All organisms live in a real, physical world. A core challenge for developmental psychologists is to explain how individuals come to know that world. Virtually any explanation—irrespective of whether it is rooted in a theory that emphasizes biological hard-wiring, associative learning, or self-directed constructive processes—recognizes the key role played by the individual's direct exploration of, and interaction with that real, physical world. As humans, however, we learn about our world not only by interacting with it directly, but also by using depictions of it, that is, external representations that convey information about some aspect of the physical world. Representations are as varied as verbal descriptions, photographs, maps, satellite images, paintings, television images, diagrams, graphs, blueprints, numerical equations, x-rays, and scale models (e.g., see Ittleson, 1996; Liben, 1999; Tversky, 2001).

It is readily apparent that one subset of these representations will be difficult for children to understand and will require social guidance to master. These are arbitrary or unmotivated representations, that is, those that do not have inherent similarities to their referents. Much of our educational curriculum is directed to teaching children how to understand and produce representations such as verbal language and mathematical notation whose referential meaning is assigned by convention.

At first glance, it may appear that another subset of these representations—those that have been called spatial-graphic representations (Liben, 1999)—will be easy to understand and will require little formal or informal instruction to master. These are two-dimensional representations in which at least some aspects of the way that graphic marks are arranged are motivated by (that is, correspond to, or are isomorphic with) the spatial features of the referents for which they stand. For example, a line drawing of a cat may be expected to be easy to interpret because the relative size, shape, and position of the head, ears, nose, and whiskers of the drawn cat are isomorphic with the size, shape, and position of the head, ears, nose, and whiskers of the real cat. Consistent with the expectation that spatial-graphic representations may be understood relatively easily is research showing that even infants categorize pictorial representations similarly to the way they categorize the objects they represent. For example,

DeLoache, Strauss, and Maynard (1979) reported that after 5-month-old infants were habituated to an actual object, they then responded to photographs similarly to the way they would if they had been presented with additional objects. That is, they remained habituated if the photograph showed the same object, but responded with renewed attention if the picture showed a novel object.

Despite the indications that even very young children can see through graphic representations to the referents that lie beneath them, there is ample evidence that young children do not understand spatial-graphic representations fully. In this chapter I review conceptual arguments and empirical data leading to the conclusion that mastery of spatial-graphic representations does not occur automatically and early, but instead follows a gradual and sometimes effortful process that extends well into (and even beyond) childhood.

The mastering of spatial-graphic representations is a multifaceted achievement. In the remainder of the introduction, I overview the representational, spatial, and aesthetic facets of mastery. In the second section, I highlight earlier developmental approaches to these three domains. In the third section I focus on our conceptual and empirical work on graphic representations. In keeping with the placement of the current chapter within Part III, Childhood, I draw most of my examples from work with children who have entered the school years. I do, however, include some material from both younger (preschool) and older (college) age groups as a way of addressing, respectively, the foundations on which the achievements of childhood rest and the more sophisticated levels of mastery to which at least some individuals may be presumed to be heading. In the closing section, I offer some conclusions based on work to date, and suggest some fruitful areas for additional research.

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