Formal Operational Stage Research Articles

Teaching Rational Ideas Rational-Emotive Education

Middle school educators encounter youngsters at a critical point in their cognitive development. The period from age 11-13 is maturational time when youngsters reach the stage of formal operations, giv ing them the opportunity to move from childlike to adultlike thought.1 As never before, youngsters have the capacity to think abstractly, use logic, construct values, morals, and beliefs, take an objective view of themselves and the world, and use their thinking to prevent and resolve emotional problems. They have the capacity to do all these things, but will they? Will they actualize their cognitive capacity and make the transition form childlike to higher-order ideation?

The Significance of Piaget's Formal Operations Stage in Education

Despite a relative lack of attention on the part of both developmental and educational researchers, there are some grounds for believing that Piaget's stage of formal operations is the single stage in his sequence having the most profound and far-reaching implications for education. Following a review of the existing theory and research pertaining to formal operations, some of these potential implications are explored. They arise primarily, it is argued, from indications that the stage of formal operations, unlike the earlier stages in Piaget's sequence, may never be attained by some significant number of individuals. Lastly, some obstacles to fully realizing these implications are discussed.

Adult Cognition: Piagetian Based Research Findings

The work of Jean Piaget, widely recognized as pertinent to childhood cognition, has in recent years generated significant research based on adult samples. Because traditional Piagetian em phasis has been on young children the potential application of Piaget's theory to help in understanding and in explaining adult cognition has not been widely appreciated. Increasing in terest in adult development, however, has stimulated additional speculation and investigation in to the questions of adult cognition, including efforts to conceptualize adult cognitive develop ment in Piagetian terms. Application of Piagetian concepts to the study of adult cognition has occurred across a wide range and heretofore only limited efforts have been made to organize a review of the Piagetian literature on adult cognition around selected central issues. This extensive review, based on adult samples, reports the research findings concerning three specific topical issues that are of interest to the adult educator. The topics reviewed include the necessity, universality and persistence of the formal operations stage. Based on the literature reviewed, it is concluded that each of the topics requires further study, analysis and conceptualization.

The child's right to give informed consent to psychiatric treatment.

Abstract Following a review of the rights of children under the law, the authors conclude that there are some recent legal developments which may herald an eventual recognition in law that age by itself cannot be meaningfully used as the sole criterion for restricting to adults the right to give informed consent to psychiatric treatment. The authors argue that the right to informed consent is actually in the best interests of children as well as service providers. Furthermore, there is extensive evidence that developmental stage is a more accurate determinant of cognitive ability than is age, thereby suggesting that at least some persons under eighteen (e.g., children at the stage of formal operations, or perhaps even those at the concrete operational level) are intellectually capable of rendering truly informed consent to treatment. Recommendations are made which, until the law clearly recognizes the legal right of certain children to make certain contracts (e.g., consent to treatment), will continue to ...

Developmental Sequences in Perception and Interpretation of Ambiguous Sentences

The present research assessed the normal development of ability to perceive and interpret lexical and syntactic ambiguities in 40 grade school children, 10 kindergarteners, 10 second-graders, 10 fourth-graders, 10 sixth-graders, and 10 college students. Eight lexically ambiguous, eight syntactically ambiguous, and four unambiguous control sentences were presented for interpretation of their alternatives in meaning. Each experimental sentence was associated with four pictorial choices. Significant increases in the ability to perceive and interpret the alternative meanings of the lexical ambiguities occurred at or before the fourth grade (mean age 10 yr., 0 mo.) while significant changes for the syntactic and deep-structure ambiguities occurred at or before the sixth grade (mean age 12 yr., 0 mo.). Reaction times proved significantly shorter for the unambiguous than for the ambiguous sentences but remained stable over the present age range with the exception that the median reaction times between first and second responses decreased significantly between second grade and college level. The findings suggest that the ability to process lexical ambiguities increases and stabilizes during the concrete operational stage while the ability to process syntactic ambiguities stabilizes during the formal operational stage (Piaget & Inhelder, 1969).

Eliciting Formal Operations

There is considerable disagreement concerning the age of onset and universality ,..)f attainment of Piaget's stage of formal operations. This study examines developmental differences in response to brief prompts in the use of a formal operational approach to the solution of two tasks. The subjects were 10 males and 10 females from each of Grades 5, 8, and 12. Three tasks requiring the formal operational skill of separating and testing variables were given to each subject. Results suggest that almost all the subjects could readily'understand and utilize the approach of separating variables and tescing each one while holding all others constant. Furthermore, the results support Piaget's claim that formal operations are available to nearly all normal young adults. Implications for the development of logical competence are discussed. (SJL) *********************************************************************** Documents acquired by ERIC include many informal unpublished * materials not available from other sources. ERIC makes every effort * * to obtain the best copy available. Nevertheless, items of marginal * * reproducibility are often encountered and this affects the quality * * of the microfiche and hatdcopy reproductions ERIC makes available * * via the ERIC Document Reproduction Service (EDRS). EDRS is not * responsible for the quality of the original document. Reproductions * * supplied by EDRS are the best that can be made from the original. *********************************************************************** ^ Eliciting Formal Operations Fred W. Danner and Mary Carol Day Learning Research and Developrnent Center University of Pittsburgh U S. OEPARTME NT OF HEALTH, EOUCATION & WELFARE NATIONAL INSTITUTE OF EDUCATION THIS 00CUMENT HAS BEEN REPRODUCED EXACTLY AS RECEIVED FROM THE PERSON OR ORGANIZATION ORIGINATING IT POINTS OF VIEW OR OPINIONS STATED CIO NOT NECESSARILY REPRESENT OFFICIAL NATIONAL INSTITUTE OF EOUCATION POSITION OR POLICY Two formal operations tasks were presented to children from grades five, eight, and twelve--first, in the open-ended fashion used by Inhelder and Piaget and then with prompts in the use of a formal operational strategy. None of the young subjects and less than half of the older subjects were able to solve the first task on their own. A few of the younger subjects and nearly all of the adolescents, however, performed at a formal operational level on a transfer task. Eliciting formal operations by prompting and then measuring transfer appears to be a promising method for assessing logical compe-

Solving three-term series problems: A comparison of two stages of cognitive development

Abstract Piaget has suggested that three-term series problems cannot be solved until the formal operational stage, when the child can deal with the task in hypothetical terms, using serial ordering operations in conjunction with implication. Research carried out with 12-year-old subjects demonstrated that ability to solve three-term series problems was not associated with ability to solve a formal operational task (oscillation of a pendulum). A second experiment with 7-year-old subjects showed that success in solving verbal three-term series problems was related to ability to seriate objects which are physically present. It was concluded that the verbal task involves serial ordering operations rather than formal operational structures.

Significant physics content and intellectual development—cognitive development as a result of interacting with physics content

Increasingly during the past 20 years intellectual development has been recognized as the central purpose of education. The Piagetian model of intellectual development tells us that each student must engage a subject in a manner appropriate to his or her present stage of development if he or she is to advance to the next stage of development. When applied to college physics teaching, this theory implies that the large fraction of introductory physics students who are at the concrete operational stage of development must observe physical phenomena directly while they themselves are manipulating the equipment. Only in this way can they progress to the formal operational stage that characterizes professionals in the field.

INTELLECTUAL AND MORAL DEVELOPMENT IN ADOLESCENCE

Summary. 65 girls between 12 and 15 years of age were presented with four of Kohlberg's ‘moral dilemma’ stories and Inhelder and Piaget's ‘floating bodies' problem. The relation between level of moral judgment and formal operations was found to change from negative in Kohlberg's earlier stages to positive for the later stages of moral judgment. It was concluded that reasoning at the stage of formal operations is a precondition for progress to Kohlberg's Types 5 and 6 in moral judgment.

The ontogenesis of intelligence: Evaluating the Piaget theory

T HE COMPLEXITY and the far-reaching implications of Jean Piaget’s theory of the ontogenesis of intelligence have been evaluated in a variety of ways by different investigators. Piaget’*3 has postulated 4 stages in normal intellectual development: sensorimotor (birth to 2 years); preoperational (2 to 7 years); concrete operational (7 to 11 years); and formal operational (above 1 I years). Crucial to an understanding of these 4 stages is Piaget’s concept of conservation (sameness, invariation) applied to matter and quantity. Conservation refers to the idea that the mass of an object remains the same no matter how much the form changes. Prior to the attainment of this concept, during the sensorimotor stage, the child’s thought is dominated by his perceptions. He cannot cancel out the effects of change in order to focus on elements of an experience which remain unchanged. During the preoperational stage, the child begins the development of language and recalls his repertoire of actions and responses to objects he encounters; it is “preoperational” because his thought processes are not yet reversible. He may be struck by similarities in the properties of objects, but he does not by his own actions arrange and disarrange them so that objects are ordered and related. During the third stage of concrete operations, reversibility of the thought process relating to a manipulation of an object is present, but the child’s thinking is still bound to direct experience. Piaget postulates that this reversibility of thought is essential before classification and seriation can occur. After entering the final stage of formal operations, the person can construct theories and make logical deductions without the necessity for direct experience. The experiments which Piaget utilized in deriving his theory of development of logical thought have been repeated by various investigators. The first replication study by Estes4 did not establish the stages postulated by Piaget. However, in general, later and more technically rigorous studies have supported his findings regarding the sequence of stages in terms of conservation of number and quantity.5-7 However most of the replication studies suggested that the stages are not as clearcut as proposed by Piaget and the development in a given child may be uneven (i.e., he may attain conservation in one task and not reveal it in another).8*g The replication studies have the common defect that each studies different groups of children over time to observe development. Goodnow studied Chinese school boys and found that there is gross similarity in performance on Piaget’s conservation tasks among boys of different nationality and education. Piaget also maintained that the attainment of the concept of conservation of

THE PENDULUM PROBLEM: PATTERNS OF PERFORMANCE DEFINING DEVELOPMENTAL STAGES

Summary. Performance on Inhelder and Piaget's pendulum problem was obtained as a validating measure in a study of the transition from concrete to formal thinking. The sample consisted of 236 children aged from 10 to 14 years. A detailed scoring procedure was devised, which distinguished method from content aspects of performance on the problem and which allows categorisation of each child into one of nine developmental stages. Quantitative performance scores were also derived.Overall level of performance on the pendulum problem is strongly related to age, but not to sex or to school attended. In general, the results support Inhelder and Piaget's account of the transition from concrete to formal thinking. However, a specific problem, for their theory, arises from the relationship between method and content aspects of performance in the early formal operational stage (IIIA). This problem is discussed in detail and attention is drawn to the effects of a child's expectations on his performance.

The development of figurative language in children

Children in the third, fourth, and fifth grades were asked to do three different tasks in an attempt to determine their ability to use figurative language. Results for a Composition task showed that children produced a greater number of frozen than novel figures and that the absolute level of such usage decreased over grades. Results for a Multiple Sentences task revealed that children produced more frozen than novel figures and that both showed a marked increase over grade. Results for a Comparisons task indicated that figurative language increased over grade, and that for this task children used more novel than frozen figures. Taken in conjunction with earlier work, these data suggest that children are able to use figurative language well before theycan explain the exact nature of the relationship linking elements of the figure. In Piagetian terms, this implies that children use figurative language in the stage of concrete operations but cannot explain such usage until the stage of formal operations.

Negative Numbers

Summary According to Piaget, children who have not yet reached a stage of Formal Operations are unable to cope with concepts involving second‐order relations. Subtraction of negative integers necessarily involves second‐order relations. Children at a level of Concrete Operations are more dependent on models than students who have reached the Formal Stage. No existing teaching model of negative numbers fully represents all the phenomena involved in operations on negative numbers. This paper suggests that children be introduced to negative numbers through various models but that, apart from addition, operations on integers be delayed until the stage of Formal Operations.

A Comparison of Premise Types in Hypothetico-Deductive Thinking at the Stage of Formal Operations

A Comparison of Premise Types in Hypothetico-Deductive Thinking at the Stage of Formal Operations

A generalization of Piaget's logical-mathematical model for the stage of formal operations

The Piagetian logical-mathematical model for the stage of formal operations is presented. Weaknesses and limitations of the model are depicted and then a generalization of the model is presented along with a set of assumptions based on a hierarchial stage-theoretic view of formal thought with which the generalization complied. The Boolean algebraic structure of combinatorial thinking and the regular Boolean permutation group structure of hypothetico-deductive thinking are discussed. The method of designating the formal transformations in the groups descriptive of formal thought using the symmetric-difference operation is cited. The method of positive intersection generators is then employed to indicate the primitive formal transformations proper to a level of formal thought. The two smallest proposed groups descriptive of formal thought with their respective generators are displayed. Comparisons of the generalization with the Piagetian model are then instituted indicating the greater scope, adequacy, and sufficiency of the generalization in the explanation of formal operations. The usefulness of the generalization is indicated in various ways such as in the designation of the formal transformation used by an individual in a hypotheticodeductive situation.

The Effect of Interest onHorizontal DéCalageat the Stage of Formal Operations

The Effect of Interest on<i>Horizontal DéCalage</i>at the Stage of Formal Operations

Psychology of Children’s Cognitive toward Language Development

This paper aims to explain how the Cognitive Psychology supports the language development on children. The supporting data was taken from some related books and journals. The data collection is conducted through the proper source collection used for obtaining various information related to the topic. Then the information obtained from many sources was analyzed. The result of the analyses shows that the language acquisition process begins even since infancy period. In this process, the cognitive psychology supported it. In the process of acquiring the language, the children will pass through four steps of Cognitive process namely, sensorimotor stage, pre-operational stage, concrete operation stage, and formal operation stage. The entire stages are related to human’s age. In addition there are some assumptions of children’s cognitive development which are children’s schemas, assimilation, accommodation, and equilibration. Keywords: Cognitive, Cognitive Psychology, Language development

Comments on the INRC group

AbstractIn Piaget's theory, cognitive behavior in sonic problem situations can be likened to a four‐group—a mathematical group whose elements consist of four transformations. These four transformations are represented as follows: I (identity), N (negation), R (reciprocal), C (correlative). The INRC group has logical and physical “realizations,” i.e., different systems which exemplify its properties. Piaget holds that the INRC group and combinatorial structures can only be found at the stage of formal operations. In the snail problem, referred to by Easley, a snail is placed on a board which rests on a table. The snail can move from left to right or right to left while the board is stationary. Likewise, the board can move in either direction while the snail is stationary. Finally, the snail and the board can move simultaneously in either direction. In the following note Easley presents an analysis of the snail problem in terms of the INRC group.

THE DEVELOPMENT OF FORMAL THINKING IN VERBAL COMPREHENSION

Summary. This paper describes the results obtained by the investigators in their efforts to establish whether the inferences that secondary modern school children and pupils in further education draw in history, geography and literature texts correspond to the formal operational stage of reasoning as postulated by Piaget in his theory of mental development. Further, it was sought to provide answers to the following questions: Do the results obtained correlate more closely with mental or chronological age? Is there any significant sex difference shown in the results? Do the results show any significant difference by age?