Theoretical Foundations

Figure 12.3 depicts the "Embedded Model" that I have used to conceptualize children's developing understanding of spatial-graphic representations. Although the figure is graphically complex and requires an extended discussion to explicate it completely (see Liben, 1999), the core ideas are relatively straightforward and can be highlighted here briefly.

Most broadly, the model rejects a simple "transparency" view that assumes a viewer (here the child) automatically sees through the representation and understands the referent for which it stands. Instead, the model assumes that understanding a given representation relies on the viewer's use of constructive perceptual and cognitive processes directed at both the referent and the representation itself. The former allows the child to construct direct knowledge of the referent, and the latter to construct "mediated" knowledge. Further, the model posits that there is a third target to which these constructive processes are directed—representational strategies. Thus, to fully understand the meaning of a graphic representation, it is necessary to appreciate something about the media-specific techniques (e.g., photography or cartography) relevant to a particular representation. Absent this understanding, the child runs the risk of inappropriately inferring that some quality of a representation is meant to carry meaning about a quality of the referent, and thus leading to what I have called a "mis-mediated" understanding of the referent. As these processes continue, the child's understanding of which qualities reside in the referent and which qualities reside in the representation progresses. The milestones of understanding are summarized in Table 12.2, while Table 12.3 links these competencies to age.

Empirical Work Referential Understanding

A core question concerning referential understanding concerns the emergence of understanding of the denotative meaning of representations. There is considerable research asking whether individuals show this understanding virtually from birth or if they instead must develop it gradually, and if the latter, what kinds of perceptual, neurological, physical, and social experiences contribute to its development. Most of the research exploring this foundational knowledge concerns the chronological period well before that covered by the current chapter. That is, errors suggesting general confusion between representations and referents are typically made by children younger than 3. For example, it is infants and toddlers who have difficulty appreciating that a location shown in a scale model stands for

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