Concrete Operational Tasks Research Articles

The Effects of a “Family” Analogy on Class Inclusion Reasoning by Young Children

This paper investigates the role of analogies in logical reasoning as an important aspect of scientific thinking. In particular, we studied the role of analogical reasoning in the solution of Piagetian concrete operational tasks. Halford (1993) has suggested that 4- to 5-year olds should be able to solve Piagetian class inclusion tasks on the basis of analogies to the relational structure of the nuclear family. This idea was tested in two studies. Analogy effects on class inclusion reasoning were indeed found. These effects were strengthened by the provision of hints to use an analogy and by deeper initial processing of the relational structure of the analogy. The family analogy was applied equally to sets of natural kinds and artifacts. These results suggest that children use familiar relational structures as a basis for logical reasoning. It seems likely that analogies will be core to scientific reasoning as well.

Assessing Africans' Cognitive Development: Judgment Versus Judgment Plus Explanation

Abstract The purpose of this study was to investigate how Botswana children in Southern Africa would perform on Piagetian concrete operational tasks when judgment versus judgment plus explanation was used as the criterion. The use of judgment only as a criterion led to a statistically significant proportion of children passing the Piagetian tasks. We concluded that, although Africans are relatively at ease when assessed on the basis of judgment responses only, the use of both judgments and explanations of Piagetian tasks is rather inhibiting for some and poses both linguistic and cultural problems that may impede successful performance.

Concrete operations and attentional capacity

In order to test predictions regarding the attentional capacity requirements of Piaget's stage of concrete operations, a battery of concrete operational tasks (class inclusion, transitivity of length and of weight, multiplication of classes, multiplication of relations) and two measures of attentional capacity (backward digit span and the Figural Intersection Test) were administered to 120 first, second, and third graders. With the exception of class inclusion, the results supported the hypothesis that three units of capacity would be necessary for solving each concrete operational task. Class inclusion was considerably casier than the other concrete operational tasks and was solved by nearly all children, a result which suggests that this version of the class inclusion task could possibly be solved without operational reasoning. The data also supported the prediction that transitivity of length and of weight, although differing in overall difficulty, would not differ in capacity demand. Instead, the horizontal decalage between length and weight was explained in terms of children's tendency to infer relative weight from relative size.

Functions, operations, and decalage in the development of transitivity.

The hypothesis that some attempts to reduce the performance demands of concrete operational tasks may have allowed children to solve those tasks with preoperational functions was tested by administering two previously used versions of the transitivity task for length and weight to 120 children 6 to 9 years of age. In the standard Piagetian version of the task, comparison objects were presented only two at a time, with no correlation between length or weight and spatial position. In the alternate version, objects were ordered in space by length or weight, but placed too far apart for differences in length to be seen. As predicted: (a) the standard version was solvable only through an operational composition of premise relations, but the alternate version allowed children to recode length or weight as a function of spatial position; (b) the functional solution was easier and developed at an earlier age than the operational solution for length as for weight. In addition, the decalage between length and weight was found to result from children's tendency to infer weight as a function of size rather than from an operational composition of premis e relations.

Development of concrete operational thought and information coding in schooled and unschooled children

In this study, we examine the influence of schooling and age on the development of concrete and operational thought and information processing as measured by non‐Piagetian tasks. One hundred schooled and 100 non‐schooled children in the age brackets of 6–8 and 10–12, and 50 4–6‐year‐old preschool children from a relatively homogeneous socio‐demographic background in a rural part of India were given four tests for information‐coding processes. Half of the subjects in each group were also given four Piagetian concrete operational tasks. As predicted, performance on Piagetian tasks increased as a function of age only, whereas the effects of schooling, age, and their interaction were clearly observed for coding processes. It is concluded that information‐processing modes rather than concrete operational skills are more sensitive to cognitive consequences of schooling.

A RELATIONSHIP BETWEEN SIMULTANEOUS‐SUCCESSIVE SYNTHESIS AND CONCRETE OPERATIONAL THOUGHT

In two studies, performance in concrete operational tasks was related to individual differences in simultaneous‐successive processing. Although the studies were carried out in culturally different populations (in Canada and in India), it was observed that children who prefer simultaneous to successive processing did better in the Piagetian tasks of conservation, transitive inference, and class inclusion. But performance in class inclusion appeared to be helped by both processes in the study in India. On the whole, rational as well as empirical reasons were found to claim that simultaneous processing is utilized in the successful solution of concrete operational tasks.

Cognitive Style, Operativity, and Mathematics Achievement

Previous investigations of the effects of field dependence-independence or the level of operational development on the mathematics achievement of children in the lower elementary school grades have involved the administration of concrete operational tasks (e.g., classification, conservation, and seriation). The present study was designed to examine the influence of these factors on the mathematics achievement of sixth, seventh, and eighth graders by using formal operational tasks (i.e., combinations, propositional logic, and proportionality). Results were analyzed using total mathematics achievement test scores as well as scores on subtests of computation, concepts, and problem solving. Field-independent students scored significantly higher than field-dependent students on the total mathematics, concepts, and problem-solving tests. High-operational students scored significantly higher than their low-operational peers on all tests. Educational implications of the findings are discussed.

Moral and cognitive development in delinquent and nondelinquent children and adolescents.

Moral and cognitive development of delinquents and nondelinquents were investigated--96 boys and girls at three ages: 10-11, 12-13, and 14-15-16 years. Moral judgment was assessed via the Defining Issues Test, and moral conduct by a resistance to temptation task. General cognitive development was explored with Piagetian-like tasks: two concrete operational tasks, two formal tasks, and a role-taking task. With the exception of role-taking, the delinquents were found generally to lag behind nondelinquents in terms of moral and cognitive development. With increasing age, disparate performances between the two groups were consistently shown, with delinquents always lower than nondelinquents. The delinquents were also less likely to resist temptation than the nondelinquents, though no age differences were noted.

ľApprentissage De La Notion ďInclusion De Classes Chez De Jeunes Enfants Baulés (côte ďivoire)

Abstract This training study of the concept of class inclusion follows a previous paper on the training of the conservation of liquids (Dasen et al. 1979). Twenty-eight African (Baoule) children, aged 7 to 9 years, were attributed to two groups, matched on age, schooling and performance on a pretest comprising 5 concrete operational tasks. Fourteen subjects who performed at stages 1 or 2 on class inclusion were trained according to a method adapted from Inhelder et al. (1974). The training effect was measured during two post-tests at the interval of one month. The results show a stable training effect in half of the subjects; there is a statistically significant generalization to other concepts of the same stage. This finding, which is similar to what has been reported for European children, supports the hypothesis of connections between operational concepts based on the common structure of the 'grouping'. A 'time lag' of about 2 years in the development of class inclusion appears when comparing Baoule an...

TEACHING PERSPECTIVE ABILITY TO FIVE‐YEAR‐OLDS

SUMMARY. Five‐year‐olds were individually trained in a structured programme of perspective problems. Compared with a control group (N=6), the children in the experimental group (N = 12) transferred their learning to both ‘near’ transfer tasks involving perspective‐taking and ‘far’ transfer tasks (other concrete operational tasks). Children trained in a matrices task (N=6) transferred their learning to other ‘near’ transfer tasks (related matrices problems), but failed to achieve higher scores than controls in the perspectives tasks. Therefore, perspective ability requires not only an operational level of thought, but also the specific skill of adopting another's viewpoint.

Developmental inter-relationships among concrete operational tasks: An investigation of Piaget's stage concept

One hundred and one primary school children were tested on eight concrete operational tasks. Each child's performance on each task was classified as either preoperational, transitional, or fully operational. Cross-classification tables were constructed showing the joint classification of children's performance on all possible pairs of the eight tasks. Two models of intertask relations, Wohlwill's ( The study of behavioral development. New York: Academic Press, 1973 ) divergent-decalage and reciprocal-interaction patterns, were evaluated for their fit to the cross-classification data using χ 2 goodness-of-fit procedures. Instances of both these patterns were identified in the data. The findings give some support to Flavell and Wohlwill's modification of Piaget's stage concept, in which individual groupings (e.g., seriation) are the structural basis of the interrelationships among concrete operational tasks. Tasks based on the same rule showed a degree of developmental interdependence (reciprocal-interaction patterns), while tasks based on different rules appeared to develop independently (divergent-decalage patterns). However, only one-half of the cross-classification tables were adequately described by either the divergent-decalage or the reciprocal-interaction patterns.

Modes of information integration and Piagetian measures of concrete operational thought

The purpose of the study was to investigate the relationships between modes of information integration and performance on a variety of Piagetian concrete operational tasks. The sample consisted of 180 6- to 8-year-olds. Factor analysis of the Piaget tests revealed five interpretable factors: conversation of substance—equality, conservation of substance— inequality, conservation of number, class inclusion, and matrices. Factor analysis of the marker tests for information integration revealed two factors: simultaneous and successive. All the Piaget measures, with the exception of class inclusion, were related to the simultaneous factor. Class inclusion was weakly related to the successive factor.

Qualitative differences in concrete and formal operational tasks

Five concrete and five formal tasks were administered to 64 second-, fourth-,sixth, and eighth-grade subjects. A significant grade effect ( p ⩽ .01) but no significant sex effect or interaction was found. A cluster analysis indicated that four of the five formal tasks grouped together, two of the five concrete tasks grouped together, and the rest of the tasks remained isolated. These results were interpreted as supporting both Piaget's qualitative hypothesis and the structural characteristics of the concrete and formal stages.

An Analysis of Synchrony between Concrete-operational Tasks in Terms of Structural and Performance Demands

ToUSSAINT, N. A. An Analysis of Synchrony between Concrete-operational Tasks in Terms of Structural and Performance Demands. CHILD DEVELOPMENT, 1974, 45, 922-1001. A set of tasks theoretically presumed to require equivalent logical competence (multiplication of classes, multiplication of relations, seriation, and transitivity) was administered to 32 first graders and 32 second graders. The performance demands were made equivalent by equating across tasks the amount of stimulus information and response requirements. Response measures emphasizing the operative and figurative aspects were compared within each task. Correlations indicated that the operative measures were the most successful in producing a high degree of correspondence in the levels of performance across tasks. Factor analyses confirmed the theoretical distinction between operative and figurative factors. The findings are discussed in relation to the importance of incorporating the figurative-operative distinction in the assessment of logical concepts.

An Analysis of Synchrony between Concrete-Operational Tasks in Terms of Structural and Performance Demands

An Analysis of Synchrony between Concrete-Operational Tasks in Terms of Structural and Performance Demands

An information processing analysis of some piagetian experimental tasks

One of the fundamental problems in the study of cognitive development is the determination of the developmental relationship between particular cognitive skills. An indication of its complexity is provided by the research literature centered on Piaget's concept of a “stage” in intellectual development. The first steps in an attempt to tackle this issue from a new methodological orientation based upon an information processing analysis are presented. A simple model of the problem-solving processes which appear to underlie successful performance on a range of experimental tasks testing concrete operations is described. It is analogous to a computer assembly system, with the major processes consisting of encoding of external stimuli, assembly of a task-specific routine from a repertoire of fundamental processes, and execution of the task-specific routines. The postulated fundamental processes are described in detail, and task-specific routines sufficient to perform successfully are described in terms of the fundamental processes. It is argued that since the complex task-specific routines consist of components that contain motivational and attentional mechanisms, no simple ordering of concrete operational tasks can be expected. Some new directions for experimental work are suggested.