Anne L. Dean

Classes, collections, and distinctive features: Alternative strategies for solving inclusion problems☆

Abstract This study analyzed the strategies that children ages 5 through 8 years used on two modified versions of Inhelder and Piagets ( The early growth of logic in the child . New York: Norton, 1964) class inclusion task. In two experiments, children were tested on Wilkinsons ( Cognitive Psychology , 1976, 8 , 64–85) “percept” inclusion task in which distinctive features marked both supraordinate and subclasses. It was hypothesized that children who fail standard Piagetian inclusion tasks succeed on the “percept” task by counting and comparing mutually exclusive features rather than using features as markers for classes and subclasses. The hypothesis was supported by childrens performances on “percept” tasks in which solutions based on feature counting conflicted with solutions based on consideration of class inclusion relations. In two other experiments, children answered part-whole and part-part comparison questions in which both terms were described as classes and/or subclasses, or in which one of the two terms was described as a collection (e.g., a bunch of grapes). These experiments contrasted Markman and Seiberts ( Cognitive Psychology , 1976, 8 , 561–577) “organization” hypothesis that the greater psychological integrity of collections facilitates reasoning on part-whole comparison problems with the hypothesis that the faciltative effect results from the “large number” connotation of collective nouns. Results on collection problems in which parts were described as collections supported the “large number” hypothesis. Results were discussed in terms of their implications for Piagets theory.

Sequential ordering in children's representations of rotation movements

Abstract This study compared Marmors state-comparison mental rotation task and a movement recognition task with respect to the level of sequence knowledge required for correct performance. The movement recognition task assessed childrens understanding that pivot position and the shape of a rotating object remain invariant throughout the movement. Based on an analysis of development in childrens counting, we hypothesized that explicit knowledge of sequence relations is not needed on the state-comparison task but is needed on the pivot and shape recognition task. In Experiment 1, 5- and 7-year-old children performed on the state-comparison task and an ordering task involving a Mickey Mouse figure. In Experiment 2, children between the ages of 5 and 13 years performed on a pivot and shape recognition task and an ordering task involving rotating squares. As predicted, the results indicated that 5-year-olds can execute a mental rotation on the state-comparison task but cannot sequence states in the rotation movement, whereas sequencing was a prerequisite for identification of incorrect movement sequences on the recognition task. The implications of these findings for development in childrens kinetic imagery were discussed.

A comparison of reaction time and drawing measures of mental rotation.

Abstract The present study examined the hypothesis that errors in childrens drawings of objects in anticipated states of rotation result from their inability to imagine the objects in those states. The hypothesis was tested by comparing childrens performances on a drawing version and a reaction-time (RT) version of J. Piaget and B. Inhelders (Mental imagery in the child, New York, Basic Books, 1971) rotating squares task. On the RT task, children were differentiated into three groups according to their patterns of preparation and decision times and their decision errors. One group (A) included mental rotaters, operationally defined according to three criteria borrowed from L. Cooper and R. Shepard (In W. G. Chase, Ed., Visual Information Processing, New York, Academic Press, 1973) . A second group (B) included children who failed to meet the criteria for mental rotation, but evidenced an ability to imagine some changes in the squares position. These children responded more quickly and accurately on vertical-horizontal (V-H) angle trials (90° and 180°) than oblique angle trials (45° and 135°). A third group (C) included children who provided no evidence of any systematic imaging strategy. On the drawing task group A children drew both oblique and V-H states correctly, group B children could draw V-H but not oblique states, and group C children could draw neither. These results were interpreted as evidence that the problems that children have in drawing are common to the problems they have in preparing a mental image. The results were discussed in terms of claims that drawing errors result solely from drawing conventions ( S. Kosslyn, Image and Mind, Cambridge, Mass., Harvard Univ. Press, 1980 ) or from poor motor coordination ( G. S. Marmor, Cognitive Psychology, 1975 , 7, 548–599).

The development of children's mental tracking strategies on a rotation task

In two experiments, 5- to 13-year-old children were required to mentally track the rotation of a pointer around a circular backdrop, and to indicate the pointers imagined position on the backdrop at the sound of a signal. In Experiment 1, children imagined the pointer rotate around its end point. In Experiment 2, children imagined the pointer rotate around its midpoint, and indicated the position of one of its two ends at the time of the signal. The end to be indicated was not specified by the experimenter until the time of the signal. Thus, children were required to use an imaging strategy that could keep track of the changing positions of both ends of the pointer. In both experiments, children older than 8 years of age generated linear distance X time functions indicating mental tracking, but younger children did not. In Experiment 2, the proportions of children at each grade level using holistic or part-to-part strategies to mentally track the pointer were comparable, as were mental tracking rates. The results were discussed in relation to both recent research on childrens counting, and Piagetian and information-processing views of mental imagery development.

Instinctual Affective Forces in the Internalization Process: Contributions of Hans Loewald

This article focuses on the role of instinctual/affective forces in internalization, a process that both Piaget and Vygotsky identified as the primary mechanism underlying the development of higher mental structures and functions. Although important differences exist in these two theorists’ conceptualizations of internalization, they shared the view that internalization builds cognitive structure by reconstituting external interactions in a new form on an internal plane. Despite acknowledging the social context of these external interactions, however, neither theorist paid adequate attention to the instinctual/ affective components of the internalization process. To put intellectual development back into its instinctual/affective context, a third theory is introduced – that of Hans Loewald, a contemporary psychoanalyst. Loewald shares Piaget’s and Vygotsky’s emphasis on internalization as the basic way of functioning of the human mind, but integrates instinctual/affective forces into the process. The most comprehensive and integrated picture of internalization and its instinctual/affective components may emerge from the mutual application of all three theories to problems of mutual interest.

Way-Stations in the Development of Children's Proportionality Concepts: The Stage Issue Revisited.

Abstract This study examined developmental interdependencies among childrens solutions to three proportionality tasks: balance beam, probability judgment, and juice mixture. The specific goal was to assess J. F. Wohlwills (1973 , The study of behavioral development , New York: Academic Press) notion of “way-stations” in development, toward which interrelated cognitive skills or concepts converge according to their own unique time tables. Two predictions consistent with the “way-station” notion were confirmed. First, consolidation of a given level of performance across all three tasks was a prerequisite for higher level performance in any of the three task domains. Second, the process of extending a given level of knowledge across task domains was accompanied by modifications in childrens representations of variables or relations involved in their current problem-solving strategies. It was speculated that extension and elaboration are mutually facilitative processes, and that their interaction helps to explain why way-stations are not only descriptive entities, but also of functional value for cognitive development. This interpretation was contrasted with alternative interpretations suggested by R. Cases (1985 , Intellectual development: Birth to adulthood , Orlando, FL: Academic Press) and K. W. Fischer and S. L. Pipps (1984 , in R. J. Sternberg (Ed.), Mechanisms of cognitive development (pp. 45–81), New York: Freeman) theories for similar data patterns.

Understanding and solving probability problems: A developmental study

Abstract Childrens understanding of what variables and relations are important in problem structures, and their use of these variables and relations in problem solving, were examined. One hypothesis suggests that knowledge of relevant solution variables is a prerequisite for encoding those variables, which in turn is a prerequisite for learning new strategies that use those variables. An alternative hypothesis holds that knowledge of relevant variables is an outcome, rather than a precursor, of efforts to invent new strategies. In the current studies, children between the ages of 5 and 13 years were given Piaget and Inhelders (1975, The origin of the idea of chance in children, New York: Norton) two-set, alternative choice probability problems. In Experiment 1, problem understanding was assessed by asking children to construct two-set problems that could test whether a learner understood how to solve a model problem type. In Experiment 2, understanding was assessed by asking children to modify model problems to make them harder for a learner to solve. In both experiments, children modified or reproduced only those properties of model problems used either correctly or incorrectly in solving the models. These results partially support both hypotheses, and suggest a mechanism by which problem solving knowledge develops.

Knowing and Imaging Spatial Relations

This study examined the imaging processes that children at different operatory levels used on a spatial rotation task. A procedure was devised in which children were required to draw states of movement to an end-state which gradually and imperceptibly changed from the geometrically correct to an incorrect position during the course of the drawing. The quality of childrens anticipation of the rotation movement was assessed on the basis of whether children drew the geometrically correct end-state, ended their drawings at the incorrect slide end-state, or drew a different and arbitrary end-state. Thequality of childrens hindsight was assessed on the basis of the frequencies and timing of corrections to previously drawn states occasioned by the changing end-state. Relations between childrens patterns of performance on the imaging measure and their level of performance on Euclidean geometric operations tasks generally confirmed predictions based on Piaget et al.s (1960) theory of relations between childrens spatial anticipatory imagery and their knowledge of the structure of Euclidean space.

Rules versus cognitive structure as bases for children's performances on probability problems

Abstract The present study compared two hypotheses about childrens solutions to Piaget and Inhelders (1975) two-set alternative choice probability problems. The first was that children follow rules that specify a temporally ordered sequence of tests and decisions (Siegler, 1981). One prediction of rules is that children who know strategies that combine variables within sets (e.g., ratio or subtraction strategies) will only use them on problems that require such strategies (conflict problems), whereas lower level (nonconflict) problems will be solved by directly comparing the values of variables between sets. The second hypothesis was that once children develop knowledge of within-set solutions to probability problems, they apply them to both conflict and nonconflict problems. The results supported the latter hypothesis. The majority of children who solved conflict problems using within-set strategies explained at least one nonconflict problem by referring to within-set combinations. Results were discussed in terms of their implications for cognitive development and for instruction.

Figural factors and the development of pictorial inferences

The role of figural characteristics in the development of pictorial inferences was examined. Two versions of 10 three-picture story sequences were presented to kindergarten and third-grade children. One version maximized while the other minimized figural similarity among pictures. After viewing the sequences, the children were asked to discriminate old study pictures and inferentially consistent new pictures from distractors. While the kindergarteners identified significantly fewer inference pictures than the third graders in all conditions, there was less difference between the grades in the figurally similar conditions. Overall, the kindergarteners identified the fewest inference pictures in the presence of distractors that figurally matched the study pictures. These results indicate that although the pictorial inferences drawn by kindergarteners are heavily influenced by figural representations, such figural dependency cannot account for all of the observed developmental differences.