Distance distortions in children's cognitive maps: an examination of the information storage model

Second graders (mean age = 7-8), fourth graders (mean age = 9-8), and sixth graders (mean age = 11-11) walked two paths located in and around their school. Children in the Unsegmented condition estimated the distance and time taken to walk a path that was relatively undifferentiated in terms of the number of qualitatively different areas of the school through which it passed. Children in the Segmented condition made the same estimates for a path that went through different areas (segments) of the school (i.e., cafeteria, hall, vestibule, and outside the building). Children at all three grade levels estimated that the distance traversed in the Segmented condition was longer than the distance in the Unsegmented condition. This difference was not significant on the time measure. It was concluded that (1) paths with a large number of segments are perceived as being longer than paths of the same length with fewer segments, (2) distances along paths with few segments are underestimated, (3) distances along paths with many segments may be overestimated as a function of developmental level, and (4) only younger children may have used time to estimate distance.     

Children's cognitive maps of large-scale spaces: Effects of exploration,direction, and repeated experience

Kindergarteners and third graders (mean ages 5–10 and 8–9 years) repeatedly encountered a model town and then constructed the town from memory. In Experiment 1, the effect of different types of exploration on the development of a cognitive map was assessed. Children who were directed to walk within the town placed buildings more accurately than children who had walked along the town's perimeter. Children who walked within the town and were directed to the spatial relationships among buildings had the highest placement accuracy. Third graders were more accurate than kindergarteners across the three types of exploration. In Experiment 2, children were permitted to explore the town alone for an unlimited amount of time. Under these conditions, third graders still placed buildings more accurately than kindergarteners. A comparison of Experiments 1 and 2 indicated that children developed more accurate cognitive maps when motor activity and attention were directed by the experimenter as opposed to being directed by the child. Accuracy improved with repeated walks and constructions in both experiments, and the results of Experiment 3 suggested that constructing facilitated the development of the cognitive map as much as walking. It was concluded that third graders' cognitive maps were more accurate than kindergarteners' maps due to differences in the speed of acquisition and storage of spatial information.     

Differences in the search rate of children and adults in short-term memory

When people recognize a test item as belonging or not belonging to a previously presented set, recognition latency increases with the number of items in the set. Although some evidence suggests otherwise, it is currently held that the rate of this increase is the same for children and adults. In contrast, the present experiments indicated a much slower search rate for second graders (mean age = 7.33 years) than for seventh (mean age = 12.50 years) and twelfth graders (mean age = 17.25 years). Moreover, search rate for second graders was invariant under instructions which did or did not emphasize speed and with presentation of the memory set in either the auditory or visual modality. Experiment II showed that the slow search rate for children was not due to differences in encoding between children and adults.     

Facilitation of attention to number and conservation of number

This study examined the relation between number conservation and attention to number, density, and length or area in kindergarteners (age 5 years, 8 months) and third graders (age 8 years, 11 months). Attention was assessed by the dimensional preference technique, using triads. Both the attention and conservation tasks included stimulus factors known to facilitate or hinder conservation: small or large numbers of objects, nonlinear or linear arrays, and trials ordered from easiest to hardest, hardest to easiest, or randomly. The number of objects and type of array affected both tasks similarly and there was an order effect in the attention task. There was an increase in attention to number from kindergarten nonconservers to kindergarten conservers to third-graders. Possible developmental interactions between attention and conservation were suggested.     

Does the human odometer use an extrinsic or intrinsic metric?

It is commonly assumed that path integration is based on an extrinsic measure of the objective distance traversed during locomotion. In contrast, biological odometers may rely on embodied intrinsic measures, such as idiothetic information specific to an action mode. We investigated this question using a distance reproduction task in which participants traveled an outbound distance and then reproduced that distance using the same or a different action mode. The extrinsic model predicted that distance reproduction should be invariant across action modes, whereas the intrinsic model predicted invariance only within an action mode. In Experiment 1, we held the outbound mode constant while varying the response mode (walk–walk, walk–throw) and corrected for response production error (view–walk, view–throw). In Experiment 2, we crossed different gaits in the outbound and response modes (walk, gallop). In both cases, we found that distance reproduction was significantly more accurate when the outbound and response modes matched, consistent with the intrinsic model. The results indicate that the human odometer preferentially relies on an intrinsic, rather than an extrinsic, metric. This solution is sufficient to support successful path integration within an action mode (but not across action modes), without the difficulties of objective distance estimation.     

The Frequency and Intensity of Negative Attitudes Expressed in Play Therapy: A Comparison of Well-Adjusted and Disturbed Young Children

The relationship of age and IQ to response inhibition in children was investigated in two experiments. Two tasks were employed: a “walk slowly” task designed to measure motor inhibition and a simple matching task designed to measure cognitive inhibition. In Experiment I, the Ss were 20 “normal” children at ages 4, 5, 6, and 7 years of age. Response inhibition was found to increase with age. In Experiment II, the Ss were 48 institutionalized retardates, half between the ages of 8 to 12 and half between the ages of 13 to 17. Half of each age group had IQs between 40 and 55, and half had IQs between 56 and 70. Motor response inhibition varied as a function of age but not IQ, while cognitive inhibition varied as a function of IQ but not age.     

Performance of retarded adolescents and nonretarded children on one- and two-bit logical problems

Groups of adolescents of retarded and borderline intelligence, ranging in IQ from 44 to 80 and in mean MA (mental age) from 8 to 12 yr, and groups of nonretarded children ranging in mean MA from 6 to 12 yr, were given logical problem solving tasks. In the nonretarded groups, on a one-bit problem only the kindergarten children (mean MA = 6 yr) failed to perform above chance, and were not tested further. On a two-bit problem, only the first graders (mean MA = 7 yr) failed to perform above chance.Conversely, in the low IQ groups, only the borderline group (mean MA = 12 yr) performed reliably above chance on the one-bit problem, and none performed above chance on the two-bit problem. There is a profound deficiency in low IQ individuals on certain tasks requiring logic and foresight, and MA markedly over-estimates their performance relative to the performance of nonretarded individuals.     

Developmental and individual differences in pure numerical estimation

The authors examined developmental and individual differences in pure numerical estimation, the type of estimation that depends solely on knowledge of numbers. Children between kindergarten and 4th grade were asked to solve 4 types of numerical estimation problems: computational, numerosity, measurement, and number line. In Experiment 1, kindergartners and 1st, 2nd, and 3rd graders were presented problems involving the numbers 0-100; in Experiment 2, 2nd and 4th graders were presented problems involving the numbers 0-1,000. Parallel developmental trends, involving increasing reliance on linear representations of numbers and decreasing reliance on logarithmic ones, emerged across different types of estimation. Consistent individual differences across tasks were also apparent, and all types of estimation skill were positively related to math achievement test scores. Implications for understanding of mathematics learning in general are discussed.     

Developmental changes in attention-deployment skills

The ability to efficiently allocate attention between two tasks differing in payoff was investigated developmentally. Ten subjects from each of three grade levels (second, fourth, and college) performed an auditory and a visual memory task simultaneously. Modality of the primary task, difficulty of the primary task, and difficulty of the secondary task were varied factorially within subjects. The difference between primary and secondary performances increased with age: All college students, about half of the fourth graders, and none of the second graders showed a meaningful degree of differentiation between primary and secondary tasks.     

The effect of orthographic structure on word recognition in a visual search task

The effect of the orthographic structure of the stimulus field on the visual search performance of third graders (8-8 years), sixth graders (11-7 years) and adults was investigated in three experiments. In Experiment 1, where the predesignated target was one word, subjects of all ages searched equally fast through fields consisting of words, pseudowords, and nonwords. In contrast, subjects of all ages displayed effects of orthographic structure when searching for instances of a semantic category (Experiment 2) or for three words (Experiment 3). Subjects searched faster through nonwords than through pseudowords and faster through pseudowords than through words. The use of orthographic structure to facilitate search did not increase with age, suggesting that children of the youngest age group were already making maximal use of intraword redundancy.     

小学儿童对习俗时间的时距判断

本研究选取“星期”这种习俗时间系统作为实验材料,通过让被试完成范畴性的时距判断任务,即让被试判断某一给定的日期是否属于某一参照日期之后３天中的某一天,探讨了小学儿童对习俗时间的认知加工过程的发展。结果表明,小学儿童对习俗时间的认知加工成绩随年龄的增长而不断提高,在认知加工过程中,具有显著的“距离效应”和“边界效应”,随着两个日期之间时距的增加,反应时逐渐增大,正确率逐渐降低,当两个日期之间的时距为３天时,反应时最长,正确率最低。而且,儿童可以直接运用数字系统来解决习俗时间的问题,他们的认知加工策略包括数字计数、数字运算和表象判断。     

Shedding new light on an old problem: The estimation of shadow sizes in children and adults

Two experiments using the 'projection of shadows' paradigm investigated multidimensional reasoning, implicit and explicit knowledge, and the nonlinearity concept in 5-, 9-, and 13-year-olds and adults. Participants estimated the resulting shadow lengths of differently sized objects, placed at varying distances from a light source. Experiment 1 (N=80) revealed that, on the group level, 5-year-olds took both object size and light-object distance into account when estimating shadow size. Moreover, half of the children in this age group even considered the subordinate distance dimension. In addition, we found a large discrepancy between implicit and explicit knowledge about shadows in 5-year-olds that decreased with age. Finally, only a minority of older participants and very few younger children recognized the nonlinear relationship between light-object distance and shadow size, suggesting domain dependence of the nonlinearity concept. Experiment 2 (N=20) predominately replicated the findings for 5-year-olds using slightly different stimuli.     

Distance estimates of children as a function of acquisition and response activities

Second and sixth graders (8 and 12 years of age, respectively) experienced a large-scale environment either actively or passively followed by a distance estimation task requiring either active or passive activity. Second graders were most accurate in those conditions where acquisition and response activities were congruent. These children significantly overestimated distances in the passive acquisition-active response condition. Sixth graders were equally accurate across all four experimental conditions. Results are discussed in terms of the complex interaction between acquisition factors and task demands which influence interpretations about spatial representations.     

When is a question not answered? The understanding of young children of utterances violating or conforming to the rules of conversational sequencing

Knowledge of the conventional rules of conversational sequencing enables a speaker or listener to evaluate the pragmatic use of an utterance. This study explored young children's ability to discriminate among utterances that violated or conformed to these rules (Experiment 1), and ability to explain rule violations (Experiment 2). In both experiments children were read short episodes containing utterances that conformed to the rules in that the utterances were used appropriately in the episodic context of utterance, or utterances that violated the conversational rules of contingency, relevance, or informativeness. In Experiment 1, kindergarten, and first- and second-grade children (5, 6, and 7 years of age) were asked to discriminate among the conforming and rule violating utterances by assigning each utterance to one of two female conventional and unconventional speakers. The results showed that the first and second graders, but not the kindergarten children, generally discriminated among the utterances. In Experiment 2, first and third graders (6 and 8 years of age) were asked to explain the rule violations. The results showed that only the third graders consistently generated correct explanations. These results suggest that children can use the rules of conversational sequencing to evaluate the need for an inference to the speaker's intent in deliberately violating a rule by 6 or 7 years of age, but do not correctly infer that intent until they are 8 or 9 years old.     

Barrier effects in the cognitive maps of children and adults

To study spatial representation, Kosslyn, Pick, and Fariello (Child Development, 1974, 45, 707–716) asked preschoolers and adults to learn toy locations in a room divided into quadrants. When asked to rank order the closeness of toys, preschoolers exaggerated distances between objects separated by opaque or transparent barriers; adults distorted across opaque barriers only. The findings were interpreted as showing that children's spatial representations may rely more than adults' on functional distance and/or that children may have more difficulty than adults keeping many objects in mind simultaneously (integrative processing capacity). The Kosslyn et al. procedure was repeated here with first graders and adults, using either rank ordering techniques or direct distance estimations. Interactions of age and barrier appeared for the rank ordering measure only. Children showed a greater tendency than adults to group their rankings by quadrant. With the distance estimation measure, adults were quantitatively more accurate than children, at least among males; barrier effects interacted with sex and distance, but not age. These findings suggest the importance of integrative processing capacity, and that different dependent measures may tap different processes.     

The effect of line configuration on perceived numerosity of dotted lines

Estimates of the number of objects in a line are made in many different situations. This paper demonstrates that besides the actual number of dots, aspects of line configuration affect the perceived numerosity of dotted lines. Experiment 1 provides evidence that the highly studied “clutter effect” in distance perception research replicates to the numerosity domain so that lines made up of more segments are perceived to contain more dots. Experiments 2–5 provide nomological validity for the recently proposed “direct distance” effect in distance perceptions by showing that numerosity perceptions are higher the greater the euclidean length between the line end points and by manipulating euclidean length in three orthogonal ways: the relative length of segments (Experiment 2), the angle between segments (Experiment 3), and the general direction of segments (Experiment 4). Experiment 5 conceptually replicates the results of Experiments 2–4 utilizing stimuli-based versus memory-based judgments and a discrimination task. Experiments 6 and 7 extend the research on spatial perception by demonstrating that the use of euclidean length as a source of information is inversely related to line width, with width varied through clutter (Experiment 6) and total line length (Experiment 7). Overall, the results demonstrate that the robustness of the euclidean length effect is contingent on the salience of alternative spatial heuristics-specifically, euclidean width. Theoretical implications are discussed.     

Distance estimation from cognitive maps

Four experiments investigated map clutter as a source of distortion in subjects' estimates of distance. In Experiments 1 (incidental learning) and 2 (intentional learning), subjects estimated distances between pairs of points on a memorized map. In both experiments, estimates increased as a linear function of the number of intervening points along the route. In Experiment 3, subjects estimated distances while viewing the map. The effect of clutter was reduced but not eliminated. In Experiment 4, the clutter effect was demonstrated using subjects' preexperimental knowledge of United States geography. Psychophysical power functions relating true to estimated distance provided a good fit to both memory and perception data. These results suggest an analogy between perceptual and memorial processes of distance estimation. A model proposed to account for the data assumes that subjects perceptually scan a route (or image of a route) from start to destination and use scan duration to determine path distance.     

Detection of color in rotating objects by infants and its generalization over changes in velocity.

In three experiments, infants between 8 and 20 weeks of age were familiarized during habituation trials to either a stationary or revolving patterned cylinder (Experiment 1) or to the same object when it was revolving at one of two angular velocities (Experiments 2 and 3). In the postfamiliarization trials, angular velocity was changed with the color of the pattern either the same as or different from that in the familiarization trials. The results showed that the infants were not only sensitive to movement and changes in velocity but to the color of the moving pattern. Furthermore, this response to color generalized across changes in angular velocity. These findings indicate that a necessary condition for identity constancy, detection of an object property with object transformations, is present between 8 and 20 weeks, prior to the stage of manual manipulation of objects. A number of subsidiary findings concerning movement discrimination at 55 and 100 cm viewing distances by 11- and 17-week-old infants are also described.     

Selective attention and the processing of integral and nonintegral dimensions: A developmental study

In two experiments, first- and fourth-grade subjects (age 6 and 9 years) performed a speeded card-sorting task with either integral or nonintegral dimensions. The dimensions were so arranged that subjects sorted on three types of task: (1) single dimension, (2) correlated dimensions, and (3) orthogonal dimensions. Results of the first experiment indicate that both first- and fourth-grade subjects sorted integral dimensions in a manner not qualitatively different from that of the adult (Garner & Felfoldy, Cognitive Psychology, 1970, 1, 225–241). In comparison with single-dimension tasks, performance was facilitated on the correlated-dimensions tasks and interference was observed on the orthogonal-dimensions tasks. Performances with nonintegral dimensions revealed an age-related processing difference. Fourth graders sorted nonintegral dimensions like the adult; no differences in performance were observed between the tasks. In contrast, first-graders sorted nonintegral dimensions as if they were integral. Interference was consistently observed on orthogonal-dimensions tasks. On correlated-dimensions tasks, interference was observed on easy tasks and redundancy facilitated difficult tasks. In the second experiment, first graders showed consistent facilitation on the correlated-dimensions task; all other results were indentical to those of Experiment I. The results were interpreted as consistent with perceptual learning theory (Gibson, Principles of perceptual learning and development. New York: Appleton-Century-Crofts, 1969).