Table 122

Progressive Competencies in Understanding External Spatial Representations

I. Referential Content. The viewer begins to identify the referential meaning of the representation, with varying ease depending upon the physical similarity of representation and referent. Thus, the viewer "understands" the representation in the sense of identifying the denoted referent, but appears to confuse them (as in trying to pick up a depicted object).

II. Global Differentiation. The viewer identifies the denotative meaning of the representation, distinguishes the representation and referent, and responds to each differentially. The viewer does not, however, reflect upon the correspondence between the two. The "stand for" relation is implicit in identification, but not generally subject to intentional manipulation.

III. Representational Insight. The viewer distinguishes between representation and referent, and intentionally interprets or assigns "stand for" meaning to the representation. Representational insight occurs first for objects that are inherently representational (as a photograph) and only later for objects that do not normally function as representations, but rather are most salient as objects in their own right (as a scale model).

IV. Attribute Differentiation. The viewer comes to appreciate that some, but not all attributes of the representation are motivated by attributes of the referent, and that some, but not all attributes of the referent motivate graphic attributes of the representation. Until doing so, the viewer inappropriately expects that attributes of the representation necessarily mimic attributes of the referent (as in inferring that a red line means a red road) and that attributes of the referent will necessarily be mimicked by attributes of the representation (as in expecting that a large building will appear large in the representation).

V. Correspondence Mastery. The viewer extends the prior understanding of attribute differentiation to develop understanding of the formal representational and geometric correspondences between representation and referent. The former allows the viewer to understand the referential content of symbols; the latter allows the viewer to understand the referential meaning of graphic space.

VI. Meta-representation. The viewer is able to reflect upon the mechanisms by which, and the purposes for which, graphic representations are created, including understanding that different correspondence rules and conventions are used in different media (as in maps vs. graphs), different traditions (as in Western vs. Asian art), and different renditions (as in a world map in a Mercator vs. a Peters projection). As a result, the viewer is able to understand representations not simply as convenient substitutions for referents, but rather as cognitive tools that enrich understanding of the referent, and to select among them appropriately for particular purposes.

Reproduced from Liben (1999) with permission.

the analogous location in the referent room (DeLoache, 1987); and who show signs of profound scale errors as in trying to sit down on a dollhouse-sized chair (DeLoache, Uttal, & Rosengren, 2004).

By the age of about 3 years, children are typically able to appreciate the referential intent of spatial-graphic representations as a whole, that is, to demonstrate facility in the first three competencies shown earlier in Table 12.2. It is at this age and beyond that we have concentrated our research. The specific studies I describe are those in which we show children spatial-graphic representations (either aerial photographs or maps) of large-scale environments (such as a city or a college campus), and ask them to identify the referential content.

In our initial work (Liben & Downs, 1991), we interviewed children age 3 to 6 years with a series of place representations such as a road map of Pennsylvania, a small scale aerial photograph of Chicago, and a medium scale aerial photograph of the local community. We began with general questions about the referent such as What do you think this shows? Even the youngest children answered correctly at the holistic level in that they almost uniformly provided some kind of place-related response, even if some were imprecise or inaccurate about the specifics (e.g., "A city . . . because there's so much stuff in there-houses, roads, buildings." "It's a lots of buildings." "It's a big state." "That's the United States. Because the United States has a lot of people and a lot of cars and a lot of roads.").

Most of these young children were, however, confused when answering identification questions about specific components of the representations. Their errors implied that they were having difficulty differentiating between attributes of the representation and attributes of the referent (see Table 12.2), with spatial attributes proving to be especially troublesome. In discussing the challenges of spatial

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