Children's numerical skill and judgments of confidence in estimation

This study investigated how children's fluent use of a basic numerical skill is related to their perceptions of confidence on a task of quantitative estimation. One hundred four 10th graders (age 15.7 years) were categorized according to level of numerical fluency as assessed by timed tasks of counting in various nonunity increments. They then made estimates of large numbers of dots and rated how confident they were on each trial. The estimation task varied according to two within-subject factors of task difficulty. It was found that counting skill was related not only to accuracy in estimating, but also to the appropriateness of the children's confidence in their responses. Skillful children made judgments that corresponded with actual task difficulty. A derived calibration score corroborated ANOVA findings of the interaction of skill level and task difficulty on confidence ratings. It also revealed that while girls were less confident than boys, they were actually more realistic in their judgments. Findings are discussed in terms of (a) the effect of stimulus knowledge on awareness of task difficulty and (b) sex differences in achievement-related expectancies.     

Interpreting inclusion: A contribution to the study of the child's cognitive and linguistic development

Six experiments are reported which examine the young child's ability to compare included and nonincluded sets. Results indicate that with certain forms of task presentation most 3- to 5-year-old children can compare part with whole. Further, errors which occur in inclusion tasks are similar to errors which occur in tasks involving comparison of nonincluded sets. Thus young children can solve inclusion problems, and their customary failure to do so does not arise because the problem requires comparison of a whole with an included part. Employing a distinction between intended tasks (those which the adult wishes the child to complete) and received tasks (those which the child, in fact, completes) the studies indicate how linguistic and perceptual aspects of the presented information may interact with the child's assumptions about the nature of the task to be completed.     

Processing of identity and position information in normal and disabled readers

Processing of identity and position information was investigated in normal and disabled readers at two grade levels (third/fourth grade and sixth grade). Two partial-report tasks were used. The identity task consisted of visual presentation of a five-letter array, followed by a probe letter. Subjects responded yes for a match and no for a mismatch (identity response). The identity + position task was identical except that an additional response was required on correct yes trials: subjects reported the position of the probe letter in the array (position response). Both grade level and reading ability differences were found on the identity response measure, but not on the position response measure. Results were inconsistent with the hypothesis that disabled readers have difficulties in processing order information. Reader ability differences in identity processing attenuated somewhat with age. Serial position functions for both identity and position responses suggested the presence of a left-to-right scanning operation in both age and ability groups. Reader ability differences in processing letter identities were discussed in the context of current theories of reading acquisition.     

Early discrimination among small object collections

Two studies are presented which examine the young child's ability to discriminate between two small object collections on the basis of numerosity and to maintain that discrimination across changes in number-related cues. A transfer procedure and counting tasks were also included. In Study 1, 2-, 3-, and 4-year-olds were reinforced for choosing either a two- or three-item array when length-density cues were manipulated across two training phases of 20 trials each. Training was followed by a transfer task in which one- and four-item arrays were displayed. Most 2-year-olds were able to learn the discrimination while at the same time displaying little quantitative ability. Further, their transfer responses were transpositional in nature. In Study 2, 2-year-olds were given a similar discrimination task in which numerosity was contrasted simultaneously with length-density and area-brightness cues. Again, most children learned the discrimination and transferred that learning on the basis of relational cues.     

Less is not more: Further observations on nonlinguistic strategies

In an attempt to clarify the role of nonlinguistic preferences in children's responses to the words more and less, children 3–4 years of age were administered three tasks. Two of these required the child to indicate which of two arrays had more or less items, as instructed; the third task required the child to point to any one of two arrays. Children consistently selected the arrays with more items on all three tasks. The present finding of a response bias necessitates a reinterpretation of earlier studies of more and less. The results are discussed in terms of the full and partial semantics hypotheses as articulated by E. Clark.     

Some analyses of the verbal encoding deficit of alcoholic Korsakoff patients

Two experiments were designed to assess Korsakoff patients' ability to encode verbal information on the basis of its physical, nominal and semantic properties. The first investigation employed Wickens' release from proactive interference (PI) technique; a procedure that allows an assessment of a subject's ability to encode verbal information on the basis of its semantic properties. It was discovered that on tasks involving only a rudimentary verbal analysis, such as the ability to discriminate letters from numbers, the Korsakoff patients demonstrated a normal release from PI. However, on tasks that required a more sophisticated level of semantic encoding, such as those based on taxonomic class inclusion, the patients failed to show release from PI. The second investigation employed Posner's reaction time technique which assesses a subject's ability to encode the physical and nominal properties of simple verbal materials (letters). The results of this study showed that Korsakoff patients are impaired on even these rudimentary encoding tasks, which led to the proposal that Korsakoff patients' semantic encoding deficit might stem from an initial impairment in the speed at which physical and nominal properties of verbal information are analyzed.     

The production and verification tasks in mental addition: An empirical comparison

We respond to A. Baroody's comment (1984, Developmental Review, 4, 148–156) with an empirical comparison of the production and verification tasks. With the exception of performance at the first grade level, the two tasks yield essentially identical conclusions. The results of an adjunct task, in which the rate of mental counting was assessed, suggest that children as young as second grade are relying on memory retrieval to a significant degree. In contrast to Baroody's speculation, there appear to be no widespread difficulties associated with results from the verification task. Furthermore, the task permits a more analytic examination of performance and underlying mental process than is afforded by the production task. We conclude by reiterating the empirical support for a model of fact retrieval, and suggesting that accessibility of the arithmetic facts is the basic factor which underlies both fact retrieval and procedural knowledge performance.     

Reversible operations in the balance scale task

The development of two types of reversible operations was examined in three tasks involving a two-armed balance scale. The first type of reversible operation, compensation between dimensions, was shown to undergo considerable development between eighth grade and college. Even eighth graders were inconsistent in applying compensation to those versions of the balance scale task that required it. Some subjects, primarily preschoolers, used the given information in a way that was the opposite of that required for correct answers, a result that has been reported for other tasks requiring compensation. A second type of reversible operation, termed “correspondence of patterns”, was also tested and it was tentatively concluded that the responses of the modal college student are not fully reversible in this sense. This finding is also similar to results obtained in judgments of time, speed, and distance and in social judgment studies with college students.     

The influence of task variation and maintenance tasks on the learning and affect of autistic children

Analyses of autistic children's learning and affect have begun to consider the role of antecedent variables, including the manner with which tasks are sequenced within instructional sessions. Within the context of a simultaneous-treatments design, this experiment evaluated autistic children's affect and rate of task acquisition under three experimental conditions. The conditions were (1) a constant task condition in which only one acquisition task was presented per session; (2) a varied-acquisition-task condition, in which 10 acquisition tasks were randomly interspersed throughout each session; and (3) a varied-with-maintenance-task condition, which randomly interspersed 5 acquisition tasks and 5 which had been previously acquired. The results showed significantly more efficient learning under the varied-maintenance condition, with no consistent differences separating the other two conditions. In addition, observers' ratings of the children's affect showed that the most positive judgments were produced by the varied-maintenance condition. The varied-acquisition condition was next while the constant task condition always produced the least favorable ratings. These findings are discussed in relation to the literature on massed versus distributed practice, stimulus variation, and success-induced motivation. The implications for upgrading the treatment and education of handicapped children are also reviewed.     

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 χ² 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.     

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

This study analyzed the strategies that children ages 5 through 8 years used on two modified versions of Inhelder and Piaget's (The early growth of logic in the child. New York: Norton, 1964) class inclusion task. In two experiments, children were tested on Wilkinson's (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 children's 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 Seibert's (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 Piaget's theory.     

Children's relative number judgments: One-to-one correspondence,recognition of noncorrespondence,and the influence of cue conflict

Although one-to-one correspondence can be seen as a component of successful counting, number conservation, and relative number judgments, there is evidence of considerable discrepancies between children's competencies in these different tasks. Concerning relative number judgments there are strikingly different claims concerning the ability of young children to make one-to-one correspondence-based judgments. In part these discrepancies reflect differences in criteria. Four experiments are reported in which 5-year-olds' relative number judgments of small and large number displays with and without perceptual aids were studied. Children were found to respond to local rather than global density differences and to benefit from the provision of perceptual aids on both small and large number displays with one exception, namely, large number displays where the longer row is less numerous.     

Cognitive processing and motor execution in the lexical decision task: a developmental study

We investigated lexical decision making in children and adults by analyzing spatiotemporal characteristics of responses involving a hand movement. Children’s and adults’ movement trajectories were assessed in three tasks: a lexical decision task (LDT), a pointing task that involved minimal cognitive processing, and a symbol task requiring a simple binary decision. Cognitive interference on motor performance was quantified by analyzing movement characteristics in the LDT and symbol task relative to the pointing task. Across age groups, movements in the LDT were less smooth, slower, and more strongly curved to the opposite response option, and these interference effects decreased steadily with age. Older children showed stronger interference effects than did adults, even though their reaction times were similar to adults’ performance. No comparable effects were found in the symbol task, indicating that task characteristics such as response mapping and decision selection alone are not able to explain the developmental differences observed in the LDT. Our results indicate substantial overlap between cognitive processing and motor execution in the LDT in children that is not captured by computational models of visual word recognition and cognitive development.     

Dual-task interference as a function of cognitive processing load

Sixteen subjects from the Naval Submarine Medical Research Laboratory participated in a dual-task study designed to measure processing requirements of a choice reaction time (RT) task. Two levels of choice RT stimulus-response (S-R)compatibility were tested with each of two tracking tasks to provide different levels of dual-task loading. In one tracking task, the target's temporal-spatial pattern was fixed; in the other, the target's path was a function of the subject's performance. In the choice RT task, compatibility was treated as a between-subjects factor, while the number of alternatives (set size) within a sequence was a within-subjects variable. Choice RT results indicated that compatibility and set size interacted; the increase in response latency as a function of set size was much greater when compatibility was low. An increase in choice RT response latency occurred when the secondary tracking task was added. Within a given compatibility level, this dual-task decrement was constant for all levels of set size; however, the magnitude of the dual-task decrement varied as a function of S-R compatibility, being greater when compatibility was low than when it was high. For these data, a model like Sternberg's (1969) stages model is seen to have more explanatory value than a pooled processing capacity model (e.g., Norman and Bobrow 1975).     

A reappraisal of the relation between performances of quantitative identity and quantitative equivalence conservation tasks

Previous studies of children's performance on quantitative identity and equivalence conservation problems in the number domain are suggested to be flawed because of the low numbers of items in the arrays. In Experiment 1, children were tested on three different number versions of identity and equivalence conservation tasks. Their performance varied with the number of items and no child was found to pass a large number version of an equivalence conservation task and fail the corresponding version of an identity conservation task. In Experiment 2 the notion that the contextual effect of asking two similar questions might underlie the difference in performance on the two tasks was tested and rejected. The results are discussed in relation to recent analyses of conservation problems.     

The meaning of before and after for preschool children

Preschool children's understanding of temporal relationships was examined in terms of their comprehension of sentences containing clauses linked by before and after. The relative importance of order of mention and main-subordinate relations strategies in children's interpretation of temporal order information was also evaluated.Divergent error patterns emerged on the tasks; omissions prevailed on the two tasks involving response to commands, reversals prevailed on the other. Further examination revealed that omissions reflected ambiguity in the linguistic structure of commands. Thus the effect of main-subordinate relations was confounded with directness of command. On all comprehension tasks, however, performance was superior on sentence forms in which order of mention and order of occurrence correspond.     

Framing effects in judgment tasks with varying amounts of information

Subjects were asked to make evaluations in each of three tasks—a gambling task, a consumer judgment task, and a student evaluation task. Each task involved two important attributes, but information about one attribute was missing on some trials. Half of the subjects received a version of the task in which a key attribute was presented in positive terms (e.g., probability of winning a gamble) and half received a version in which that same attribute was presented in negative terms (e.g., probability of losing a gamble). Even though the information was objectively equivalent in the two versions of each task, there were two significant framing effects. (1) In all tasks, responses to two-attribute stimuli were more favorable in the positive condition than in the negative condition. (2) When the key attribute was missing, evaluations of one-attribute stimuli relative to evaluations of two-attribute stimuli were lower in the positive condition than in the negative condition. Results were discussed in terms of the constructs of prospect theory and information integration theory.     

Masked nonword repetition effects in yes/no and go/no-go lexical decision: A test of the evidence accumulation and deadline accounts

The pattern of masked repetition priming effects for word and nonword targets differs across tasks: Maskedpriming effects in lexical decision occur for positive responses (i.e., words), but not for negative responses (nonwords), whereas masked-priming effects in the cross-case same-different task occur for positive responses (same), but not for negative responses (different)—regardless of lexical status. Here, we examined whether masked nonword priming effects are greater when the task involves an active go response to nonwords than when it involves the standard yes/no procedure in lexical decision. The obtained masked repetition priming effect for nonwords was of similar size in yes/no and go/no-go tasks. This finding is compatible with accounts of nonword priming that posit that nonword responses are produced by actively accumulating evidence for the nonword alternative in yes/no and go/no-go procedures, whereas it is inconsistent with the assumption of a deadline for no responses in the yes/no task.     

Predicting compliance behavior from moral judgment scales

Two experiments with college males examined the relationship between moral judgment and compliance in a modified Asch paradigm. In Experiment 1 moral judgment was assessed with the written form of Kohlberg's dilemmas. Stage of moral judgment interacted with type of compliance, with Stage 4 subjects showing a compromise response between their own perceptions and the responses of others. In Experiment 2 moral judgment was assessed with Rest's Defining Issues Test. Compliance was found to be negatively related to level of moral judgment. The relationship found between moral judgment and compliance in the two experiments was interpreted in terms of a trend away from external standards and toward internal standards with higher levels of moral judgment.