Space

Space, like many other concepts that seem intuitively simple, is in actuality difficult to define. Philosophers have debated the question, What is space? since antiquity (see Jammer, 1954; Liben, 1981). Within psychology, space has been studied in a number of arenas. For example, questions about visual space (e.g., how people see distance, depth, or size of objects in their visual field) are studied within the field of visual perception (e.g., Gibson, 1979; Marr, 1982), those about motor space (e.g., how people interact with the immediately surrounding physical space as in walking through it or grasping at objects within it) are addressed within the field of kinesiology or motor performance (e.g., Rosenbaum, Meulenbroek, Vaughan, & Jansen, 2001), those of large-scale space (e.g., how people develop and then rely upon cognitive maps as they think about and travel through familiar neighborhoods or novel cities) are studied within the field of environmental psychology or behavioral geography (e.g., Downs & Stea, 1977; Lynch, 1960; Stokols & Altman, 1987), and questions about mental space (e.g., how people rotate mental images of objects or figures) are studied within cognitive psychology (e.g., Shepard & Cooper, 1986).

Within developmental psychology, the same kinds of questions have been addressed, but with a particular focus on describing and explaining at what point in life these skills emerge and mature. Developmental psychologists have also generally been more concerned than their nondevelopmental colleagues with the study of group and individual differences (e.g., Eliot, 1987; Liben, 1991, 2002; Linn & Petersen, 1985; Thomas & Turner, 1991) as a way to provide insights into how spatial development is linked to organismic variables (e.g., inherited spatial abilities, see Thomas, 1983) and experiential factors (e.g., participation in certain kinds of activities, see Signorella, Jamison, & Krupa, 1989).

The theoretical and empirical controversies surrounding spatial functioning are much like those concerning representational functioning discussed earlier. That is, research has involved cataloguing how early, and under what conditions, spatial processes and representations emerge. Again, it was Piaget (1954) who posited a gradual and extended period of spatial development. He suggested that it took the entire sensorimotor period for infants to develop such fundamental ideas as the understanding that they are separate entities from the space that envelopes them, that objects continue to exist in space even when unseen, and that the various perceptual spaces (e.g., visual space, tactile space, auditory space) can be integrated into a single, encompassing whole. Further, he argued that even those kinds of accomplishments fell under the relatively primitive domain of spatial action or behavior. It was not until children entered the preschool years that spatial representation was said to emerge.

With respect to spatial representation, Piaget and Inhelder (1956) posited that during the preschool years, children constructed topological concepts that involve "rubber sheet" spatial qualities, that is, those remain unchanged as a surface is stretched (e.g., open vs. closed figures; on vs. next to). Children were then said to construct projective and Euclidean (or metric) concepts. The former involve "point of view" qualities, that is, those that change with the viewer's perspective (e.g., right vs. left or in front vs. behind) and the latter involve the use of abstract spatial systems such as Cartesian coordinates, allowing conservation of distance and angle. As was true for representation, investigators who followed Piaget have reported far earlier emergence of spatial functions. For example, investigators have reported young infants succeeding in integrating cues across perceptual modalities (e.g.,

Starkey, Spelke, & Gelman, 1983), grasping accurately at objects in space (Jonsson & von Hofsten, 2003), and demonstrating sensitivity to locations with substantial metric precision (e.g., Newcombe & Huttenlocher, 2000).

The "early versus late" and "qualitative versus quantitative change" controversies that have been evident in the literature on spatial behaviors during infancy have likewise been evident in the literature on spatial concepts and representations during childhood. For example, in contrast to Piaget's description of the gradual and relatively late emergence of children's abilities to understand projective and metric concepts, others have reported very early metric and angular inferences in wayfinding (e.g., Landau, Gleitman, & Spelke, 1981) and uses of vertical and horizontal coordinate axes to locate points in space (Somerville & Bryant, 1985). Debates, often heated, concern what successes and failures do and do not mean (e.g., see Blaut, 1997a, 1997b; Downs & Liben, 1997; Liben, 1988, 2003a; Liben & Downs, 1989, 1997; Mandler, 1988; Newcombe & Huttenlocher, 2000; Morrongiello, Timney, Humphrey, Anderson, & Skory, 1995)

Aesthetics

Of the three domains, aesthetics has received the least attention, perhaps an index of a more general view that art is an expendable luxury in both academic research and public education. Yet, art appears to be a part of all human societies, even when physical survival is at risk (Winner, 1982). Its ubiquity, alone, makes it worthy of developmental inquiry. Further, aesthetic development may be linked to development in realms as varied as cognition, self-identity, self-esteem, and intergroup relations (see Liben & Szechter, 2002).

Most developmental work on aesthetics has centered on the visual arts. Parsons (1987), for example, proposed a five-stage model of children's developing understanding and appreciation of art that begins with idiosyncratic aesthetic preferences based on a specific feature (as in liking a painting because it is predominated by one's favorite color) and ends with judgments incorporating multiple factors such as style and artistic intent. Other developmental psychologists have been concerned primarily with children's developing artistic productions (e.g., Golomb, 2004; Milbraith, 1998).

Data from controlled empirical work are consistent with the notion that children begin by making aesthetic judgments by focusing on content, and only later develop an aesthetic that also includes style (e.g., Freeman, 1995; Gardner, 1970; Gardner & Gardner, 1970, 1973). Some investigators have suggested that full sensitivity to aesthetic properties such as composition (the way the components of an art work are organized) does not appear until adolescence (e.g., Winner, Rosenblatt, Windmuel-ler, Davidson, & Gardner, 1986), although others have argued that even young children can display aesthetic sensitivity if given age-appropriate tasks and if an aesthetic stance is modeled by adults (e.g., Callaghan, 2000; Callaghan & MacFarlane, 1998; Hardiman & Zernich, 1985).

Taken together, the history of theory and research in all three topics—representation, space, and aesthetics—lead to the conclusion that it is probably more productive to avoid framing research questions in dichotomous terms (e.g., "Do children at age X have capacity Y?") and substitute more nu-anced questions such as "Under what conditions and with what experiences is some representational, spatial, or aesthetic sensitivity evident?" We have tried to use the latter kinds of questions in guiding our program of research, described next.

RESEARCH ON CHILDREN'S DEVELOPING UNDERSTANDING OF SPATIAL-GRAPHIC REPRESENTATIONS

Overview

This section of the chapter is focused on our program of research. I begin by describing conceptual frameworks, and then sample from our empirical work on children's developing understanding of the representational, spatial, and aesthetic meaning of spatial-graphic representations.

Figure 12.3 The Embedded Model of the developmental understanding of spatial-graphic representations. Adapted from Liben (1999) with permission.
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