Facets of Understanding

The premise of the work discussed in this chapter is that understanding graphic representations involves a number of facets, summarized in Table 12.1. The first, referential meaning, is the most obvious: recognizing the denotative meaning of the representation. For example, when a viewer who is asked to interpret a painting of a cat answers "It's a cat," the viewer has demonstrated understanding of referential meaning. However, as Figure 12.1 reminds us, images like these are not, in fact, their referents. The painting of the cat is a painting, not a cat, just as the image in Figure 12.1 is a photograph, not a pipe. Being aware of a representation's own existence as a representation constitutes the second facet of understanding, representational awareness.

But even having interpreted the referential meaning of a representation and having recognized that the representation is a thing in itself, it remains challenging to appreciate these two roles simultaneously. Thus, a third facet of understanding, representational duality, is reconciling that something can have an existence in its own right and simultaneously carry meaning about something else (DeLoache, 1987; Potter, 1979). What is challenging is not only recognizing duality at the general level of the representation, but also at the level of individual parts of the representation (which have been called, respectively, "holistic" and "componential" levels, see Liben & Downs, 1991). For this third facet, the user must understand that some qualities of the representation are informative about the

TABLE 12.1

Facets of Understanding Spatial-Graphic Representations

Referential meaning Representational awareness Representational duality

Spatial meaning

Aesthetic awareness Aesthetic duality

Identifying the referent

Recognizing that there is a representation as distinct from the referent Differentiating qualities that carry "stand for" meaning and qualities that adhere in the representation itself at both global and componential levels

Understanding representational vantage point; interpreting spatial qualities of and among referents; and integrating spatial relations among referent, representation, and user Appreciating that there is an aesthetic quality of graphic representations Differentiating aesthetic qualities of the representation from aesthetic qualities of the referent

Figure 12.1 Photograph inspired by Magritte's painting, Ceci ne'est pas une pipe. Reproduced from Liben (2003a) with permission.

referent, and some are simply qualities of the representation itself. For example, the location of the ears on the photographic cat carries referential meaning about the location of the ears on the real cat, but neither the flatness nor size of the image implies anything about the flatness and size of the real animal. Instead, these latter qualities adhere in the representation.

A fourth facet involves understanding several kinds of spatial meaning contained in representations. Included is information about the vantage point from which the referent is depicted. As shown graphically in Figure 12.2, vantage point is defined along three spatial dimensions: viewing distance (the contrast between a close-up vs. a distant photograph of, for example, a pipe), viewing angle (the slant along the vertical axis, as in the contrast between viewing a pipe from directly overhead vs. viewing it from straight ahead), and viewing azimuth (the direction from which the referent is approached, as in the contrast between viewing a pipe from the side vs. from its end). Representations also provide information about spatial features of individual components of the referent (e.g., the curved shape of the pipe's bowl), spatial relations among components of the referent (e.g., the right

angular connection between the pipe's bowl and stem), and relations between one referent and another (e.g., the pipe is on the table).

The final facets of understanding listed in Table 12.1 lie in the aesthetic domain, focusing on the expressive nature of representations. Aesthetic awareness refers to understanding that the representation may be interpreted or experienced with respect to dimensions such as beauty or emotional impact; aesthetic duality refers to differentiating between expressive or aesthetic experiences that are afforded by the representation as distinct from those that would be afforded by the referent itself.


The domains identified as relevant for understanding spatial-graphic representations—representation, space, and aesthetics—have important histories within developmental psychology. I next highlight past approaches and controversies within each.


Representations are the tools that enable the child to move from thinking and reasoning about the here and now, to thinking and reasoning about things that are not currently in view (e.g., a toy in the next room or a grandparent who visited last week), have never been in view (e.g., a new school), or could never be in view (e.g., a unicorn). Although there is little controversy that representation is central to cognition, there is considerable controversy about how early and in what form the ability to form and use representations emerges.

In a classic and broad theory of representational development, Piaget (1951) argued that infants' representational capacity develops only gradually. At first, infants interpret only indices. These are inherent parts of referents (e.g., smoke is an index of fire), and because they are not completely distinct from the referent, are not considered to be true representations. Piaget proposed that the true symbolic function develops gradually during the sensorimotor period (roughly the first two years of life). Infants first come to understand representations that are motivated by the referent (referred to as symbols, as in a picture of a cat), and then understand those connected to the referent by arbitrary assignment (referred to as signs, as in the word "cat"). Bruner (1964) proposed an expanded developmental progression, suggesting that children begin with action-based or enactive representations (as in representing a rattle with a shaking hand), then use visually-isomorphic images or iconic representations, and finally use arbitrary symbols such as words. Although their terminologies differ, Piaget and Bruner shared the view that the ability to understand representations is not inborn, and that there is an age-linked progression in the types and flexibility of representations available.

More recent work has suggested that the ability to create and access some kinds of representations is present extremely early. For example, even within a day or two of birth, infants have been found to imitate adults' facial actions, a finding taken to imply that infants encoded and stored and later retrieved some representation of the observed event (Meltzoff & Moore, 1977). Also taken as suggestive of babies' ability to form and use representations are demonstrations that information acquired from one sensory modality is extended to another. For example, 1-month-old infants given either a bumpy or smooth pacifier to suck (tactile modality) were found to prefer looking at the matching picture (visual modality) of that pacifier (Meltzoff & Borton, 1979). These and related recent empirical studies have resulted in some heated debates (e.g., see Haith, 1998; Mueller & Overton, 1998; Smith, 1999; Spelke, 1999) about whether there is true representation during infancy.

Once the focus is on toddlers or preschoolers, however, there is little question about the existence of representational thinking. By this age, the key questions concern whether representational systems undergo qualitative or merely quantitative development, what kinds of representational systems are available (e.g., numerical, linguistic, spatial), and whether young children are able to consider multiple (especially conflicting) representations simultaneously or in quick sequence (e.g., Zelazo, Mueller, Frye, & Marcovitch, 2003).

Another major research thrust has been aimed at identifying mechanisms that facilitate children's developing representational competence during and beyond the preschool years. For example, research has addressed the impact of parents' tendency to discuss objects, people, or events that are spatially or temporally distant (e.g., Sigel, 1978; Sigel & McGillicuddy-De Lisi, 1984), parents' guidance of their children's understanding of words and pictures (e.g., Gauvain, de la Ossa, & Hurtado, 2001; Snow & Ninio, 1986; Szechter & Liben, 2004), exposure to a bilingual environment (e.g., Bialystok & Martin, 2004), and experience with representational media such as videotape (e.g. Troseth, 2003). Researchers have also sought to catalogue children's emerging meta-cognitive understanding of specific representational systems and distinctions among them (e.g., Bialystok, 2000; Ferreiro & Teberosky, 1982).

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