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indicate eight locations. Children were asked to place stickers on the plan map to show the locations indicated on the aerial photograph.

With respect to location variables, and as hypothesized in the selection of the locations that were queried, items that allowed solution via topological concepts such as "on" or "next to" generally elicited better performance than items that required metric or quantitative reasoning. For example, the item at a clear and unique bend of the breakwater was answered correctly by 29% and 70% of the first and second graders, respectively, whereas an item located on one of many similar buildings whose identification required metric concepts (e.g., judging distances from some other distinct location) was answered correctly by only 0% and 19% of the same age groups.

With respect to user variables, one generalization that emerges from the data is clear improvement in performance with age. For example, the modal response (42%) in Grade 1 was failing to be correct on even a single item, a score that was almost unheard of (4%) by Grade 2. These data suggest that handling the simultaneous changes in graphic medium, scale, and different representational content of the two representations (i.e., the fact that the map represented only a portion of the area shown in the photograph) was completely overwhelming for many of the first but not the second graders. In addition, the maximum score was four correct in Grade 1 but seven correct in Grade 2, and an analysis of variance revealed significantly higher mean scores in the older children. The age difference is unlikely to be attributed to formal instruction given that neither aerial photographs nor mapping tasks like these were included in the children's elementary school curriculum. Instead, it is more likely to reflect general development in both representational and spatial skills during middle childhood. Equally or perhaps even more striking than the age-linked differences, is the wide range of performance within a given grade. For example, within Grade 2, performance ranged from erring on every single item out of eight, to erring on only one item.

The city aerial task could be expected to be challenging because the referent space (Chicago) was entirely unknown, the vertical perspective of both photograph and map which—although shared—was unfamiliar, and the viewing distance of the photograph was great. A different set of challenges was presented by the school aerial task given to first and second grade children (Liben & Downs, 1986). Introductory tasks familiarized children with directional arrow stickers, a map of the school neighborhood, and an aerial photograph of their school (see Figure 12.7). Children were then shown slides of eight aerial photographs of the school, and asked to place arrows on the map to show the direction from which the building had been photographed. This task could be expected to be somewhat easier than the city aerial task because the photographs depicted a familiar rather than an unfamiliar referent and used a smaller viewing distance with a somewhat more familiar viewing angle (oblique rather than nadir). However, the task could be expected to prove even more challenging because it required linking spatial information across representations with two different viewing angles (the oblique angle photograph and the vertical angle map) and queried children's understanding of viewing direction (azimuth) rather than simply location.

Figure 12.7 Aerial photograph and neighborhood map of school used in school aerial task.

Performance was scored by measuring the angular displacement from the correct arrow placement. Even using a lenient margin of error (± 45°), most children in both grades (93% and 87%, respectively) were correct on fewer than half the items, with no age-linked increase, and with no child performing perfectly or almost perfectly. These findings are consistent with the observation that projective (point-of-view) tasks continue to be challenging throughout childhood and even during adulthood.

The pattern of differential performance across items shows that although performance was low overall, it was not random. For example, there appeared to be some systematic tendency to mistake another centrally-located building for the school, or to mistake the rear of the school for its side. Unfortunately, we were unable to vary desired image variables (e.g., azimuth, distance) systematically because of constraints imposed by terrain, cloud cover, and possible flight paths at the time the aerial photographs were taken. Systematic control of viewing angle and azimuth was, however, possible in the terrain perspective task discussed next.

In this task, nine computer-generated line drawings of the local topography were created from different viewing azimuths and angles (see Liben & Downs, 1992). First and second grade children were asked to indicate the direction from which the topographical region had been drawn by placing an arrow sticker on a contour map, and, responses were scored for the degree of divergence from the correct angle. Although there was some slight age-linked advance in performance, again what was most striking were the similarly low scores in both grades (averaging, respectively, only 1.9 and 2.0 correct out of 9 possible). When the quality of the errors is taken into account, however, an age-linked difference is evident: in Grade 1, errors tended to be dispersed evenly over 360° whereas in Grade 2, errors tended to cluster near the correct response. Apparently older children are better able to understand the directional information, but still have difficulty in understanding or in demonstrating that understanding with precision. Interestingly, and consistent with earlier observations of the wide range of performance within any given age is the fact that even as roughly one-fifth of the children at each grade were correct on none of the items, a single child at each grade performed perfectly or nearly perfectly on all of them.

As on other tasks, different items elicited different performance systematically rather than randomly. In general, performance was better on the items for which the correct response faced toward one of the corners of the contour map than for items that faced toward one of the sides. Further research is needed to disentangle the extent to which the corner advantage is due to the match between the corners of both representations, and whether it would still be evident if only one or neither of the two representations had graphically-defined corners (implemented, for example, by using a circular rather than a square contour map).

The final task discussed in this section is the photo-map task (Liben, Kastens, & Stevenson, 2002). In this task, participants were shown eye-level photographs of everyday environments like parks, rooms, and campus vistas. With the photograph in view, participants were asked to place an arrow on a plan or oblique map to indicate where the photographer was standing, and the direction in which his camera was pointing when the picture was taken.

To date, the photo-map task has been given to several samples of fourth-grade children who have been participants in research designed to evaluate the efficacy of a map-use curriculum (see Liben et al., 2002), and to several samples of college students who have been participants in studies examining the role of individual differences and task variables on map use. To provide illustrative data, Figure 12.8 shows one photograph and composite maps of responses from one illustrative sample of each age.

Among the adults, a large cluster of responses (marked as cluster A in Figure 12.8 is correct within a generous margin of error. With two exceptions (responses E and F), even the erroneous arrow placements appear to reflect at least an understanding that the camera was aimed down a path between a building and a tower. Errors suggest inattention to or confusion about viewing direction, about which building appears in the photograph, or both. For example, responses B, C, and cluster G suggest a failure to appreciate that the camera must be positioned so that in the photograph, a building would be to the right rather than to the left of the tower. If one were inattentive to that right-left relation, it would be possible that building #2 or #3 could have been the building appearing in the photograph

Figure 12.8 Composite of arrows placed by adults (left) and children (right) to show position and direction of camera for photograph shown above. Letters (for responses) and numbers (for key buildings) have been added to adult composite to facilitate discussion. Images reproduced from Liben et al. (2002) with permission.

(responses B and C), or that the camera was positioned near a different face of building #4 (response cluster G).

Among the children, not only are there very few correct responses, but performance is far more varied, and strategies are harder to discern. One clear contrast between the children's and adults' responses is that the children are not even uniformly able to identify the critical referential links between the photograph and map. For example, it appears that many of the children had difficulty identifying the representation of the free-standing, tower-like building on the map (labeled #6 on the adult composite). Several children placed their arrows to point at the tower-like part of the large building (#4). It should have been apparent from the photograph that it was the former (#6) rather than the latter (#4) given that the tower in the photograph goes down to ground level and is not embedded within a building. At least one child placed the arrow facing directly toward a rectilinear building with no tower-like structure in sight, and many showed right-left confusions like those discussed for adult respondents.

Taken together, these data suggest that as late as fourth grade, many children have difficulty interpreting the meaning of spatial-graphic representations, and that not only children, but also adults find it difficult to understand the links between representations of given referents when the task challenges point-of-view (or projective) concepts.

Insofar as the photograph is meant to be a proxy for the kind of visual experience one would have if one had actually been standing in the real environment, the photo-map task is transitional to the next category of tasks, that is, to tasks that assess respondents' ability to extract information from a real, currently experienced space, and communicate that information by performing some response on a spatial-graphic representation.

Linking Experienced Environments to Spatial-Graphic Representations

The research discussed in the prior section involves tasks in which there are representational challenges at both input and output. That is, to perform successfully on the described tasks, participants must be able to extract spatial meaning from one graphic representation and then demonstrate that understanding on another graphic representation. In contrast, the research discussed in the current section requires participants to use graphic representations for the output stage only; spatial information is gathered by looking at or moving around in the real, physical environment.

In a taxonomy of methods used to study spatial representation (Liben, 1997a), the former tasks would fall under the rubric of "Representational Correspondence Methods" because they require participants to relate two representations (e.g., a photograph and a plan map). The latter would fall under the rubric of "Production Methods" because they require participants to produce [or modify] a representation by using knowledge collected from a real, physical space. Before turning to illustrative "production" research, it is important to acknowledge that it is also possible to use tasks in which participants gather spatial information from a spatial-graphic representation and then demonstrate their understanding by an action in a real, physical space (called "Comprehension Methods"). To date there has been relatively little research of this kind, probably because of the greater practical difficulties it presents. For example, consider a task in which children are asked to record the location of a novel object placed in their classroom on a copy of a map (a production task) versus the reciprocal task in which children are asked to place the object at a location indicated on a map (a comprehension task). Only the first task permits many children to perform the task simultaneously and independently, and only the first task provides an automatic record of the child's response. Recording where the child places the real object in the real room creates what is in essence a comprehension task for the researcher, who may or may not have advanced enough spatial skills to record responses accurately him or herself. Ongoing research employs comprehension methods (e.g., Kastens & Liben, 2004) but until more data are available, it is not yet possible to know whether or not the two kinds of tasks—comprehension and production—are truly reciprocal. Table 12.5 lists three tasks discussed next to illustrate research in

TABLE 12.5 Environment-To-Representation Tasks

Task name

Stimulus (information obtained from . . . )

Response (indicated on .

Query: . . ) Location?

Query: Orientation?

Object location

Surrounding familiar classroom; familiar objects

Plan map

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