Developing an understanding of graphic representations in children and adults: The case of GEO-graphics

Cognitive

Development,

7, 33 l-349

(1992)

Developing an Understanding of Graphic Representations in Children and Adults: The Case of CEO-Graphics Lynn S. Liben Roger M. Downs The

Pennsylvania

State

University

Graphic representations are important for symbolic thought and communication. Here we provide a general definition of graphic representations and discuss some similarities and differences to more commonly studied linguistic representations. We then focus on characteristics of one particular type of graphic representation--those that represent the world or “geo” and hence, “CEO-graphics.” Through the use of models from cartography, we highlight qualities of representational and geometric correspondences between the referent space and the GEOgraphic representation, and suggest that an understanding of these graphics rests on the child’s developing representational and spatial skills more generally. Empirical data on elementary-school children’s interpretations of GEO-graphics illustrate the emergence of understanding in this domain. Finally, we suggest that the development of children’s understanding of representation may be characterized as progressing from syncretism, to syncretic representation, to naive conventional representation, and finally to meta-representation.

A central concern for virtually any student of cognitive development is the child’s growing ability to understand and use symbols. Symbols allow one to perform mental manipulations on referents that are difficult or impossible to manipulate physically, either because the referents are geographically distant (as in symbolizing-through images or words-grocery shopping while seated at one’s office desk); beyond one’s physical capacity (as in lifting one’s car onto one’s shoulders); or not susceptible to manipulation in the real world (as in Much of the empirical research described in this article was collected as part of a grant from the Institute of Education (No. G-83-0025). We are grateful for NIE’s financial assistance, but note that the opinions, findings and conclusions are ours, and do not necessarily reflect the views of the NIE or the Department of Education. This article is part of a continuing collaborative effort by the two authors, and thus order of authorship is arbitrary. Correspondence and requests for reprints should be sent to Lynn S. Liben. Department of Psychology, 417-B Moore Building, Penn State University, University Park, PA 16802 (BITNET: L33@PSUVM) or to Roger M. Downs, Department of Geography, 322 Walker Building, Penn State University, University Park, PA 16802. National

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February

10, 1992

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imagining trees that walk or any other hypothetical condition, be it created for science fiction or scientific research). Symbols are essential for an individual’s own thought; shared symbol systems allow communication among people in ways that would otherwise be not only more difficult, but often impossible. In this article, we focus our comments on a subset of symbols by discussing qualities of graphic representations in general. and by providing illustrations from our empirical research that has been concerned with individuals’ growing understanding of one type of graphic representation in particular. GEO-graphics. In the final section, we offer some general conclusions about the developmental emergence of an understanding of symbols more generally. Graphic Representations: Definitional Issues Although the bulk of attention within developmental psychology has been focused on linguistic symbol systems, our work is focused instead on ~t+nphic~ symbol systems. There are several reasons for our interest in graphic representation. One reason actually stems from the fact that it has received relatively little attention: We believe that in this domain, research data are relatively unlikely to be “contaminated” by parents’ and teachers’ instructional attempts. As an illustration, educated parents generally encourage and drill their preschoolers on letters and numbers, but few probably think to instruct their children in graphic skills. Other reasons for our interest lie in the nature of graphic representation itself. To explicate this nature, it is necessary to define what we mean by the term “graphic representation.” As with most domains, the definition is surprisingly difficult, and becomes even more so as soon as one moves out from the prototypical center of the concept and toward the fuzzy boundaries.’ With that caveat, we offer the following tentative definition: A graphic reprcscntationis composedof marks(points. lines. shading. colors) on a two-dimensional surfacesuch that the marks carry meaning through the propcrtics of their spatial arrangement on the surface (size. shape, density, and distribution). The spatial arrangement is designed to stand for some referent, be it real, constructed, or imagined (e.g.. my pet collie. dogs in general, the gross national product. unicorns, Boston, Tolkein’s Mi&l/c ,&H/I). Given this definition, clear exemplars of graphic representations include representational drawings and paintings, prototypical maps, photographs. graphs, and diagrams. Instances that are questionable as members of the category include holograms, braille maps, plastic relief maps, and collages or paintings that are

I Definitionalissues.basesfor decisionsabout cutcgorymcmbcrship.and theoreticalconscquencesof suchdecisionsarediscussed al greaterlengthin Libenand Downs (I 992). See also Bertin (1983).Goodman(1976).and Tbftc (1990)for discussions of highly rc’icvanttopics.

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three-dimensional through the application of objects or thick paint. Instances that fall outside the category include three-dimensional representations such as scale models and sculpture, as well as objects that are not meant to be representational at all (e.g., a beach ball that is used as a beach ball rather than, say, as a representation for the earth). Particular graphic representations may carry meaning through the use of symbol systems that are not in and of themselves spatial in nature. This is true, for example, when different colors on a map are used to indicate different land elevations above sea level, and a verbal legend is provided to indicate the connection between particular colors and particular elevations. Nevertheless, critical referential meaning is provided by the spatial arrangement of graphic marks on the surface. To continue this example, it is the distribution of colors over the paper that conveys meaning about the distributions of land lying at different elevations in the region represented by the map. This graphic-spatial mode of conveying meaning is in contrast to a verbal representation in which, for example, one might describe the lay of the land verbally, either in general or highly specific terms. As the previous example demonstrates. one cannot distinguish linguistic from graphic representations along the dimension of “arbitrary” versus “motivated” symbols. Graphic representations may, in whole or in part, be based upon arbitrary symbols that may or may not be conventional; for example, using blue to represent water (arbitrary and conventional) and using chartreuse to represent regions over 2500’ above sea level (arbitrary but not conventional). Some graphic representations are iconically motivated by the referent (as in the icons developed for the international road sign system, or those for some computer software). Often, however, the obvious connection between symbol and referent is obvious only as a result of experience or inferential capacities (as illustrated in the next section by children’s difficulty in interpreting seemingly obvious iconic symbols on maps). It is also impossible to distinguish linguistic from graphic forms by the medium alone. That is, insofar as language may be depicted with marks on a twodimensional surface (i.e., presented in written form), the superficial nature of linguistic representation may be similar to that of graphic representation in some cases (i.e., both are made by marks on a two-dimensional surface). Importantly, however, the two modes are distinguished by the one-dimensional arrangement of the linguistic marks on the page versus the two-dimensional arrangement of the graphic marks. That is, text employs a one-dimensional, directed-linear “string” of pieces of information (letters comprising words, words comprising sentences, etc.). Although one must know and use the particular ordering system that controls the direction of the orthographic string (e.g., top-left to bottomright, as in English orthography. or top-right to bottom-left, as in Hebrew), the spatial arrangement of the string on the page carries no meaning and is therefore not an essential part of the communicated meaning. In contrast, the two-dimen-

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sional arrangement of the marks in a graphic representation is integral to the meaning of the graphic representation. As an illustration of this fundamental difl‘erence. consider the panels that comprise the typical newspaper cartoon. Within each panel. two-dimensional graphic rules of representation apply. For example, a bird shown on top of a box means something different from a box shown on top of a bird. But between panels, only rules of order apply. As readers of English, we read panels from left to right, but the meaning would remain unchanged if the panels were presented vertically instead. Unlike the case of the bird and the box, the meaning remains unchanged whether Panel I is to the left of. or on top of Panel 3.’ As another example. consider the following: versus L.,t The referent in both cases is the four-legged furry creature that meows. Admittedly. in the context of a paragraph of otherwise entirely 6-point type. the reader may interpret the former as meaning a big cat and the latter as meaning a little cat. But, in actuality. when the reader infers relative size information about the cats based on the size of the type used for the words. it is because the reader is also using the marks on the page as graphic representations rather than as purely linguistic symbols. Just as qualities of the graphic mode of representation may penetrate the linguistic mode (as illustrated by the CAT example). nonspatial linguistic symbols may penetrate an otherwise graphic representation. as when “OS” are used in a line graph to create the data line for older children and “Ys” to create the line for younger children. It is probably only in rare, and perhaps unnatural hybrids that the two modes are roughly in balance or in conflict as illustrated in Figure I. Although in practice the two modes do not always appear in their pure form, in theory we believe that it is critical to dif‘erentiate between them in order to understand the characteristics and unique powers of each. Furthermore. we argue that an important developmental task in the realm of symbolic development is coming to understand that there are essential difierences between different symbolic modes. It is the child’s failure to appreciate such differences that might be understood as lying beneath the amusing phenomenon reported by Bialystok (1992) in which the child thinks that the words “ant” and “elephant” (but

CAT

2 Note rhar the contrasts

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forms of these modes. Languagss may use two- or three-dimensional spxc IO convey meaning. This condition occur in .4merican Sign Language. for cxamplc. in which Gzc and placcmcnt of signs cxplicirly carry some olthc waning. and in wne caclr alloy. for ~imulrancous rather than scqucnlial proccssin~. Likwiw. it is pobsiblr to uw 3 graphic rcprcscntalion in 3 scquenlial manner under certain conditions. lfonc ib pcnnitfcd 10 set only a small portion of a eruphic rcpresrntation a~ a time (as. e.g.. in a “srrip map” such as the kind provided by rhc American Automobile Association: or as when a blind person feels only ;I single raiwd line on a Braillc map). the procesbcs of inrcrprelalion become more similar IO those described for language than for graphic\. To the dcgrcc that the graphics-user inlegralcs the informalion acro)Is encounters. the spalial nalurc of the graphics communication process is rcinslatcd. Thcx cnumplcs illustrate the fuzzy boundurws and dctinitional difticuhies alluded to wrlicr.

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Figure I. Examples of hybrid representations in which graphic modes are atypically redundant (left) and in conflict (right).

and linguistic

perhaps not “grasshopper” and “cow”) quite reasonably apply to small and big animals. respectively. Here the spatial-graphic qualities (linear extension of the word) are intruding into the interpretation of linguistic text. As this example makes clear, it is neither the intended function nor the physical form of the properties of linguistic marks that determine their meaning. Given our analysis, the characteristics of the graphic mode that are essential for carrying meaning are the properties of the spatial arrangement of graphic symbols. In the following section, we discuss a subset of graphic representations that we have studied extensively. GEO-Graphics:

Theoretical

and Applied

Concerns

In our program of conceptual and theoretical work, we have focused on graphic representations representing some portion of the world, or “geo” and hence, “GEO-graphics.” We have included various forms of place representations such as familiar cartographic maps, aerial photographs, remotely sensed images, line drawings, room plans, cartograms. and so forth. (We have also made use of scale models that involve many of the same spatial issues as two-dimensional place representations, but fall outside of the definition of graphic representation given earlier. see Liben & Downs, 1989a). Our focus on GEO-graphics is motivated by a number of issues, both practical and theoretical. At the practical level, it allows us to draw upon our dual disciplinary backgrounds of developmental psychology (Liben) and geography (Downs), and in addition, provides the opportunity to apply our theoretical and empirical work to the very real and current need for the formulation of programs for geographic education (e.g., Downs, Liben. & Daggs, 1988; Downs & Liben, 1991; Liben & Downs, 1989b: 1992). At the theoretical level, it permits us to import existing, well-developed models and techniques from cartography into the psychological task of analyzing what skills may be involved in understanding representations of a three-dimensional referent on a two-dimensional surface. Before discussing the application of these models, however, one must dispel a

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seemingly common assumption among many noncartographers that GEO-graphits are simply accurate reproductions of the world as it is (Downs, 198 I; 1985). At its extreme, the absurdity of this position is obvious as caricatured by Lewis Carroll (1893. p. 169): “What do you consider the largesr map that would be really useful’?” “About sis inches to the mile.” “Only sir ittckes!” exclaimed Mein Herr. “We very soon got to six yards to the mile. Then we tried a hundred yards to the mile. And then came the grandest idea of all! We actually made a map of the country on the scale of o mile fo tire k/e!” “Have you used it much’?” I enquired. “It has never been spread out, yet,” said Mein Herr: “the farmers objected; they said it would cover the whole country and shut out the sunlight! So we now use the country itself. as its own map. and 1 assure you it does nearly as well.”

In its less extreme (and more invidious) fomr, the position has some currency in the developmental literature. That is, there appears to be some acceptance of the position that in some cases, the graphic representation itself has all of the critical information that is available in the referent, and thus the task of reading a graphic is tantamount to perceiving the referent itself. We have referred to this view as the “RE-presentation” interpretation of place representations (Downs & Liben, 1988; Liben & Downs, 1989a). The RE-presentation view is well illustrated by a quotation from Blaut, McCleary. and Blaut (1970) who suggested that even very young children can readily understand aerial photographs because the graphic transformations involved in going from the three-dimensional space of the world to the two-dimensional space of the photograph draw upon perceptual constancies already mastered during infancy. In sum. the process of map-reading involves three transformations: one of perspective, rotation, or projection; one of distance. or scale; and one of semantic interpretation, from abstract sign to signification. these three transformations are reminiscent of shape constancy. size constancy, and symbolic behavior, respectively. as these latter might appear at the level of macro-environmental events. Stated differently. the mapping transformations seem to involve an extension of the basic operations employed in learning the world of small objects. Indeed, if the relationship is close, then we might be led to predict that the two syntactic transformations. scale and projection. will emerge at an early age, since the constancies are developmentally primitive. (p. 339)

In contrast to this position. we have argued (Downs & Liben, 1988) that as soon as one produces anything but a duplicate of the referent (an identity transform), the graphic is not a RE-presentation of the referent, but rather a symbolic representation of it. As such, the representation is not transparent to the viewer

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simply through perceptual processes of the kind discussed by Blaut et al. (1970). Thus, we have argued that even GEO-graphic representations are not simply opportunities for presenting a singular. accurate miniaturization of some portion of the world. but instead are symbolic, creative visions about the world being communicated to an intended audience by one who has that vision (be it cartographer, photographer, or artist) (Downs, 198 1, 1985). For most people, the notion of creative visions is probably more readily accepted when the graphic mode is “painting” and the content is “environment” than when the graphic mode is “cartography” and the content is “geography.” We believe that in part the difference derives from the fact that most people, at least in this culture. are constantly bombarded by a diverse range of artistic representations. This exposure is explicit in art museums and art courses in which people are directly and repeatedly shown radically different visions of the same world. But even for those who have never visited a museum or taken an art course, exposure to a range of artistic renditions of the environment is almost unavoidable. Cartoons, advertisements, cereal boxes, television, picture books, toys, and fabric patterns (among others) provide a host of differing kinds of graphic representational images. In contrast. most people are exposed to only a very limited range of geographic representations. Schools most commonly use small-scale, colored, political world maps drawn in a Mercator projection. Travelers typically use oil company road maps or standard road atlases for navigation (which occurs, again typically, with motor vehicles). It is not surprising that people. including educators, end up with a belief in “the Gospel according to Rand McNally” (Wohlwill, 1973, p. 167). and with highly restricted views of the form and function of maps (Downs & Liben. 1987, 1988: Downs et al., 1988; Liben & Downs, 1989b, 1991). It is in the attempt to go beyond a restricted view of GEO-graphics, and to analyze the basic skills that the viewer must draw upon for understanding maps, that it becomes especially useful to turn to the discipline of geography, in general, and cartography, in particular. The essential prerequisite for understanding GEO-graphics is an appreciation for the fact that any one graphic representation of place is selective with respect to both what is represented, and the means by which it is represented. Importantly. it is not only that a representations cannot contain all that was in the original space (as it would in a life-size replica), but rather than it should not. Only if cartographers are selective in highlighting , generalizing, and omitting information can they create representations that serve the intended communicative function. Figure 2 (p. 338) provides one means of organizing a discussion of the cartographer’s decisions about both representational and geometric correspondences (see Liben & Downs, 1989a). Essential, of course, is rohat is to be represented. This decision is more than simply identifying the geographic loca-

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Figure 2. Geometric qualities of the CEO-graphic.

tion (the “where”) of the map. For any single “place.” one might depict political units, rainfall, soil type, oil production, cancer rates, population dispersion patterns, and so forth. Contents are virtually limitless, as they may include any domain in which a spatial analysis is of interest. Importantly, decisions about the purpose and thus content of the map are not independent of the seemingly more purely spatial, or geometric qualities of the map. This interconnection is seen most easily with respect to map scale (or, as depicted in Figure 2, by the disrancc of the eye from the referent space). If, for example, the cartographer is creating a map to aid in predicting areas of future global dispersion of a disease such as AIDS, a small scale map of the past history of its spread would be most appropriate. 3 This map might be compared with other small scale maps of the same area showing population density, drug use, concentration of gay communities, and so forth, to predict future dispersion. Alternatively, if the cartographer is creating a map to explore the precise mechunism by which a disease is spread, it might be appropriate to create a large-scale map. For example, by mapping the incidence of disease on a street map of London in the middle 1800s. Snow (see Gilbert, 1958) recognized a link to the location of water pumps, and thereby hypothesized that contaminated water led to the spread of cholera. Cartographic decisions about map scale (a spatial, geometric issue) are of necessity interdependent with cartographic decisions about the kinds of information and symbols used (a representational issue). A very small-scale map (such as the representation of the earth shown on a recent 29e postage stamp) can do little more than distinguish land from water through colors. It omits even large refer3 We use the terms “small-scale” (mapping a large area of mferem space, as in a world map) and “large-scale” (mapping a small arca of referent space, as in a room plan) as they are used in cartography. The usage of these terms is sometimes reversed in psychological literature.

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ents such as lakes, rivers, cities, and mountain ranges, as well as smaller referents such as railroad stations, park sites, roads, and shopping centers. But symbols for referents such as these are possible on very large-scale maps. Even maps at the same scale may make use of differing representational symbols in relation to the purpose of the map. Thus, two maps of the same scale may provide detailed information about the lay of the land and ignore differentiations among road types, or the reverse. The two different maps would be useful for orienteers versus drivers in road rallys. The map user’s understanding of the overall referential context of the map may help the map user in understanding the referential meaning of the individual symbols of the map (that is, understanding its meaning at the “holistic” and “componential” levels, respectively, see Liben & Downs, 1989a). In addition to decisions about the representational correspondences between referent space and map are decisions about the geometric correspondences. One such correspondence, map scale, has already been discussed. A second geometric aspect of the map is viewing azimuth, that is, the position from which the referent space is depicted (see Figure 2). To illustrate, Figure 3 (p. 340) shows the same referent space (a portion of the local Centre County, Pennsylvania terrain in which Penn State is located) from two different viewing azimuths. A third geometric correspondence, viewing angle, refers to the height from which the referent space is viewed. The representations shown in Figure 3 are at a 30” viewing angle, that is, they are shown from an angle 30” above the horizon, creating an oblique map. Shallower viewing angles create views that correspond more closely to eye-level or elevation views (useful, e.g., in representing what one might see from a proposed condominium window); greater viewing angles allow for a greater amount of detail about otherwise hidden topography. Increasing the viewing angle to 90” creates the familiar overhead or orthogonal view such as that shown in the contour map in Figure 4 (p. 341). The geometric system used to project from the three-dimensional referent space of the globe to the two-dimensional representational space of the map also results in noticeably different representations. The “Greenland effect,” for example, in which Greenland takes up a proportionally greater amount of paper-space than its true area in global-space, results from the use of a Mercator projection rather than an equal-area projection that preserves area rather than angles. (At least one spatial property-area, direction, distance, or shape-must be distorted in the course of depicting a three-dimensional space on a two-dimensional surface, see any introductory geography or cartography text, e.g., Robinson, Sale, Morrison, & Muehrcke, 1984). Having analyzed GEO-graphics in this way, it becomes clear that if the individual using the GEO-graphic is to understand fully its referential depiction, that individual would need to have some well-developed understanding of representation in general, as well as an understanding of spatial concepts in particular. It is

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Figure 3. Perspective representations of the local terrain. North was the 0’ viewing azimuth; viewing azimuth of representation on top is 45” clockwise from North; viewing azimuth of representation on bottom is 315” clockwise from North. Viewing angle of both figures is 30”.

this general orientation that has driven our empirical work. The general thrust of our work has been to study children’s developing understanding of GEO-graphics in relation to children’s conceptual development. Our view is that children’s mastery of maps is dependent upon their developing understanding of symbols more generally, of logical reasoning, and of integrated spatial conceptual systems.

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EMPIRICAL

ILLUSTRATIONS

In this section, we provide some brief illustrations from our empirical research of the development of the understanding of GEO-graphics. The developmental data come from three major sources. First are data from an interview study of 30 preschool children who were shown a variety of place representations such as aerial photographs, state road maps, and city tourist maps (see Downs & Liben 1987) and asked questions about their content, functions, and origins. Second are data from classroom activities. Over the course of many years, we have worked with classes of students from kindergarten through graduate school. Here we discuss work with elementary-school children for whom we prepared geography lessons that incorporated a variety of exercises such as those in which students were asked to draw maps (e.g., sketch maps of their classroom and school); to examine locations that had been indicated on one representation, and

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show the isomorphic locations on another representation (e.g.. by placing stickers on a contour map to show the locations of flags planted on a scale model); to indicate viewing azimuths (e.g.. by placing arrows on a map of the school neighborhood to show the direction from which photographs of the school had been taken); and similar tasks (Liben & Downs. 1986, 1989a). Third are data from more traditional laboratory tasks in which children were asked to show locations of objects placed in a room under various mapping conditions (e.g.. Liben & Yekel, 1990). Illustrative Symbolic Immaturities The various kinds of data collected in these different settings are consistent with the general conclusion that most children in the preschool and early elementary school grades have difftculty in fully appreciating symbols’ duality and arbitrariness. By middle childhood, however. there is generally good understanding of these basic properties of symbols. (There also appears to be a developmentally growing appreciation for the power or utility of place representations. although this point is not considered further here; see Liben & Downs, 1991.) Evidence for misunderstanding both the duality and arbitrariness of symbols is derived from responses showing children’s failure to separate the graphic characteristics of the symbol from the physical characteristics of the referent. Misunderstanding can be seen in the child’s overextension of iconic qualities (either from the symbol to the referent or from the referent to the symbol); as well as in children’s oversubscription to graphic conventions. With respect to iconicity, we observed many situations in which the child identified some characteristic of the symbol (shape, size, color. etc.). and then inappropriately inferred from it that the referent must also share that same characteristic. For example, a number of preschool children thought that a road shown in red on the map meant that if you went to that road. it would actually be red. Other preschoolers apparently found the color iconicity so powerful that they inferred a referent of the same color, even though that referent was absurdly unlikely in the context of a road map. Illustrative were preschoolers who thought that the yellow areas on a map of Pennsylvania (standing for built-up areas such as Harrisburg) showed “eggs” and “firecrackers.” Likewise, children overextended symbols’ shapes, as in thinking that the Rand McNally compass rose showed the “sun,” “a basketball stadium.” or “the place where the lifeguard sits.” Expectations of iconic matches between referent and symbol also occurred in the reverse direction, such that the child assumed that some characteristic of the referent should necessarily be evident in the symbol. Thus, for example, some preschoolers rejected the possibility that a red line could show a road “because roads are gray.” In either kind of iconicity error (i.e., assuming that a characteristic of the symbol implies a characteristic of the referent [red line must mean red road], or a

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characteristic of the referent must be represented in the symbol [a gray road must be depicted in gray]), there is a failure to understand the arbitrary and mutable nature of the referent/symbol relation. With respect to conventions, we have seen evidence that children appear to adhere rigidly and inappropriately to “rules” that they seem to believe are necessary. Rules from one graphic form (such as the domain of drawing) may be inappropriately imported into the map domain. Preschoolers’ responses to our request to find “grass” on a vertical, black-and-white aerial photograph of Chicago are revealing in this regard. Some errors seemed to result from the problems of iconicity noted above, as when children asserted that they could not find grass because “grass would be green and there’s no green.” Some errors, however, seemed to result from importing the convention from drawing that grass should be at the bottom of the paper. That is, in response to our request to find grass, several children pointed to the bottom edge of the photograph that was closest to their own body. (The photograph was presented flat on the table in front of the child.) One preschooler’s response was especially revealing in that after pointing to the bottom of the photograph, she spontaneously rotated the paper 180” and, pointing to the “new” bottom edge, said “Now the grass is here.” We have also observed overextension of conventions with respect to orientation in first- and second-grade children who commonly believe that north must be at the top of the map. Likewise, we have observed many children producing canonical graphic representations of generic places even when asked for representations of a particular place from a specified viewpoint. For example, when asked to show what their school building would look like to a bird flying overhead, looking straight down, many children produced generic frontal elevations of several story buildings rather than a roughly correct u-shaped plan view of their two-story school (see Downs & Liben, 1990). Similarly, when asked to produce a map of a section of Chicago based on an aerial photograph given to each individual child, some children produced generic representations of “city” with cars, roads, and houses rather than a specific, presumably orthogonal map (see Liben & Downs, 1991). In each of these errors of convention, there is again a failure to understand the contingent and flexible nature of the referent/symbol relation. Overextension of iconic qualities and oversubscription to graphic conventions are both indicative of the struggle to extract meaning from symbols. Illustrative Spatial Immaturities In addition to observing children’s difftculty in understanding the general nature of symbols, we have observed young children’s difficulties in understanding the spatial structure of place representations. Consistent with Piaget and Inhelder’s ( 1956) position that children master metric and projective spatial concepts only gradually, we have seen many indications of children’s confusions in understanding the scale and viewing angle of the map.

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Scale confusions were evident in interpreting a variety of place representations. Preschoolers denied that a line on the Pennsylvania road map could be a road with reasons such as “It’s not fat enough for two cars to go on.” Another denied that a rectangular shape on an aerial photograph of the local community could be his father’s office building “Because his building is huge . it’s as big as this whole map!” Spontaneous misidentifications likewise demonstrate scale confusions. as when boats in Lake Michigan (shown in the Chicago aerial photograph) were commonly interpreted as “fish” (see Liben & Downs, 1991). Demonstrations of young children’s difficulties in understanding the viewing angle may be found in the sample errors to the Chicago aerial in which buildings lined in parallel were interpreted as “bookshelves.” a parking area bounded by an oblique line was interpreted as a “hill,” tennis courts were thought to be “doors.” and a baseball field was interpreted as an “eye.” In each of these cases. the child’s interpretation would be sensible if the component of the place representation in question were a frontal or elevation view. rather than an overhead or plan view. Thus, for example. an overhead view of tennis courts on an aerial photograph and a plan view of a double sink on a classroom map (see Liben & Yekel, 1990) do. indeed, look like elevation views of paneled doors. Adults’ Misconceptions and the Role of Expertise The illustrations given above have been focused on errors made by young children. Indeed. in our work we have seen significant progress between lower and upper elementary school grades. For example. fifth-grade children routinely produce the very same kinds of arbitrary symbols (e.g., asterisks for file cabinets) that children only two years younger had rejected as hilariously funny (see Downs et al.. 1988). But to note that there is age-linked progress, and to contend that this progress is in part attributable to underlying progression of representational, logical, and spatial concepts more generally. is not to assert that older children and adults never make the kinds of errors we have found common among children. On the contrary, from our experiences working with adults (e.g., in workshops with teachers and classes with college students) we have seen informal evidence that adults, too, may overextend qualities of the representation to the referent. For example, many adults appear to believe that Greenland is larger than Brazil, presumably as a consequence of having been exposed primarily to a Mercator projection; or that Alaska is far from the Soviet Union. presumably as a consequence of using primarily world political maps that divide the world at the Bering Strait. Similarly. we have encountered many strong opinions even among adults about the necessity of following certain conventions. Many teachers, for example, insist that north should be at the top of all maps (see also Rhodes, 1970, a book for children about maps that asserts that “north is always at the top of the map,” p. 46); that water must be shown in blue; and the like (see Liben &

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Downs. 1989b). These examples and others suggest that it is not only cognitive immaturity, but also restricted experience with different forms and functions of maps that constrain individuals’ interpretation of place representations. CONCLUSIONS First, we would argue that. taken together, the findings across a variety of tasks are consistent with the general position that the ability to understand, produce, and use GEO-graphics emerges gradually. Place representations are not simply re-presentations of pieces of the world (Downs, 1981). As a consequence, they cannot be “read” perceptually in precisely the same ways that the real, encountered environment can be “seen” visually. Instead they must be understood as symbolic representations and interpreted within a symbolic context. Second, we would argue that our data are consistent with the notion that the kinds of errors made by young children are those that might be expected on the basis of more general limitations of their cognitive systems. Elsewhere we have provided some empirical data linking children’s performance on mapping tasks to their perfomlance on tasks designed to assesstheir spatial concepts (Liben & Downs, 1986) and their logical skills (Downs et al., 1988). Third. however, we believe that cognitive-developmental limitations are only a portion of the explanation for children’s difficulties. Another large part of the explanation lies in the fact that most individuals encounter only a very limited set of GEO-graphic forms and functions. In conceptualizing developmental progression. then, we argue for the simultaneous contributions of both ontogenetic development and domain-specific knowledge in establishing an interpretive, symbolic context (see Downs & Liben. 1991). Moreover, that symbolic context is not a monolithic. all-encompassing structure from which older children and adults operate with confidence. Interpretive errors can occur at any age, in any context. Those concerned not only with the theoretical implications of this work, but also with the educational applications at both elementary and advanced levels must attend to both ontogenetic and experiential factors (Downs et al., 1988; Downs 6r Liben, 199 I ; Liben & Downs, in press). Finally. we would suggest that our findings in GEO-graphics. like those from other symbol systems discussed elsewhere in this issue, fit within the following (tentative) model of levels of mastery of representation. At first. the child’s approach to representations may be characterized by syncretism. At this level, insofar as the child interprets the representation at all. he or she reacts to it as if it were the referent itself. The symbol-as-object is not differentiated from the symbol-as-symbol. The symbol does not have a dual existence as thing and representation. There is a fusion with no separation. This approach is probably evident in persistent fomi only among very young individuals, as when infants repeatedly try to pick patterns off a crib sheet. However, syncretic reactions appear even among older children, as when a child turns a

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piece of paper over to see the back of an object depicted in frontal view on the reverse side. Even adults may respond in this way, as when one of us has noticed herself. while coding videotapes, moving her head to the side of the screen in an attempt to see what happened to the side of the original referent room: or as when adults first encounter a trompe l’oeil painting and interpret it as a “real” rather than a representational scene. A major difference between infants’ and adults’ responses. however, is the persistent nature of the fomler versus the fleeting nature of the latter. Adults immediately recognize that they have been either foolish or fooled. In syncretic representation, the individual correctly understands that the symbol “stands for” the referent, but incorrectly fuses aspects of the symbol and referent. Included are fusions in both directions. Individuals may infer that what are in actuality only arbitrary qualities of the representation are in fact qualities motivated by the referent. and thus that these qualities of the symbol depict qualities of the referent (as in inferring that a red line used to stand for a road must mean that the road. too, is red). Similarly. individuals may infer that known qualities of the referent should be evident in the representation (as in insisting that grass must be shown in green: or as in thinking that a photograph of an ice cream cone will be cold, see Beilin, 1991). In syncretic representation there is the understanding of a dual existence as thing and representation; there is limited understanding of separation of components of the representation; but there is inappropriate fusion of components of both. In naive conventional representation there is an understanding that relationships between symbol and referent are arbitrary ones. At the same time, however, there is only a naive (or novice) understanding of those relationships such that certain aspects of the representational system are thought to be necessary, or at least preferred (e.g.. north at the top). For the most part, such naive beliefs are probably implicit. and readily given up upon reflection and/or instruction. In naive conventional representation. the duality of the symbol is understood, separation is achieved, and fusion does not occur, but the nature of the symbol-referent relation is seen as necessary rather than contingent. Finally, with adequate reflection or instruction. individuals can reach the final level of meta-representation, in which they understand the varieties of representations. the relative utility and power afforded by different representational systems, the circumstances under which one might use one rather than another; and so forth. It is with meta-representation, for example, that one can understand the contrasts between linguistic text and graphic representation proposed in the introduction to this article. The level of meta-representation opens up the power of symbol systems to the user. Symbols do become flexible, creative, contingent tools for capturing and going beyond aspects of the real world. In closing, it is useful to reiterate our position on the dual roles of both development and learning (see Liben, 1987) for acquiring an understanding of symbols, in general, and GEO-graphics, in particular. We believe that the mean-

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ingful use of any symbol system is linked to the user’s general appreciation for the symbolic function. While we are skeptical that this appreciation is in place from birth, we are prepared to agree that it is achieved in some basic way by toddlers (as suggested by Piaget, 1952) and perhaps even earlier (e.g., see Mandler, this issue). To hold that the rudimentary bases for understanding and using representations are in place. however, is not to suggest that there is yet mastery of the needed cognitive-developmental skills. Analyzing the formal characteristics of the representational system (via cartography in the case of GEO-graphics. via linguistics in the case of language, and so forth). helps to identify the specialized underlying cognitive skills that should be in place for understanding the representational system in question. For GEO-graphics. spatial concepts are especially critical, and thus we have attempted to assessthe relation between the individual child’s developing spatial concepts, and that child’s ability to use and produce GEO-graphics (see Liben & Downs, 1986). But as is suggested by adults’ misconceptions and limitations, one cannot expect the full understanding of GEO-graphics-especially at the meta-representational level-to emerge without considerable exposure to various place representations. and without direct discussion of the power and utility of different representations and representational systems. Furthermore, recent data bring into question the assumption that adults universally achieve mature levels of spatial competence (see Downs & Liben. 1991; Liben, 1992; Merriwether & Liben, 1990), and thus it may be necessary to provide experiences aimed at enhancing the general level of spatial skills as well as those that foster an understanding of graphic representations in particular. What is already clear. however. is that the domain of GEO-graphics provides a window through which to view a variety of issues in cognitive development, and one that-even at the risk of “contaminating” responses from future subjects-should take its place among the more commonly studied representational systems in the exploration of the emergence of symbolic thought.

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