondence between Piaget’s description of intellectual growth from infancy through adolescence to maturity and the challenges associated with classroom learning is a compelling relationship for educators. The two Piagetian developmental periods most closely aligned with school-age children, namely, the concrete and formal operational periods, formed the framework for much discussion and interest among educators. Behaviors, abilities, and characteristics commonly associated with these two periods and with learning science were introduced to science educators. Curriculum and learning tasks based on Piagetian tenets were designed to improve the learning of science. Two different, but not mutually exclusive, strategies in curriculum development were pursued. One focused on the nature of concrete activities needed to move students from the concrete period to the formal period and were often short-term-intervention instructional techniques. The other, which has come to be closely associated with the learning cycle and conceptual change teaching, emphasized the mental processes of learning science concepts, although concrete activities were integral components of the these teaching strategies as well. The results of these efforts revealed that learning science is a very complex process for many reasons. Continuing efforts to identify and characterize the sources of learning difficulties in more detail reveal additional layers of difficulties. All of this brings us to a position where the theories from the field of cognitive science presented in this set of papers can be informative and useful pieces of information to help us understand the learning process and the difficulties students have in learning science. Piagetian theory has had a profound effect on the way we think about learners and learning as well as the methods by which this dynamic development process is translated to learning environments. Contemporary cognitive science theories such as those described in the papers presented at the Piaget symposium refocus attention on the fundamental functions of organization and assimilation/accommodation in intellectual development. Literature Cited 1. von Glasersfeld, E. In Constructivism in Education; Steffe, L. P.; Gale, J., Eds.; Lawrence Erlbaum: Hillsdale, NJ, 1995; Chapter 1, p 6. 2. von Glasersfeld, E. In Constructivism in Science Education: A Philosophical Examination; Matthews, M. R., Ed.; Kluwer: Norwell, MA, 1998; Chapter 2. 3. Flavell, J. H. The Developmental Psychology of Jean Piaget; Van Nostrand: New York, 1963. 4. Piaget, J. Hum. Devel. 1972, 15, 1–12. 5. Greenbowe, T.; Herron, J. D.; Lucas, C.; Nurrenbern, S. C.; Staver, J. R.; Ward, C. R. J. Educ. Psychol. 1981, 73, 705–711. 6. Lawson, A. E. In Handbook of Research on Science Teaching & Learning; Gabel, D., Ed.; National Science Teachers Association; Macmillan: New York, 1994; Chapter 4. 7. Herron, J. D. J. Chem. Educ. 1975, 53, 146.
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