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Piaget's System of 16 Binary Operations: An Empirical Investigation
Abstract
In their 1958 work, B. Inhelder and Piaget offer a single protocol as their only evidence that a fully developed formal operational thinker uses all 16 binary operations of truth-functional logic. The present study attempted to replicate the Inhelder-Piaget results with a random sample of 18 9-yr-old, 19 12-yr-old, and 20 16-yr-old Ss. Not one of the Ss used more than 5 of the 16 operations, and there was no developmental trend with regard to the number of operations used (p > .05). A trend was manifest, however, since the more developed reasoner used the same operations as the less developed reasoner, but in a more complex and sophisticated manner. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
... Ginsburg tells us what to do; Smith tells us why. In contrast, poorly implemented replications of the Genevan méthode (e.g., Bynum, Weitz, & Thomas, 1972;Weitz, 1971;Weitz, Bynum, Thomas, & Steger, 1973) and philosophically naïve criticisms of it (e.g., Siegal, 1991Siegal, , 1999aSiegal, , 1999b seem to have negative impacts far beyond what any informed view might expect (see Bond & Jackson, 1991, on Bynum et al.;see Lourenç o &Machado, 1996 andSmith, 1999 on Siegal). ...
Piaget’s method of data collection has always appeared quite unorthodox to psychologists raised on the Anglophone diet of standardized, objective, and experimental scientific method where results were routinely presented following some sort of routine statistical analyses. Piaget’s books revealed him as merely chatting to few children - mainly his own and apparently, just a few others - about the moon, about their drawings of bicycles, and most famously, how skinny glasses held more juice than fat ones did. Interesting for sure - but hardly replicable, scientific psychological experiments: The questions changed, the procedures changed, and none of the results showed means and standard deviations. Considering the number of published papers and books, we remain surprised by the small space Piaget gave to explaining his method. Although the hundreds of protocol extracts, meant to illustrate his theory, correspond to almost half of the pages of each published volume, the mention of any detailed data collection, setting, or precise method eventually used in the reported investigations is rare and generally very vague: “You place in front of the child a certain number of flowers…”; “… it is useful… to have the child drawa picture…” (see Tryphon, 2004). This lack of clarity has given rise to many criticisms of Genevan researchers’ “bad habits,” such as nonrigorous experimental conditions, small, non-representative samples, and lack of quantitative analyses (Flavell, 1963).
... Martorano, 1977). It was also shown that this stage is reached fairly late and often only partially (Prêcheur, 1976;Schwebel, 1975) and that the formalization using the INRC group was not entirely satisfactory because adolescents actually use few binary operations in reasoning and do not display all the mobility of the INRC group (Weitz, Bynum & Thomas, 1973; and for the well-known « Gou protocol » [Inhelder & Piaget, 1955, pp. 90-93], Bynum, Thomas & Weitz, 1971). ...
From 1984 to 1988, a longitudinal study was conducted with 104 children born in 1980. This study was devoted to the development of Piagetian concrete operational thought, using 25 classical Piagetian tasks. Seven years after the end of the study, 62 children from the original sample were again examined in relation to formal thought, general intelligence and spatial and verbal abilities. This paper analyses the data obtained and the relationships between concrete and formal thought. The main results show: (i) the low average attainment in formal thought among 15-year-old adolescents; (ii) the reliable measurement of general intelligence provided by Piagetian tasks; and (iii) the strong relationship between early competence in number manipulation and later access to combinatorial and formal thought.
Educators have been interested in Jean Piaget’s theory of cognitive development as a means of linking developmental level, concepts that can be grouped, and instructional strategy. Also, considerable effort has been directed to acceleration of the child’s developmental level. Many researchers, wishing to generalize to large numbers, have turned away from Piaget’s technique to group paper-and-pencil tests. Attention has been focused on the psychometric properties of these tests and their statistical links with other constructs.
This review takes the following perspectives. First, there is a questionable relationship between the observed products of mental effort and their underlying mental strategies. There is evidence of a many-many rather than a one-one relationship between solution and strategy. Second, when viewed from its own experimental statistical perspective, much of the research suffers from serious methodological flaws. Third, attempts to prescribe instructional strategies that accelerate intellectual development have borne little fruit. The review closes with suggestions for a redirection of emphasis on the application of Piaget’s theory to education.
Piaget's theory of cognitive development, in particular his ‘stage theory’, is having a significant influence on thinking about school science curricula. In the trend to more informal and child‐centred methods, his ideas have formed a base for many primary science programmes over the world. Until fairly recently, however, the impact of his thinking has not been felt in secondary science programmes. There are now signs that this is changing. The Piagetian model, particularly the stage theory, is being used in this country and elsewhere as both a scale on which to measure scientific development and an explanatory system to account for the difficulties secondary school pupils encounter in understanding scientific ideas. With this growing awareness of Piaget's work and its implications among secondary science teachers and curriculum developers perhaps it is timely to take a step back and review the status of the work critically. Since it is addressing itself to the relevance of Piagetian theory to learning science at the secondary school level, the focus of this paper is specifically on studies which relate to the development from concrete to formal level thinking. The first part outlines Piaget's general epistemological position and specification of the formal level of thought. This is followed by a discussion of three areas of problem with the Piagetian analysis: problems inherent in the specification of the logical model of formal thought; assumptions underlying Piaget's research methodology; and some problems with empirical findings. The second part of the paper comments on consequent problems in attempts to apply the Piagetian ideas to secondary science education. The paper ends by assessing the aspects of Piagetian work which may contribute to science education in the future.
Two propositional reasoning tests were administered to eighth-grade boys and girls. Each item on one of the tests was used to assess Ss' comprehension of a basic rule for one of four types of propositional logic, whereas each item on the other test was used to measure Ss' abilities to solve “who-done-it” problems involving two of the four types of propositional logic. The results showed significant differences in Ss' performances according to the type(s) of propositional logic involved in a given item. Surprisingly, however, the interdependence of Ss' performances on the two tests was minimal. The results were discussed in terms of research and theory regarding formal operational thinking.
The role of formal logic in the development and investigation of science education is analysed. Firstly, the way in which teachers use language, logical and otherwise, is described and the necessary use of logical relations in the learning of abstract concepts and ideas is investigated. The conclusions drawn from the literature indicate that learners have great difficulty in comprehending the normal logic implied in ordinary words such as ‘because’ and ‘therefore’, and that the more difficult the context, the more likely it is that even the most common logical argument will be misunderstood. Less common logical words may be misunderstood by a majority of typical pupils in science lessons.
Secondly, the development of efficient cognitive processes in the context of science curricula is investigated. The conclusion drawn from literature describing experiments (rather than suggestions based more in philosophy) suggests strongly that formal logics probably have little to offer science educators. It is argued that until science teaching starts to base itself more on ‘natural strategies’, in much the same way as it is now looking seriously at ‘alternative frameworks’ as the basis for concept development, process development in science teaching will not seriously affect the ability of most pupils to solve either scientific or everyday problems more efficiently.
Lawson (1 979) addresses two questions of considerable importance to science educators and Piagetian psychologists. They are: is there evidence to support the contention that a unified, structured whole of operations underlies the formal operational schemata of combining variables, controlling variables, and proportions and, if
A central purpose of education is to improve students' reasoning abilities. The present review examines research in developmental psychology and science education that has attempted to assess the validity of Piaget's theory of formal thought and its relation to educational practice. Should a central objective of schools be to help students become formal thinkers? To answer this question research has focused on the following subordinate questions: (1) What role does biological maturation play in the development of formal reasoning? (2) Are Piaget's formal tasks reliable and valid? (3) Does formal reasoning constitute a unified and general mode of intellectual functioning? (4) How does the presence or absence of formal reasoning affect school achievement? (5) Can formal reasoning be taught? (6) What is the structural or functional nature of advanced reasoning? The general conclusion drawn is that although Piaget's work and that which has sprung from it leaves a number of unresolved theoretical and methodological problems, it provides an important background from which to make substantial progress toward a most significant educational objective.
All our dignity lies in thought. By thought we must elevate ourselves, not by space and time which we can not fill. Let us endeavor then to think well; therein lies the principle of morality. Blaise Pascal 1623‐1662.
Recently Piaget's model of cognitive development has been seriously questioned. This questioning was due partially to the inadequacy of the model in explaining creative, scientific and mature thought in adulthood. Various proposals have suggested the existence of a fifth stage in cognitive to represent adult thought. A second tradition has focused on the Piagetian model as a competence model. This has initiated a search for an appropriate performance model to describe the processes by which knowledge is actively constructed and applied. The present work reviews the theoretical positions and the research relevant to issue and proposes a synthesis through which cognitive development can be viewed as being both product and process, competence and performance, structure and function simultaneously.
According to Inhelder and Piaget, a fully developed formal operational thinker uses all 16 binary operations of truth-functional logic in solving problems. The only evidence offered, however, was a single protocol from the physical task, Role of Invisible Magnetism. Using this 1 protocol and the Inhelder-Piaget method of analysis, an attempt was made to duplicate the results of Inhelder and Piaget. Examples and evidence, were found for only 8 operations; 8 of the Inhelder-Piaget analyses were faulty. Several important questions are raised, e.g., do fully developed formal operational thinkers actually use all l6 binary operations of truth-functional logic? (PsycINFO Database Record (c) 2012 APA, all rights reserved)