Development of proportional reasoning: Where young children go wrong.

Previous studies have found that children have difficulty solving proportional reasoning problems involving discrete units until 10 to 12 years of age, but can solve parallel problems involving continuous quantities by 6 years of age. The present studies examine where children go wrong in processing proportions that involve discrete quantities. A computerized proportional equivalence choice task was administered to kindergartners through 4th-graders in Study 1, and to 1st- and 3rd-graders in Study 2. Both studies involved 4 between-subjects conditions that were formed by pairing continuous and discrete target proportions with continuous and discrete choice alternatives. In Study 1, target and choice alternatives were presented simultaneously; in Study 2, target and choice alternatives were presented sequentially. In both studies, children performed significantly worse when both the target and choice alternatives were represented with discrete quantities than when either or both of the proportions involved continuous quantities. Taken together, these findings indicate that children go astray on proportional reasoning problems involving discrete units only when a numerical match is possible, suggesting that their difficulty is due to an overextension of numerical equivalence concepts to proportional equivalence problems. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Estimating stimuli from contrasting categories: Truncation due to boundaries.

In this article, the authors present and test a formal model that holds that people use information about category boundaries in estimating inexactly represented stimuli. Boundaries restrict stimuli that are category members to fall within a particular range. This model posits that people increase the average accuracy of stimulus estimates by integrating fine-grain values with boundary information, eliminating extreme responses. The authors present 4 experiments in which people estimated sizes of squares from 2 adjacent or partially overlapping stimulus sets. When stimuli from the 2 sets were paired in presentation, people formed relative size categories, truncating their estimates at the boundaries of these categories. Truncation at the boundary of separation between the categories led to exaggeration of differences between stimuli that cross categories. Yet truncated values are shown to be more accurate on average than unadjusted values. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Early Development of Scaling Ability.

The map is a small-scaled version of the space it represents. It has been argued that children have difficulty interpreting maps because they do not understand scale relations. Recent research has shown that even preschoolers can solve problems that involve scaling in one dimension. This study examined whether early scaling ability extends to tasks involving two-dimensional maps and referent spaces of different sizes. Results showed that about 60% of the 4-year-olds and 90% of the 5-year-olds tested used distance information presented on a map to locate an object in a two-dimensional spatial layout. Children had more difficulties in solving mapping tasks with a larger referent space. This decrease in accuracy as a function of space size on the mapping task was greater than would have been expected on the basis of performance on a parallel nonmapping task. The results are discussed in terms of their implications for the mechanisms underlying early scaling ability. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Early sex differences in spatial skill.

This study investigated sex differences in young children's spatial skill. The authors developed a spatial transformation task, which showed a substantial male advantage by age 4 years 6 months. The size of this advantage was no more robust for rotation items than for translation items. This finding contrasts with studies of older children and adults, which report that sex differences are largest on mental rotation tasks. Comparable performance of boys and girls on a vocabulary task indicated that the male advantage on the spatial task was not attributable to an overall intellectual advantage of boys in the sample. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

What do misestimations and asymmetries in spatial judgement indicate about spatial representation?

When people are asked to judge the distance between 2 points, they may produce systematic over- or underestimations. Their judgements may also show asymmetries, as when, for example, people estimate the distance from their house to a mailbox as different from the distance from the mailbox to their house. It has been argued that such errors show that spatial representations are fundamentally nonmetric. In 3 experiments, however, the authors show that these effects can be explained by a category-adjustment (CA) model of spatial coding, in which coding is hierarchical (i.e., occurs at more than one level of measurement, with estimates based on combination across levels). In this model, coding at each level is uncertain but not distorted. Experiment 1 shows that, in a carefully controlled experimental setting, the CA model can be used to predict under- or overestimations of distances with respect to objective standards. Experiments 2 and 3 show that, when people learn maps, the CA model correctly predicts patterns of asymmetries in estimation. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Memory for the time of "60 Minutes" stories and news events.

This study tested whether impressions of the temporal distances of past events provide differentiated information about the times of events from the past months. Participants judged the times of stories from the television show "60 Minutes" that were not easily linked to contemporaneous events and, in a comparison condition, of news events. They also compared the relative recency of pairs of "60 Minutes" stories that had been broadcast the same week or during different weeks. Results showed that the times of "60 Minutes" stories could be differentiated if they fell within the past 1 to 2 months, but the times of older events were mainly undifferentiated. Memory for the temporal contiguity of "60 Minutes" stories was also very poor. The times of news stories were accurate throughout the range of times. These findings provide information about the time course over which distance information is useful. (PsycINFO Database Record (c) 2010 APA, all rights reserved)