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Figure 12.9 Composite of arrow placements (black arrows) by first-grade children asked to show the location and orientation of an adult (open arrow) when map was aligned (left) and unaligned (right) with the room. Reproduced from Liben and Downs (1993) with permission.

Response strategies are revealed not only by looking at arrow placements on individual items, but also by examining the distributions of responses across items. First, those items in which the pointing direction was parallel to one of the classroom walls tended to elicit better performance than those items that were at some oblique angle, perhaps because in the former case, the wall lines on the map provided guides for children's responses. Second, within the oblique items, the types of errors change dramatically by age. The oldest children's errors were virtually exclusively ones of precision. That is, when children in Grade 5/6 made a mistake, it was generally because they placed their arrow only a little bit off from the correct direction. In contrast, when the kindergarten children erred, their placements were generally distributed throughout 360° suggesting random responding. Children between these two ages (Grades 1 and 2) tended to err by placing their arrows directly opposite the correct orientation, suggesting that they were failing to compensate for the map rotation.

Because of practical constraints, most developmental map research (including our work) has employed maps of very small environments such as rooms or hallways rather than of large environments such as parks, campuses, or towns. The former are often not even considered to be maps by many children and adults (see Downs, Liben, & Daggs, 1988). Even more important, maps of such small spaces do not present many of the cognitive challenges presented by the kinds of maps that are typically used in daily life (e.g., for wayfinding or route planning) or in professional tasks (e.g., for recording distributions of regions affected by acid rain). For example, it is often difficult to orient maps of large environments because they may have less-differentiated landmarks (e.g., many similar paths, roads, buildings, vegetation, hills) than might be found in a small contained space such as a classroom, it is challenging to integrate information acquired sequentially (e.g., as in walking or driving through an environment) rather than simultaneously (as looking around a classroom while seated at a particular desk), and it is challenging to understand the relative scales of a very large, navigable environment and its scaled representation.

Many of these ecological challenges were incorporated into the flag location task designed as part of research (Liben et al., 2002) on the Where Are We? map-skills curriculum designed by Kastens (2000). First, eight colored flags were placed at various locations on campus field sites (either urban or rural settings). Fourth-grade children, unfamiliar with the sites, were then brought to the campus as part of a field trip, and as a group, were introduced to the map and the task in general. Each child was then launched on the task individually by an adult who gave the child a copy of the map, aligned the map with the space, and pointed out the child's current location and facing direction on the map. Children were then asked to explore the area, and when they found flags, to place colored stickers on their map to show the flags' locations.

The patterns of data showed that understanding the links between a real space and a graphic representation remains difficult during middle childhood. Scores ranged from zero correct to perfect performance, with the average in most samples at roughly 50% correct. As had been true for tasks described earlier, performance on individual items suggested differential challenges depending on relevant spatial concepts. For example, sticker placements for the black flag were closely clustered around the correct location whereas those for the red flag were scattered, not only near the correct location, but even in other sections of the map entirely. The former was on a statue that was the only statue symbolized on the map and thus topological concepts could be used to identify its location correctly ("on the statue"). In contrast, the latter was on a road which required projective concepts (to identify the correct end of the map) and Euclidean concepts (to identify the precise location along the extended linear symbol).

Conclusions

I have reviewed an assortment of tasks addressing children's developing ability to decode or communicate spatial information with spatial-graphic representations. It is important to point out explicitly that all the tasks discussed intentionally involve these representations. That is, they are not addressed to investigating what information participants may have about a space independently of these repre sentations. For example, even without an external representation, individuals may be able to figure out where they are (e.g., in front of the library) and how to get from one place to another (e.g., from the library to the movie theatre) by using mental imagery, an intuitive sense of direction, a learned motor sequence, or other strategies. At the same time, when participants perform imperfectly on some task that uses spatial-graphic representations, their difficulty might be traced to incomplete or inaccurate "real-space" knowledge or skills, rather than to difficulty in meeting the representational challenges of the task. For example, participants who place stickers incorrectly on the map for the flag location task might err not because they have difficulty relating a location in the environment to a spot on the map, but rather because they have difficulty understanding where they are in the environment in the first place. Much additional research is needed to tease apart where the challenges lie for participants, and to understand the ways in which the use of spatial-graphic representations may aid individuals' knowledge of environments just as familiarity with environments may enhance individuals' facility in using spatial-graphic representations (Liben, 2000, 2002; Liben & Downs, 2001; Uttal, 2000).

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