Application of cluster analysis to the study of piagetian stages of intellectual development

The purpose of this study was to reexamine Piagetian stages by way of the application of cluster analysis and to seek information concerning the occurrence of stages and the influence of different tasks and gender on cluster patterns. Six Piagetian tasks were administered to 182 males and 176 females ages 9 through 18 years old. Analysis and interpretation of the data suggested the following conclusions: (1) Piagetian stages exist as a general sequence through which intellectual development progresses; however, the males in the study conformed more to Piagetian stages than did the females; (2) deviation from Piagetian stages was influenced by gender and the type of task; (3) lack of synchronization of substages across several tasks suggested that Piagetian tasks were more situation-specific than indicated by Piaget, and it also helped to explain why strong, correlations among tasks at a given level have been difficult to obtain; (4) for the males, the greatest discontinuity occurred between substages IIIA and IIIB, not between IIB and IIIA as stated by Piaget; and (5) the group of 13-year-old females tended to cluster with the 17- and 18-year-old female groups, but it was not known why.     

Contributions of Piagetian and post-Piagetian theories to education

The aim of this article was to reflect on the contributions of Piagetian and neo-Piagetian theories to education. Topics analyzed included the evolution of Piaget’s and co-workers’ theory, the reaction by the scientific community to the main theoretical and methodological aspects of each period of his work, the educational potentialities of methodological and theoretical aspects of his theory, the criticisms about the potentialities of Piagetian theory for grounding educational practice. Then the emergence of the neo-Piagetian theories was described, as well as their major aims and their educational potentialities. Finally some considerations concerning the strengths and weaknesses of Piagetian and neo-Piagetian theories were presented.     

Piagetian tasks as readiness measures in mathematics instruction: A critical review

The purpose of this review was to synthesize the research on the relationship between performance on Piagetian tasks of concrete operations and performance on mathematics learning tasks in order to determine whether the Piagetian tasks make useful readiness measures. The research consistently indicates that, while there is a positive correlation between performance on Piagetian tasks and mathematics achievement, many school mathematics tasks can be mastered by children who have not yet developed the reasoning abilities measured by Piagetian tasks. This does not diminish the validity of Piaget's theory, but rather suggests that the kinds of reasoning processes identified by Piaget are not essential in solving many school mathematics tasks.     

The necessity of each phase of the learning cycle in teaching high school physics

The learning cycle is a method of teaching—it is also a curriculum organization principle and is derived directly from the mental functioning model invented by Piaget. Although Jean Piaget contributed to the formation of the learning cycle (Piaget, 1973), its present structure has to be attributed to Dr. Robert Karplus and the persons who developed the materials of the Science Curriculum Improvement Study (SCIS). It was through the SCIS activities that many of us learned how to develop curricula and teach with the learning cycle. The learning cycle is built upon the premise that three distinct phases are necessary in developing understanding of a concept, that those phases have a definite sequence, and each phase has a definite structure or form. The research done in testing the form variable has already been reported in this journal (Renner, Abraham, & Birnie, 1985). This report explores whether or not each learning-cycle phase is necessary in learning a concept.     

Just-World Reasoning in Children''s Immanent Justice Judgments

The present study investigated the belief by Piaget that immanent justice responses occur when fairness judgments override conceptions of physical causality in young (6-8 years) children's understanding of a certain type of story. The structure of Piaget's stimulus stories was analyzed, and they were found to involve 3 narrative elements: motive valence, outcome valence, and causal connection. These 3 factors were crossed to create 8 types of stories, one of which (e.g., a character with a bad motive receives a negative outcome which is noncausally related to the previous motive) was the type used by Piaget. It was predicted that 2 types of stories would yield immanent justice responses: good motive/positive outcome/noncausal and bad motive/negative outcome/noncausal. Subjects received 4 stories and answered the Piagetian immanent justice questions and rated outcome fairness. Subjects were 48 each of children in grades 1, 3, and 5 and 38 college students. Results supported the prediction that children use the belief in a just world in immanent justice judgements.     

Teaching Criminological Theory: Using a Piaget Platform to Support Higher Level Learning

This paper proposes that higher level learning of criminological theory can be accomplished by having students express a theory creatively through an art form (i.e. a drawing, a dance, a poem, or role play). This type of constructivist assignment would empower undergraduate students to be theory co-creators and allow them to be actively engaged in building knowledge off of a Piagetian platform. While Piaget’s theory was formulated to explain the cognitive development in children, neuroscience has revealed its potential for expanding cognitive capacity in adults. When students are presented with a novel task requiring fuller focus, such as being required to build new knowledge onto existing schema in a uniquely creative way, deeper levels of learning are more likely to occur and be retained.     

Applicability of the Dual-Factor Model of Mental Health for College Students

This study explores the utility of a dual-factor model of mental health in which the concepts of mental illness and mental wellness are integrated. Life satisfaction, emotional symptoms, personal adjustment, and clinical symptoms were assessed with a sample of 240 college students. Participants were organized into four groups based on levels of life satisfaction and clinical symptoms. Results appear to be consistent with previous research suggesting that psychopathology and subjective well-being are not opposite ends of an illness--health continuum, but may be better conceptualized as separate and complementary constructs related to the full range of human functioning. Implications for prevention and intervention are discussed.     

Genetic AI: Translating piaget into lisp

This article presents a constructivist model of human cognitive development during infancy. According to constructivism, the elements of mental representation-even such basic elements as the concept of physical object-are constructed afresh by each individual, rather than being innately supplied. A (partially-specified, yet-unimplemented) mechanism, the Schema Mechanism, is proposed here; this mechanism is intended to achieve a series of cognitive constructions characteristic of infants' sensorimotor-stage development, primarily as described by Piaget. In reference to Piaget's genetic epistemology, I call this approach genetic AI-genetic not in the sense of genes, but in the sense of genesis: development from the point of origin.The Schema Mechanism focuses on Piaget's concept of the activity and evolution of cognitive schemas. The schema is construed here as a context-sensitive prediction of what will follow a certain action. Schemas are used both as assertions about the world, and as elements of plans to achieve goals. A mechanism of attribution causes a schema's assertion to be extended or revised according to the observed effects of the schema's action; due to the possible relevance of conjunctions of context conditions, the attribution facility needs to be able to sort through a combinatorial explosion of hypotheses. Crucially, the mechanism constructs representations of new actions and state elements, in terms of which schemas are expressed.Included here is a sketch of the proposed Schema Mechanism, and highlights of a hypothetical scenario of the mechanism's operation. The Schema Mechanism starts with a set of sensory and motor primitives as its sole units of representation. As with the Piagetian neonate, this leads to a solipsist conception: the world consists of sensory impressions transformed by motor actions. My scenario suggests how the mechanism might progress from there to conceiving of objects in space-representing an object independently of how it is currently perceived, or even whether it is currently perceived. The details of this progression paralledl the Piagetian development of object conception from the first through fifth sensorimotor stage.     

两种儿童认知发展观的比较探究

维果茨基与皮亚杰的争论代表了发展心理学两条截然不同的发展路线,开创了认知建构主义与社会建构主义两种模式.对两人关于儿童认知发展观的不同与相同之处进行比较探究,旨在为当代认知发展的理论建构与教育实践提供新的契机.     

Genetic epistemology,history of science and science education

Conclusions The main feature of Piaget & Garcia's study (1989) is the overture of a new field of research within the Piagetian framework, namely the comparative study of individual and historical development.During the 80's, several alternative models have been offered to account for the relations between individual and historical development. However, it has been suggested that there [...] appears to be widespread agreement among Piagetians and non-Piagetians that common mechanisms and processes underlie the thinking of scientists and children at all times (Gauld 1990, p. 24–5).The development of this field of research demands that theoretical research be conducted regarding the possible patterns of relationship between individual and historical development, that should be integrated to comparative empirical research on diverse topics. Further studies would then be required to provide an empirical basis for the comparative research. In other words, this field of research demands the close collaboration between epistemologists, historians, science educators, and cognitive psychologists.We have suggested that the Piagetian model needs to provide a more convincing account of the differences between individual and historical development, and of the role of internal and external factors in the progress of science. We have also argued for an overcoming of the overemphasized structural aspects of the theory, and for an unambiguous concept of history.The non-Piagetian approaches have their own strength and may be developed as alternatives to the Piagetian model. However, our intention here is to emphasize their potential contribution to the development of Piaget's theory. In McCloskey and Kargon (1988) we may find hints to deal with the specificity of similarities in content. Nersessian (1987) provided an excellent insight on how to deal with Kuhn's concept of incommensurability. ⁵ In our interpretation, Carey's work suggest that considering the relation between content and development of structures may be a productive way of developing Piaget's theory.Finally, we would like to comment on the relationship between Piaget's theory and research on students' thinking in science. Both adopt a constructivist stance. However, the vast majority of researchers have developed a strong resistance to Piaget's theory (e.g. Novak 1978; Gilbert and Swift 1985). On the one hand, this resistance should be considered a natural and healthy tendency toward a pluralistic development of research in science education. On the other hand, it may be a consequence of the difficulty of Piaget's theory in coping with the main research findings on spontaneous reasoning. In short, while many researchers in science education have emphasized the persistence of children's, adolescents' and adults' alternative conceptions, Piaget's theory suggests that reaching the formal stage is a necessary condition to understand science. This contradiction will not be overcome while Piagetian researchers are not able to offer a better account of the differences between commonsense knowledge and scientific knowledge. Freed from the constraints of the Piagetian approach, research on alternative conceptions showed an amazing development during the late 70's and the 80's. ^6,7 Further progress, however, increasingly requires theoretical tools to manage the great amount of data already available, and models to explain, rather than just describe, individuals' thought. This task can be carried out from within different theoretical approaches. In Psychogenesis and the History of Science, Piaget and Garcia presented an updated and strong model for the relationship between individual and historical development. If used in an open-minded way, this model may contribute to the development of research in science education.This study was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico/Brazil.     

Children's play: Piaget's views reconsidered

Piaget's theoretical contributions to the study of children's play are described. The Piagetian notions of play as representing pure assimilation and as serving a consolidative function are examined. Contemporary research in which these and other Piagetian premises have been studied empirically is reviewed.     

An approach to assessing and facilitating causal language in adults with learning disabilities based on Piagetian theory

Salient characteristics associated with Piagetian cognitive stages served as the basis for developing a linguistic taxonomy of causal semantic relations. Causal statements from adults with learning disabilities and normally achieving adults were analyzed and organized within this taxonomy. A relationship between Piagetian cognitive stages and verbal expressions of causality was identified. Based on this relationship, principles of Piagetian cognitive theory were used to design assessment and intervention plans for adults with learning disabilities.     

Role of the epistemic subject in Piaget's genetic epistemology and its importance for science education

According to Piaget, a fundamental epistemological distinction must be made between the psychological and the epistemic subject. The epistemic subject is studied by the genetic epistemologist who charts development through a “common universal rationality, which develops,” whereas the psychological subject is studied by the developmental/cognitive psychologist by focusing on accidental contingencies surrounding particular people and their individual differences. The epistemic subject as compared to the psychological subject is an idealized abstraction, viz., that set of underlying epistemic structures common to everyone at the same level of development. The objective of this study is to investigate the degree to which investigators in science education conceptualize the difference between the epistemic and the psychological subjects. It is argued that just as the ideal gas law (based on the theoretical formulation of Maxwell and Boltzmann) provides a “general model” to which the real gases approximate under different experimental conditions, so we can consider (by abduction) the epistemic subject to be an “ideal knower” to which the real (psychological) subjects approximate to varying degrees. The difference between the epistemic and the psychological subjects, however, cannot be used as an “epistemological shield” in defense of Piagetian theory. Any test of the Piagetian theory must involve psychological or real subjects. Empirical testability, however, need not be equated to being scientific. An analogy is drawn between Galileo's idealization, which led to the discovery of the law of free-fall, and Piaget's epistemic subject. Research conducted in science education shows that at least for some critics the wide variations in the age at which individuals acquire the different Piagetian stages is crucial for rejecting the theory. It is argued that the real issue is not the “proportion of heterogeneity” but the understanding that Piaget, by neglecting individual differences, attempts to build a general model applicable across types of situations/subjects. The distinction between the epistemic and the psychological subjects is important not for defending Piaget's theory (which has serious theoretical flaws) but to understand epistemic transitions, for example, the one between Piaget's epistemic subject and Pascual-Leone's metasubject. It is concluded that failure to understand the distinction between the epistemic and the psychological subjects would lead to misconstruing the significance of our research findings and, what is more serious, to a lack of a historical perspective.     

A Piagetian-Based Programme for Learning “Elements and Symbols”

Piaget's learning theory on cognitive development has had considerable impact on science education (Piaget, 1964; Inhelder and Piaget, 1958; Craig, 1972). The theory classifies cognitive learning into four successive stages: (a) sensory-motor, (b) pre-operational, (c) operational, and (d) formal. Various programmes and instructional strategies have been developed based on the theory (Batt, 1980; Karplus, 1977; Renner and Stafford, 1979; Ryan, et al., 1980; Herron, 1978; Good et al; 1978). An application of this theory for teaching and learning scientific concepts is the Piagetian learning cycle (Karplus, 1977) which is of growing interest among science educators. This article intends to introduce briefly the learning cycle in general and suggest a learning cycle for teaching a topic in chemistry: “Elements and Symbols”.     

Twenty questions about student errors

Errors in science learning (errors in expression of organized, purposeful thought within the domain of science) provide a window through which glimpses of mental functioning can be obtained. Errors are valuable and normal occurrences in the process of learning science. A student can use his/her errors to develop a deeper understanding of a concept as long as the error can be recognized and appropriate, informative feedback can be obtained. A safe, non-threatening, and nonpunitive environment which encourages dialogue helps students to express their conceptions and to risk making errors. Pedagogical methods that systematically address common student errors produce significant gains in student learning. Just as the nature-nurture interaction is integral to the development of living things, so the individual-environment interaction is basic to thought processes. At a minimum, four systems interact: (1) the individual problem solver (who has a worldview, relatively stable cognitive characteristics, relatively malleable mental states and conditions, and aims or intentions), (2) task to be performed (including relative importance and nature of the task), (3) knowledge domain in which task is contained, and (4) the environment (including orienting conditions and the social and physical context). Several basic assumptions underlie research on errors and alternative conceptions. Among these are: Knowledge and thought involve active, constructive processes; there are many ways to acquire, organize, store, retrieve, and think about a given concept or event; and understanding is achieved by successive approximations. Application of these ideas will require a fundamental change in how science is taught.     

The Development of Size Sequencing Skills: An Empirical and Computational Analysis

We explore a long-observed phenomenon in children's cognitive development known as size seriation. It is not until children are around 7 years of age that they spontaneously use a strict ascending or descending order of magnitude to organize sets of objects differing in size. Incomplete and inaccurate ordering shown by younger children has been thought to be related to their incomplete grasp of the mathematical concept of a unit. Piaget first brought attention to children's difficulties in solving ordering and size-matching tests, but his tasks and explanations have been progressively neglected due to major theoretical shifts in scholarship on developmental cognition. A cogent alternative to his account has never emerged, leaving size seriation and related abilities as an unexplained case of discontinuity in mental growth. In this monograph, we use a new training methodology, together with computational modeling of the data to offer a new explanation of size seriation development and the emergence of related skills. We describe a connected set of touchscreen tasks that measure the abilities of 5- and 7-year-old children to (a) learn a linear size sequence of five or seven items and (b) identify unique (unit) values within those same sets, such as second biggest and middle-sized. Older children required little or no training to succeed in the sequencing tasks, whereas younger children evinced trial-and-error performance. Marked age differences were found on ordinal identification tasks using matching-to-sample and other methods. Confirming Piaget's findings, these tasks generated learning data with which to develop a computational model of the change. Using variables to represent working and long-term memory (WM and LTM), the computational model represents the information processing of the younger child in terms of a perception-action feedback loop, resulting in a heuristic for achieving a correct sequence. To explain why older children do not require training on the size task, it was hypothesized that an increase in WM to a certain threshold level provides the information-processing capacity to allow the participant to start to detect a minimum interval between each item in the selection. The probabilistic heuristic is thus thought to be replaced during a transitional stage by a serial algorithm that guarantees success. The minimum interval discovery has the effect of controlling search for the next item in a principled monotonic direction. Through a minor additional processing step, this algorithm permits relatively easy identification of ordinal values. The model was tested by simulating the perceptual learning and action selection processes thought to be taking place during trial-and-error sequencing. Error distributions were generated across each item in the sequence and these were found to correspond to the error patterns shown by 5-year-olds. The algorithm that is thought to emerge from successful learning was also tested. It simulated high levels of success on seriation and also on ordinal identification tasks, as shown by 7-year-olds. An unexpected finding from the empirical studies was that, unlike adults, the 7-year-old children showed marked difficulty when they had to compute ordinal size values in tasks that did not permit the use of the serial algorithm. For example, when required to learn a non-monotonic sequence where the ordinal values were in a fixed random order such as “second biggest, middle-sized, smallest, second smallest, biggest,” each item has to be found without reference to the “smallest difference” rule used by the algorithm. The difficulty evinced by 7-year-olds was consistent with the idea that the information in LTM is integrally tied to the search procedure itself as a search-and-stop based on a cumulative tally, as distinct from being accessed from a more permanent and atemporal store of stand-alone ordinal values in LTM. The implications of this possible constraint in understanding are discussed in terms of further developmental changes. We conclude that the seriation behavior shown by children at around 7 years represents a qualitative shift in their understanding but not in the sense that Piaget first proposed. We see the emergent algorithm as an information-reducing device, representing a default strategy for how humans come to deal with potentially complex sets of relations. We argue this with regard to counting behaviors in children and also with regard to how linear monotonic devices for resolving certain logical tasks endure into adulthood. Insofar as the monograph reprises any aspect of the Piagetian account, it is in his highlighting of an important cognitive discontinuity in logicomathematical understanding at around the age of 7, and his quest for understanding the transactions with the physical world that lead to it.     

Progress to conservation: Conflict or correct answer?

One of the fundamental problems in socio-cognitive conflict theory concerns what it is that leads to cognitive growth. Is it conflict per se, i.e. the fact that two contradictory opinions are brought together, or is it the presence of the correct answer which is essential for growth. In this experiment, dyads, functioning on the same cognitive level, were formed and asked to solve a conservation-of-length task. The classification of the children in the pre-test was not done according to Piagetian norms, but according to Flavell’s appearance-reality (AR) model: AR non-conservers (AR-NC), AR intermediates (AR-I) and AR conservers (AR-C). Many children who would have been scored as non-conservers in a standard Piagetian task, showed an underlying conservation competence and were classified as AR-I. The results of the interaction suggest that conflict does not lead to appropriate change in AR-NC dyads or AR-I dyads. Furthermore, the results suggest that the most effective method for AR-I to become conservers, is to make them think about a problem and then, to create consensus by confronting the children with others who have also reached the correct solution.     

Piagetian theory and the teaching of reading

An attempt is made to reconsider the implications of Piaget's theories for the teaching of reading. It is argued that the way the theories have typically been interpreted in relation to reading is unhelpful and does not accord with the behaviour of young readers. Alternative ways of linking Piagetian theory to the teaching of reading are proposed. It is considered that they both provide a more adequate explanation and offer the teacher more helpful directions along which to develop reading.