Nonconserving Children Research Articles

Mathematical fluency as a function of conservation ability in young children

This study was designed to investigate the cognitive level of development and mathematical fluency of first grade children. Piaget's conservation-of-liquid task was administered to 97 6- and 7-year-old children from two low-socioeconomic-level elementary schools. Using a counterbalanced design, conserving and non-conserving children completed separately timed lists of addition and subtraction problems. Two one-way analyses of covariance (ANCOVAs) were conducted to evaluate the fixed-factor of conservation level (conserving and non-conserving) and the two dependent variables (addition and subtraction fluency); age was a covariate. After controlling for the effect of age, the results suggest that conserving children were significantly more fluent in completing addition and subtraction problems than non-conserving children. Overall, children in the same grade and of the same age were at different levels of cognitive development; these levels had an effect on both addition and subtraction fluencies.

An electrophysiological study of discrete number conservation in children

Auditory averaged evoked responses (AERs) were collected from six scalp locations over left and right hemispheres of 10 children. The AERs were collected while the children were involved in either a conservation task or a control task involving number equality. Principal components analysis/analysis of variance (PCA/ANOVA) of the conservation task AER data allowed the author to identify two AER components related to conservation. A bilateral component at 500 msec and a right hemisphere lateralized component at 300 msec allowed discrimination between nonconserving and conserving children for the conservation task. PCA/ANOVA of the control‐task AER data revealed no differences between conserving and nonconserving children. The author interpreted these findings as indicating the existence of AER components that reflect conservation ability in children. This interpretation was supported by a discriminant function analysis of the AER data collected during the two tasks. The discriminant function analyses of the conservation task AER data allowed the author to discriminate between the conserving and nonconserving children with 80% accuracy. The discriminant function analysis of the control‐task AER data did not allow significant discrimination of the conserving and nonconserving children.

Judgments of quantity and conservation of quantity: The area of a rectangle

This study examines the relationships between perceptive judgment of quantity and conservation judgment of quantity with regard to the concept of area. Twenty children who passed an area conservation task (mean age = 8) and 20 children who failed it (mean age = 6.7) were administered an area judgment task. This task was a replication of Anderson and Cuneo's study (1978, Journal of Experimental Psychology: General, 107, 335–378). The conserving children generally appeared to apply an additive rule (the height and width rule) observed by Anderson and Cuneo in 5 year olds. The nonconserving children in contrast generally presented patterns suggesting centration on one of the two dimensions. The implications for Anderson's and Piaget's conceptions of conservation development are discussed.

Interaction and instruction in the conservation experiment

Though there has been considerable research in recent years into the ways in which children’s performance in conservation experiments is affected by the context of interaction, this has so far lacked a coherent theoretical basis. In this article, concepts from communication theory are applied to the behaviour of experimenter and subject in the experimental situation. It is argued that the child behaves according to the «metacontract» of a teacher-pupil interaction, i.e. he or she expects to receive instruction. In the classical conservation experiment of Piaget, these expectations are thwarted, because the experimenter does not conform to the rules of a teacher-pupil relationship. Instead, the experimenter follows the rules of a different metacontract—that of examination. In experiments where conservation abilities are taught, and in group interactions where conserving children cooperate with non-conserving children, the participants do behave according to the same metacontract. But the value of these studies is reduced by the exclusive attention paid to the eventual achievements of the child, instead of the cognitive processes during the learning phase.

Interhemispheric transfer and the completion of reversible operations in non-conserving children.

Evidence that concerns interhemispheric transfer deficits in young children is reviewed, and it is suggested that the late maturation of the corpus callosum may prevent the transfer and thus verbal expression of knowledge concerning equivalence relationships in non-conservers - operations normally performed by the right hemisphere. Because previous findings with "split-brain" patients indicate that interhemispheric transfer can be achieved when questions are phrased in the context of a reward (e.g., "preference"), questions concerning the conservation of a non-equivalent volume were posed to 65 non-conservers in terms of an imagined reward (preference condition). Questions also were phrased so as to require comparative-relational determinations as well as expectation of an empirical reversal of the stimulus conditions so as to determine differences/similarities in the reasoning process. Significantly more non-conservers demonstrated an awareness of empirical reversal or performed the preference relational operation correctly as compared to conditions that required comparative-relational judgments. The evidence also suggests the presence of two fundamentally distinct cognitive approaches to the problem, which appear to resist integration in children of this age group.

Nonlinguistic Knowledge, Hemispheric Laterality, and the Conservation of Inequality in Nonconserving Children.

Nonconserving children may fail to conserve because of difficulties in verbally expressing nonlinguistic knowledge of equivalence relationships. This may be partly due to an inability of the right hemisphere, which mediates the performance of internal reversals and conservation, to communicate with the speaking left hemisphere because of the immaturity of the corpus callosum. This relationship presumably results in the asymmetrical activation of the left hemisphere when verbal responses are required. To assess the possibility that nonconservers have an awareness of the reversibility of these operations, three groups of nonconserving children (N = 42) were either asked which of two containers (one of which appeared to contain more liquid, but had previously been shown to contain less) had more in it, or which (pretending they were very thirsty and it was their favorite drink) they would prefer. To assess whether nonconservers respond primarily with left hemisphere activation, patterns of lateral eye movement in response to verbal-analytic or spatial-emotional stimuli were obtained in a fourth group (N = 37). Both hypotheses were supported.

Play and cognition: Studies of pretence play and conservation of quantity

Study 1 examined the relative effectiveness of four different training conditions on the attainment of conversation of quantity. Subjects were 75 nonconserving preschoolers, ranging in age from 3.10 to 5.0 years. Treatment consisted of pretense play training, direct conservation training, a combination of pretense play and conservation training, mere exposure to the conservation tasks without the benefits of instruction, and a control condition which provided only conservation pre- and post-tests. The results of the two conservation post-tests indicated that a combination of pretense play and conservation training was the most effective condition, followed by the conservation training and then by the pretense play training. The data also suggested that the effects of the conservation-only training condition might be less stable than those attained with pretense play training. Study 2 compared the effectiveness of child initiated pretense play training with adult initiated play. Subjects were 47 nonconserving children ranging in age from 4.0 to 5.8. Treatment consisted of child initiated pretense play, adult initiated play, a condition which combined both treatments, and a control group. The results of the two conservation post-tests indicated that the child initiated pretense play training was most effective, followed by the combined condition and by the adult initiated training. The three pretense play training conditions induced significantly more conserving responses in previously nonconserving children than the control group.

Apprentissage de la conservation par observation d'un modèle

Summary The present experiment attempted to measure the impact of the reasons of conservation responses given by a model in an observational learning situation. In some of the conservation tasks that were used during a pretest either compensation, identity, or reversibility reasons could be used and in some others only one reason was relevant. Five groups of nonconserving children were exposed to the model's solution in one task of the first type : in the first group the model supplied ail three reasons ; in the second, third and fourth groups he supplied respectively a compensation, identity, or reversibility reason ; and in the last group he did not justify his judgment. The children were given ail of the pretest tasks immediately after the observation session and eight weeks later. No acquisition was reported in the last group but the results reveated a comparable improvement among the four other groups. The presentation of at least one reason by the model would therefore be both necessary and sufficient for the occurrence of learning. In those tasks that could be solved through the use of only one reason, the observer s who had been exposed solely to a reason other than the required one often appeared to be able to generate the required reason and thus showed some mastery of the conservation notion.

Identity, Compensation, and Conservation

ACREDOLO, CURT, and ACREDOLO, LINDA P. Identity, Compensation, and Conservation. CHmLD DEVELOPMENT, 1979, 50, 524-535. This study tested Piaget's assertion that true stage 3 conservation awaits the emergence of an understanding of compensation, that a recognition of identity is not sufficient, and that the anticipation of liquid conservation among otherwise nonconserving children is not an indication of conservation by identity, but is instead due to an erroneous anticipation of unchanging water levels. These assertions were tested using a modified replication of Piaget and Taponier's classic study of liquid conservation. 96 K-grade 1 children were presented a sequence of anticipation-of-liquid-conservation, anticipation-of-water-levels, and standard liquid-conservation tasks. The results, which failed to replicate Piaget and Taponier, disconfirmed Piaget's theory of pseudoconservation, but supported his assertion that an understanding of compensation is necessary for consistent conservation judgments plus explanations. The results suggest a modification of Piaget's equilibration theory of conservation development, one which elevates the role of identity.

The Importance of the Verbal Content in the Training of Piagetian Conservation Skills

FIELD, DOROTHY. The Importance of the Verbal Content in the Training of Piagetian Conservation Skills. CHILD DEVELOPMENT, 1977, 48, 1583-1592. Experiments using Piagetian tasks to probe the cognitive capacities of retarded children have shown that verbal-rule explanations are most facilitative for conservation acquisition. To determine the crucial components of the verbal rule, a 2 X 2 X 2 factorial design provided training in identity, reversibility, and compensation explanations, alone and in every combination, for eight matched groups of 48 mildly retarded, nonconserving children. Significant differences between groups were found on the posttest, particularly in the amount of generalization to untrained quantities. Identity was the primary factor in conservation acquisition; reversibility was important as well. Compensation strategy proved to be of no value to these children. Justifications offered by the subjects also were analyzed. There were significant differences in the kinds of justifications given, but these justifications did not follow directly from the kinds of training received. The quantity itself seemed to dictate the rationale: number conservation produced mostly identity justifications, for instance, and length conservation usually produced reversibility answers, regardless of training given.

Symbolic play and its cognitive significance.

This study explores the relation between symbolic play training and conservation attainment. The subjects were 30 middle-class nonconserving children, with an age range of 4.0-4,6 years and a median age of 4.3 years. After extensive pretests on conservation of quantity, 15 nonconservers were assigned to the experimental condition, consisting of three sessions of symbolic play on consecutive days, and 15 subjects were assigned to the control condition, consisting of three daily play sessions with puzzles, mosaics, and drawing tasks. Subsequent to the play sessions, the subjects were given conservation of quantity posttests. The results showed that 13 of the experimental subjects manifested some change in solving conservation problems, with 4 subjects reaching the level of full conservation attainment. Only a single subject from the control group showed a change toward conservation on the posttests. The data are interpreted as supporting a cognitive function of symbolic play.

Role of Imaginative Play in Cognitive Development

The role of imaginative play in the attainment of conservation and perspectivism was examined with a training study paradigm. 36 non-conserving kindergarten children were assigned to 1 of 3 conditions: (a) structured group training in imaginative play processes, (b) extra free-play activity in the nondirective presence of the experimenter, and (c) a control group. The first two conditions met for eight 25-min. sessions. On pre-post measures the training group showed significant increases in social-role conservation, the understanding of kinship relations and level of free-play imaginativeness, though no significant differences were found for the conservation of number and continuous quantity, or left-right judgments. The results indicate that imaginative play can be generative of new cognitive structures, under certain conditions, by the enhancement and accommodative use of psychological processes such as reflection, role integration, language, role conflict, and representational activity. A modification of Piaget's play theory was outlined. The relationship between specific kinds of play experiences and the construction of particular physical or social concepts was discussed, as well as various educational implications.

Age-related variation of topological evaluation of numerical quantity in nonconserving children.

Age-related variation of topological evaluation of numerical quantity in nonconserving children.

Age-related variation of topological evaluation of numerical quantity in nonconserving children.

Age-related variation of topological evaluation of numerical quantity in nonconserving children.

Reinforcement and reversibility in quantity conservation acquisition

Two principal issues were addressed in this experiment: (1) the effectiveness of simple contingent reinforcement in the induction of conservation concepts in previously nonconserving children; (2) the role of reversibility in conservation acquisition. Concerning (1), 20 nonconservers who were trained on liquid quantity conservation via contingent (verbal) reinforcement acquired a concept which was both superior to that of nontrained controls and statistically comparable to the naturally acquired concept. Concerning (2), the 20 Ss who received contingent reinforcement also tended to acquire reversibility explanations. Finally, it was found that one of Piaget’s two forms of reversibility (inversion) was more characteristic of the 20 reinforcement-trained conservers, while the other form of reversibility (reciprocity) was more characteristic of natural conservers.