Understanding maps as symbols: the development of map concepts in children

Spatial and mathematics skills: Similarities and differences related to age, SES, and gender

Performance on a range of spatial and mathematics tasks was measured in a sample of 1592 students in kindergarten, third grade, and sixth grade. In a previously published analysis of these data, performance was analyzed by grade only. In the present analyses, we examined whether the relations between spatial skill and mathematics skill differed across socio-economic levels, for boys versus girls, or both. Our first aim was to test for group differences in spatial skill and mathematics skill. We found that children from higher income families showed significantly better performance on both spatial and mathematics measures, and boys outperformed girls on spatial measures in all three grades, but only outperformed girls on mathematics measures in kindergarten. Further, comparisons using factor analysis indicated that the income-related gap in mathematics performance increased across the grade levels, while the income-related gap in spatial performance remained constant. Our second aim was to test whether spatial skill mediated any of these effects, and we found that it did, either partially or fully, in all four cases. Our third aim was to test whether the "separate but correlated" two-factor latent structure previously reported for spatial skill and mathematics skill was (Mix et al., 2016; Mix et al., 2017) replicated across grade, SES, and sex. Multi-group confirmatory factor analyses conducted for each of these subgroups indicated that the same latent structure was present, despite differences in overall performance. These findings replicate and extend prior work on SES and sex differences related to spatial and mathematics skill, but provide evidence that the relations between the domains are stable and consistent across subgroups.

When Color Takes Shape: Young Children Use Object Information from Their Own Drawings to Solve a Task

In two studies, we examined whether and how 3- and 3½-year-old children were able to use object information from their own drawings to solve a task. The children had to produce drawings of simple objects and then use the shape and/or color of their pictures to identify replicas of the referents depicted. The results showed a relationship between graphic production and use. In Study 1, when shape was the single distinctive cue across objects, only the older group was able to produce and use drawings effectively. In Study 2, 3-year-olds used their drawings effectively when not only shape, but also color, were available as cues to identify the objects portrayed. Although most 3-year-olds' drawings did not reflect the shape of the referents, by incorporating color young children demonstrated to recognize the intention behind their own representations and used them to solve the task. Our findings are discussed in line with intentionality and Theory of Mind.

Mathematical achievement: the role of spatial and motor skills in 6-8 year-old children

Several studies have tried to establish the factors that underlie mathematical ability across development. Among them, spatial and motor abilities might play a relevant role, but no studies jointly contemplate both types of abilities to account for mathematical performance. The present study was designed to observe the roles of spatial and motor skills in mathematical performance. A total of 305 children aged between 6 and 8 years took part in this study. A generalized linear regression model with mathematical performance as a dependent variable was performed. Results revealed that Block design (as a visuospatial reasoning measure) accounted for mathematical performance, especially among 6- and 7-year-olds but not in 8-year-olds. After controlling for the effect of the block design, mental rotation and manual dexterity predicted mathematical performance. These findings highlight the role of underlying cognitive (spatial) and motor abilities in supporting mathematical achievement in primary school children.

Geometric maps as tools for different purposes in early childhood

This study examined whether and how young children make spontaneous use of geometric maps for two different purposes: to determine and to represent the locations of objects. A total of 64 2.5-, 3-, 3.5-, and 4-year-old children solved a task with two phases in counterbalanced order; they needed to use a map to locate a toy hidden in a referent space (retrieval) and to indicate on the symbol with a sticker the location of the hidden toy (map making). Results show that there is a clear developmental progression, with 2.5-year-olds failing both phases, 3- and 3.5-year-olds succeeding only in the map making phase, and 4-year-olds succeeding in both the map making and retrieval phases. The differences between making use of maps to represent locations and locating objects in space allow for a closer comprehension of map reading as a progressive sequenced process and the factors at play as children develop symbolic understanding.

Getting the picture: iconicity does not affect representation-referent confusion

Three experiments examined 3- to 5-year-olds' (N = 428) understanding of the relationship between pictorial iconicity (photograph, colored drawing, schematic drawing) and the real world referent. Experiments 1 and 2 explored pictorial iconicity in picture-referent confusion after the picture-object relationship has been established. Pictorial iconicity had no effect on referential confusion when the referent changed after the picture had been taken/drawn (Experiment 1) and when the referent and the picture were different from the outset (Experiment 2). Experiment 3 investigated whether children are sensitive to iconicity to begin with. Children deemed photographs from a choice of varying iconicity representations as best representations for object reference. Together, findings suggest that iconicity plays a role in establishing a picture-object relation per se but is irrelevant once children have accepted that a picture represents an object. The latter finding may reflect domain general representational abilities.

The Development of Children’s Understanding of Maps and Models: A Prospective Cognition Perspective

This article takes a prospective cognition perspective in reviewing research on the development of children’s understanding of spatial symbols, such as scale models and maps. We suggest that using spatial symbols requires that children think about where an object will be found rather than where they last saw it. In addition, we suggest that as children’s knowledge of maps grows, they begin to think about large-scale space through the mediated perspective that maps provide.

Maps allow people to see and to think about multiple relations among locations, as well as spaces that are much larger than can be directly perceived. Learning about the world through maps is a good example of what Tomasello (1999) called the cultural ratchet effect; each generation can rely on information from prior generations rather than having to learn or discover it on their own. Thus, cultures share views of space through maps, and the development of the cognition of large-scale space consists in part of learning to think about the world through maps.

Kindergarten children's sensitivity to geometry in maps

Geometrical concepts are critical to a host of human cognitive achievements, from maps to measurement to mathematics, and both the development of these concepts, and their variation by gender, have long been studied. Most studies of geometrical reasoning, however, present children with materials containing both geometric and non-geometric information, and with tasks that are open to multiple solution strategies. Here we present kindergarten children with a task requiring a focus on geometry: navigation in a small-scale space by a purely geometric map. Children spontaneously extracted and used relationships of both distance and angle in the maps, without prior demonstration, instruction, or feedback, but they failed to use the sense information that distinguishes an array from its mirror image. Children of both genders showed a common profile of performance, with boys showing no advantage on this task. These findings provide evidence that some map-reading abilities arise prior to formal instruction, are common to both genders, and are used spontaneously to guide children's spatial behavior.

Exploring the effects of similarity on mapping spatial relations

Solving a map task requires transferring information acquired in one spatial context to another context, an ability that marks an important step in cognitive development. This study investigated how preschoolers' mapping performance was affected by the extent of similarity between spaces. Whereas prior work examined effects of similarity in tasks involving matching individual objects, our tasks required considering spatial relations among objects. We found that the accuracy of mapping between two spaces with somewhat different perceptual features was higher than the accuracy of mapping between spaces with identical features. Yet, a further increase in differences between the two spaces had a detrimental effect on mapping. The results suggest that some degree of similarity between spaces is beneficial to children's ability to transfer relational information. However, when the spaces have the same surface features, it may draw children's attention to individual objects and inhibit their ability to focus on common relations across contexts.

The Road to Understanding Maps

Children and even some adults struggle to understand and use maps. In the symbolic realm, users must appreciate that the marks on a surface stand for environments and must understand how to interpret individual symbols. In the spatial realm, users must understand how representational space is used to depict environmental space. To do so, they must understand the consequences of cartographic decisions about the map's viewing distance, viewing angle, viewing azimuth, and geometric projection. Research identifies age-linked progressions in symbolic and spatial map understanding that are linked to normative representational and spatial development, and reveals striking individual differences. Current work focuses on identifying experiences associated with better map understanding. New technologies for acquiring, manipulating, analyzing, and displaying geo-referenced data challenge users and researchers alike.

Mapping East London: Sketching Identity through Place

This article provides an analysis of sketch maps of a South African city drawn by local university students. The analysis is compared to previous sketch map studies in Psychology, and highlights the use and relative absence of the analytical concepts of race and class within these studies. An understanding of sketch maps as rhetorical moments is developed, that is, that these drawings represent characterisations of lived space that is ideologically embedded. Consequently, a quantitative and qualitative description and commentary is provided of the depictions and absences in these maps. From this a place identity is suggested and its implications for personal identity are discussed. In conclusion, it is argued that apartheid town planning continues to be successful in that it now accommodates a politically naïve consumerist culture.

Parental guidance in preschoolers' understanding of spatial-graphic representations

This research was designed to observe whether parents guide their children's understanding of spatial-graphic representations and, if so, to describe the quality of the strategies they use. Parents read a picture book to their preschoolers (3 or 5 years, N=31) and children completed spatial-graphic comprehension tasks. Observational data revealed a range of creative behaviors used to address the book's spatial-graphic challenges. The incidence and quality of parental spatial-graphic behaviors were significantly related to 5-year-old children's performance on spatial-graphic measures. These findings, as well as the paucity of parent attention to aesthetics or graphic production techniques, are discussed in relation to representational development and educational practice.

Symbolic representation across domains in preschool children

The study examines children's understanding of notational representation. Children 3 to 5 years old were shown a card containing a notation and told what it said. The children were asked to say what was printed on the card 3 times: when it was under a display named by the notation, when it was under a different display, and finally when it had been returned to the original position. In Study 1, the card contained a word or a picture indicating object identity or a numeral or an analogue indicating quantity. All the children could solve the problems containing pictures, numerals, or analogues, but the word condition was difficult and children believed that the word changed when the card moved to the new display. In Study 2, the comparison between object names and quantities was made more equitable by introducing easy and difficult versions of each condition. This time, there was little difference between cards indicating names and those indicating quantities but large differences in children's ability to solve the problem as a function of their familiarity with the notation that was written. The results point to weaknesses in children's understanding of how representations refer to meanings.

Realist errors in children's responses to pictures and words as representations

In three experiments we examined the judgments made by 3- to 4- year-old children about out-of-date physical representations which no longer matched their referents. The referent was a doll wearing a sticker, and the sticker was swapped for a different one after a picture had been drawn of the initial state of affairs (Experiments 1 and 2) or after the name of the doll and its original sticker had been written down (Experiment 3). We confirmed previous findings of realist errors in identity judgments for pictures and showed also that children tended to misidentify the name of a sticker in a written list to match a change to its referent. Thus, realist errors are not confined to representations which are iconically similar to their referents. Furthermore, children also judged incorrectly that the pictures and words had actually been changed, indicating that realist errors to external representations extend to operations performed on their referents as well as to their identities.