Table 123

Developmental Progression in Understanding External Spatial Representations

Competency

Age Group

Referential Global Representational Attribute Content Differentiation Insight Differentiation

Correspondence Mastery

Meta-Representation

Infants Toddlers Preschoolers Young Children Older Children Adolescents +

Infants Toddlers Preschoolers Young Children Older Children Adolescents +

Note. Shaded cells indicate focal competency under development. Cells marked with a closed circle indicate that the basic competence has been achieved, although further minor development may still be occurring. Cells marked with an open circle indicate that development of the competency is underway. Blank cells indicate that little development is yet under way. Definitions of competencies are given in Table 12.2

attributes, it is useful to return to the spatial features illustrated in Figure 12.2—viewing distance, viewing angle, and viewing azimuth.

Viewing distance affects the size of a depiction. For example, if one is representing (e.g., photographing) a building from a great distance, the representation of the building would be very small even though the building itself is very large. Viewing angle affects the shape of the representation. Thus, for example, a circular children's wading pool photographed or drawn from directly overhead (i.e., a vertical or nadir view) would be perfectly round, whereas one photographed or drawn from a slanted angle (an oblique view) would be elliptical. The task of identifying referential meaning of a component of a representation thus draws on understanding both scale and viewing angle.

Consistent with this analysis, we found that children often made errors of interpretation that could be attributed to confusion about scale. Children evidenced difficulty in separating out depicted (representational) size from actual (referent) size. One 4-year-old boy, for example, denied that a rectangular shape on an aerial photograph of campus could possibly be his father's office building because it was so small, and his father's building was "Huge! It's as big as this whole map!" Another denied that a line on a road map could show a road "because it's not fat enough for two cars to go on." Similarly, we found children made errors that could be attributed to confusion about viewing angle. Thus, for example, what was in actuality a triangular shaped parking area was misidentified by a preschooler as a "hill," an error that can readily be understood by assuming that the child was interpreting that part of the image as if it had been photographed from straight ahead (an elevation view) rather than from overhead. Similarly, we (Liben & Downs, 1991) and others (Spencer, Harrison, & Darvizeh, 1980) found preschoolers interpreting tennis courts as "doors." Again, this interpretation makes sense if one were to assume that this part of the image had been photographed from straight ahead (so that what were in reality the lines on the tennis court would appear to be panels of a door).

To study the role of viewing angle on children's ability to interpret aerial photographs more systematically, we (Liben, Dunphy-Lelli, & Szechter, in preparation) conducted a follow-up study in which preschoolers and adults were asked to identify a series of referents (e.g., baseball field, train tracks) that appeared on aerial photographs that differed in viewing angle (nadir vs. oblique views) and viewing distance (near vs. far). Consistent with the hypothesis that young children have particular problems in identifying referential meaning in spatial contexts that require interpretation of viewing angles that are unlike everyday eye-level views, children (although not adults) gave fewer correct identifications on nadir than on oblique photographs. Furthermore, the kinds of errors made by adults and children differed. Adults' errors were almost always within the domain of environmental referents and were at roughly the right scale, whereas children's errors often were not. For example, when a baseball diamond shown on a far nadir photograph was misidentified by adults, their errors were typically environmental referents such as "parking lot," "pond," or "park," whereas when it was misidentified by children, their errors included nonenvironmental referents such as "thermometer," "machine," "maze," and "dragon."

Given that the studies just described involved preschoolers, they address the lower limits of the age group relevant to the current chapter. A study that included both 8- to 10-year-old children and adults demonstrates that referential identification continues to be challenging well into childhood. In this study we asked respondents to identify seven components of three aerial images, all of which were nadir views, but varied in viewing distance. Although virtually all adults and the large majority of the children were successful in identifying referents correctly, or at least made conceptually sensible errors (e.g., identifying a parking lot as a "playground"), some children still offered some dramatic referential errors. For example, railroad tracks were identified as "an airplane in the air," "a big fly swatter," and an "oar to a boat," while a boat was identified as "a pencil," "a bird," "bird poop," and "outer space—where the world is" and, in a simple scale error, a building was identified as "a doll's house."

Taken together, these studies provide evidence that even children as young as 3 years can understand the referential meaning of spatial graphic representations at a general or holistic level, but that children considerably older are challenged in interpreting the identity of images that are depicted from unfamiliar viewpoints. It is not only spatial features of representations that continue to challenge children beyond toddlerhood. Young children may also find it difficult to separate out other kinds of referential versus representational qualities. Color appears to be particularly difficult for young children to ignore. Evidence for children's tendency to assume that the color of representations match the color of referents was first found in the interview study of preschoolers' interpretation of place representations mentioned earlier (Liben & Downs, 1991). Some charming examples of the conflation of representational and referential color were a number of preschool children who said that the red line on a road meant that the road itself was red, a child who insisted that a portion of a black-and-white aerial photograph of the local community could not possibly be a grassy area "because grass is green," and children who hypothesized that the yellow areas (cities) on a road map were "eggs" or "firecrackers."

A recent study (Myers & Liben, 2004) explored whether shared color of representation and referent continues to be a core assumption of children even as they are entering the school years. After completing a number of other mapping tasks that provided some experience in linking locations on a map to locations in a room, 5- and 6-year-old children watched two videotapes of two different adults adding dots to an oblique perspective map of a room. One adult displayed symbolic intent while adding green dots. She first picked up the paper and said, "I'm going to use this," and then, prior to placing each green dot, looked up as if watching someone else in the room, making comments such as, "Okay. Let's see. She put that one there, so [looking down at the paper] I should put my dot here." The other adult displayed a nonsymbolic (aesthetic) intent while adding red dots. This adult began by picking up the paper and said, "This isn't colorful! I'll make it prettier!" As she added dots, she mentioned her plan to hang it on the wall and selecting a red marker because red was her favorite color. Prior to placing each dot, she looked at only the paper itself, making comments such as, "I think I'll draw two red dots to make this part prettier."

After seeing the two tapes, children were then shown a photograph of each adult, and asked what each adult had been trying to do. Of the 40 children, only two could not demonstrate any understanding of either actor's intent; 25 were able to explain what both adults had been trying to do, and another 13 explained one or the other adult's intent. Children were then asked which drawing they would use to find hidden toy fire trucks. Although the adult with symbolic-intent never specified that it was fire trucks that were being hidden, she was explicit in commenting on placing the green dots to show hiding locations, whereas the adult with nonsymbolic intent was explicit in commenting on placing the red dots to make the paper look pretty. Of the 38 children who were correct in answering one or both of the manipulation-check questions about intent, 27 were incorrect in answering the question about which map they would use to help them find the toy fire trucks. That is, even though red dots had been placed on the paper simply to make it pretty, children thought that the map with red symbols would be more useful for finding toy fire trucks. Furthermore, among those children who selected the correct (green dot) map, only three of them explained their responses in a way that demonstrated representational understanding. The other eight were either unable to provide any rationale, or offered a rationale that still revealed a commitment to a color match between symbol and referent, as in a child who explained that the map he chose would be helpful because the fire trucks were green.

Although we have done no similar research with older participants, spontaneous comments and behaviors observed during our work (Liben & Downs, 1986) provide at least anecdotal evidence suggesting that the difficulty in distinguishing between qualities of representations and referents extends beyond kindergarten. For example, in a second grade classroom, children laughed aloud at the idea of using asterisks to stand for file cabinets on a map of their classroom because file cabinets do not look like stars; even many adults insist that water must be represented in blue (Liben, 2001; Liben & Downs, 1994).

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