Length Versus Distance: Bridging Gaps in Preschoolers' Knowledge

Child Development, 2009

Three experiments investigated changes from 15 to 30 months of age in children's (N = 114) mastery of relations between an object and an aperture, supporting surface, or form. When choosing between objects to insert into an aperture, older children selected objects of an appropriate size and shape, but younger children showed little selectivity. Further experiments probed the sources of younger children's difficulty by comparing children's performance placing a target object in a hole, on a 2-dimensional form, or atop another solid object. Together, the findings suggest that some factors limiting adults' object representations, including the difficulty of comparing the shapes of positive and negative spaces and of representing shapes in 3 dimensions, contribute to young children's errors in manipulating objects.

This study aims to determine if, in children, subjective perception of space is modulated by the experience of reaching distal objects by means of tools and verbal labels. We presented 7–15-year-old participants with objects located in the near and far space, and in the threshold area between these spaces (border space). Before and after a training session, separate groups of participants estimated objects’ location by providing a verbal estimation of their distance ( n D 12) or by rolling a toy car to match their location (motor-based estimation; n D 16). The training session required interaction with the targets (i.e., actively experiencing the perceived distance) and included use of a rake or a linguistic label when far objects were involved. A control condition in which training implied use of a short, ineffective tool was also tested ( n D 6). Results showed that verbal estimations were not affected by the training phase ( p > .05). In contrast, training modulated motor-based estimations relative to border space. Specifically, maximal distance of toy car displacements was reduced following all kinds of training ( p < .01). These results indicate that, similarly to adults, the boundary between near and far space is not fixed in children and that both active tool use and verbal labels can modulate this uncertain boundary.

2005

Two experiments tested the ability of 4-and 8-year-old children to encode the extent of a target dowel and later discriminate between the target and a foil having a novel extent. By manipulating the heights of containers in which we presented the stimuli we tested whether children used the relation between the dowels and containers for encoding extent.

1999

The measurement and description of polygons and paths by elementary school students was studied from a constructivist point of view. A teaching experiment was devised to promote understanding of length based on the hypothesis that as children coordinate their number concept and their one-dimensional/two-dimensional spatial concepts they gain understanding of, and build more abstracted schemes for, length and perimeter. Four fourth graders were studied in the second semester of their academic year. Four themes were encountered in the study. Children quantified length by partitive operations and later by iterative operations, gradually restructuring their internal images. They coordinated their number sequence with their spatial images as they kept shifting from making visual comparisons between objects to quantifying the extent of partitioning operations. The children represented length when they curtailed their own movements through linear space, and they coordinated several linear quantities for an object by disembedding the linear aspects of the object in space. The children appeared to progress along four levels of strategy for length, and it is suggested that progress through these levels follows from increasing integration between conceptual knowledge and figural knowledge related to the measure of length. Children gained abstraction for length and perimeter concepts as they increased the correspondence between their counting scheme, their partitive scheme, and their iterative scheme. Six instructional strategies that supported the children in creating and recognizing relevant length structures and in reflecting on relations among measures of length taken along a complex figure are identified, and implications for instruction are discussed. (Contains 1 table, 8 figures, and 54 references.) (SLD) Reproductions supplied by EDRS are the best that can be made from the original document.

Cognitive Development, 1987

The present experiments examined 7-month-old infants' ability to represent and reason about the physical and spatial properties of an occluded object. In Experiment 1, two groups of infants were tested. One group saw a screen that rotated 90 ° upwards and then, remaining vertical, slid backwards. The results showed that the infants expected the screen to stop sliding sooner when an object stood 10, as opposed to 25, cm behind it, suggesting that they (a) represented the location of the object behind the screen and (b) used this information to estimate at what point the screen should reach the object and stop. The other group of infants saw a screen that rotated upwards and then backwards, in the manner of a drawbridge. The results showed that the infants expected the screen to stop rotating sooner when an object 20, as opposed to 4, cm-high stood behind it, suggesting that they (a) represented the height of the object behind the screen and (b) used this information to judge at what point the screen should reach the object and stop. The infants in Experiment 2 also saw a screen that rotated upwards and then backwards. The results indicated that the infants expected the screen to stop sooner when an incompressible, as opposed to a compressible, object stood behind it (the two objects were of the same height). This finding suggested that the infants (a) represented the height and the compressibility of the object behind the screen and (b) used this information to determine at what point the screen should reach the object and whether it could continue rotating past this point (by compressing the object). The results of a control experiment supported this interpretation. Together, the results of Experiments 1 and 2 indicate that, contrary to Piaget's (1954) claims, 7-month-old infants can represent and reason about the physical and spatial properties of an occluded object. These results have implications for three areas of infancy research: object permanence, physical reasoning, and representation.

Spanish journal of …, 2006

The main purpose of the present study was to investigate whether in natural environment, using very large physical distances, there is a trend to overconstancy for distance estimates during development. One hundred and twenty-nine children aged 5 to 13 years old and twenty-one adults (in a control group), participated as observers. The observer's task was to bisect egocentric distances, ranging from 1.0 to 296.0 m, presented in a large open field. The analyses focused on two parameters, constant errors and variable errors, such as measuring accuracy and precision, respectively. A third analysis focused on the developmental pattern of shifts in constancy as a function of age and range of distances. Constant error analysis showed that there are two relevant parameters for accuracy, age, and range of distances. For short distances, there are three developmental stages: 5-7 years, when children have unstable responses, 7-11, underconstancy, and 13 to adulthood, when accuracy is reached. For large distances, there is a two-stage development: 5-11 years, with severe underconstancy, and beyond this age, with mild underconstancy. Variable errors analyses indicate that precision is noted for 7 year-old children, independently of the range of distances. The constancy analyses indicated that there is a shift from constancy (or slightly overconstancy) to underconstancy as a function of physical distance for all age groups. The age difference is noted in the magnitude of underconstancy that occurs in larger distances, where adults presented lower levels of underconstancy than children. The present data were interpreted as due to a developmental change in cognitive processing rather than to changes in visual space perception.

Developmental Psychology, 1985

Five-, 5'/2-, and 7-month-old infants were tested for sensitivity to relative size as distance information. Infants viewed two equidistant objects that were identical except in size. Reaching was observed as a measure of the perceived relative distances of the two objects. Infants 5'/2 months old and 7 months old gave clear evidence of sensitivity to relative size. Under monocular viewing conditions, both groups showed a preference to reach for the larger object of the pair. Under binocular viewing conditions, no difference in number of reaches for the large and small objects was found for either group. The lack of a reaching preference in the binocular condition suggests that the reaching preference observed in the monocular condition was due to the perceived spatial locations of the objects and not to a preference to reach for the larger object without regard to distance. Infants 5 months old gave no evidence of sensitivity to relative size. The finding that 5V2-and 7-month-olds are sensitive to relative size and the failure to find such sensitivity in 5-month-olds is consistent with results from other studies on infants' sensitivity to pictorial depth cues.

2005

Abstract This study explores how infants encode an object's spatial extent. We habituated 6.5-month-old infants to a dowel inside a container and then tested whether they dishabituate to a change in absolute size when the relation between dowel and container is held constant (by altering the size of both container and dowel) and when the relation changes (by altering only the size of the container but not the dowel).

Developmental Psychology, 2007

Psychological Science, 1999

This article examines the emergence of the ability to use a simple map to acquire information about distance in a larger space. It is commonly believed that scaling is a late achievement in childhood. The present study examined the origins of this ability by using the simplest of situations. In two experiments, we presented preschool children with a dot in a long thin rectangle, and asked them to use that representation to find an object in a corresponding location in a much larger sandbox. All 4-year-olds and a majority of 3-year-olds performed well on this task. We present a model that posits a simpler mechanism for scaling than that proposed in the existing literature.