Social Education 55(5) pps. 316-319
©1991 National Council for the Social Studies
According to Muir and Frazee (1986), eight skills make up the elementary map curriculum: interpreting symbols, viewing perspective, finding location, determining direction, calculating distance, computing elevation, imagining relief, and understanding scale. Those authors have also described ways of teaching these skills in a developmentally appropriate manner in an earlier issue of this journal; Muir and Cheek (1986) have also suggested a relationship between map skills and the mathematics curriculum. The first skill-interpreting symbols-is visual, or graphic, rather than spatial. The remaining seven skills, however, depend on spatial ability.
Research describes behaviors common among children who complete tasks that provide insight into children's spatial development. Researchers and curriculum developers can use these tasks to determine when teachers should introduce new skills and concepts. Teachers can informally diagnose problems children encounter in spatial reasoning by modifying the complicated exercises and administering them in classrooms.
Jean Piaget and interpreters of his work created the tasks described in this article. Five traits characterize the tasks: (1) they are administered individually; (2) they involve active manipulation; (3) they have game-like qualities; (4) they elicit a verbal explanation from the children; and (5) administrators often try to talk the youngsters out of a correct explanation to determine if the explanation is fixed or random.
This article describes briefly some common problems encountered by elementary schoolchildren with the seven spatial map skills. It describes at least one task for each skill and suggests ways of adapting the more complex exercises to the classroom. Typical responses that illustrate the children's progression of development are described in three phases. The steps do not conform with Piaget's preoperational, concrete, or formal stages, some phases constitute Piagetian substages. Administration and analysis of Piaget's tasks are described further by Copeland (1979) and by Voyat (1982). Tasks that can be illustrated appear in figure 1.
We have deliberately omitted the age at which a phase reportedly appears. Most studies follow Piaget's procedure of reporting the age level when 75 percent of students in an age group perform a given task successfully. That tradition often conceals the fact that as many as a quarter of the children at a reported age level are unsuccessful. Furthermore, comparison to norms is less useful diagnostically than is the observation of an individual child's performance.
Perspective is the ability to imagine or recognize an object from the aerial, or "bird's-eye" view. Mapping literature refers to this skill as "orientation," "viewpoint," or "orthogonal perspective." Most children lack opportunities to view geographic areas from above. As Vanselow (1974, 11) points out, "Direct experience with the environment usually occurs at the ground level, giving the individual a horizontal perspective." Perspective is fundamental to understanding the concept of a map, yet formal instruction in the skill's relationship to maps is absent in many mathematics and social studies programs.
Pedde (1966) asked children to draw a map of a three-dimensional village that contains buildings and trees (figure 1a). Drawings by younger children portrayed each object from the horizontal perspective on a single baseline. To solve the problem of an object that was behind another, children normally placed the background object on top of the one in the foreground. At a higher cognitive level, drawings combined both aerial and horizontal perspectives. Buildings, for example, often were drawn from the aerial perspective, trees and chimneys from the side. In the final stage, children began, without prompting, to depict each object from an aerial perspective.
Performance on Piaget's coordination of perspectives, or "three-mountain," task also reveals the emergence of perspective ability (Piaget and Inhelder 1948). In this exercise, the child views three model mountains of different colors and strikingly different shapes. Approximately twenty photographs of the mountains seen from different angles are shown to the pupil. While the child remains seated in one position, a doll is moved to various viewpoints (opposite the child, to the left, to the right, and in several aerial positions). The child selects the photograph that shows what the doll "sees."
Children at first egocentrically imagine that their personal viewpoint constitutes all possible perspectives. No matter where the doll is moved, the child selects the view that he or she sees. Next, when they realize that other perspectives exist, they select views other than their own, but are unable to select correctly. Finally, they recognize and accurately describe other points of view. You can replicate this task in the classroom by using three boxes, painted different colors (figure 2). Teachers can take photographs or prepare drawings from which children select the predicted points of view.
Two grid systems can be used to locate places on maps: simple alpha-numeric coordinates and latitude-longitude. Most educators agree that simple alpha-numeric coordinates (e.g., A-3, H-7) are appropriate for use with elementary schoolchildren, and a growing number of advocates (e.g., Bartz 1970, Brown et al. 1970, Welton and Mallan 1988) recommend delaying instruction in latitude and longitude until students are capable of formal, abstract reasoning.
Children who perform Piaget and Inhelder's (1948) diagrammatic layouts task demonstrate the ability to locate. The child views a three-dimensional model of an area that is divided into quadrants by an intersecting road and a stream. Different numbers of trees, barns, and sheds are arranged within each quadrant (figure 1b). The child reproduces the model having been given only the stream and the road as baselines. A young child's reproduction often bears no resemblance to the model; sometimes all of the trees, barns, and sheds are placed in the same quadrant. As spatial ability increases, the child places the correct number of objects in each quadrant, but location within the quadrant is inaccurate. Eventually, the child uses several different reference points simultaneously to reproduce the model successfully. This exercise can be modified by distributing common classroom materials-pencils, erasers, paper clips-on a paper divided into quadrants by different colored lines (figure 3).
Although pupils in elementary schools may understand directions on flat maps, they find it more difficult to apply global directions to the real world. Labeling the sides of a flat piece of paper-as on outline maps, wall maps, or in textbooks-is an insufficient method of verifying children's understanding of global direction.
Pattison (1967) found that three categories of directional concepts emerge in childhood. Youngsters first understand environmental directions, described by prepositions such as in, under, and behind. Next, children accurately use terms that express personal directions (i.e., front, forward, left, clockwise, and their antonyms). Children understand global directions (e.g., north, southeast) only after they learn environmental and personal directions. The directional categories correspond to three stages: (1) an egocentric understanding of direction only in relation to oneself; (2) inconsistent understanding of other persons' (or objects') points of view; and (3) a coordinated system that correctly imagines other persons' (or objects') points of view. A child's developmental category or stage becomes clear as he or she answers questions in order to describe the location of objects or points using environmental, personal, and global vocabulary. Interview questions for environmental, personal, and global directions, developed by Muir and patterned after Piaget's Right and Left exercise (Piaget and Inhelder 1948), are in table 1.
Calculation of distance is often used in combination with direction, as when one locates a place "X miles north of Y." A developmental approach to teaching measurement introduces each skill separately before combining them. Two Piagetian tasks assess readiness for the skill of measurement (Piaget, Inhelder, and Szeminska 1960). Since these tasks use common classroom materials, teachers can easily administer both tasks in their original forms.
Relative distance underlies all measurement concepts. A child who understands relative distance realizes that the distance AB is the same as BA even when another object, such as a screen, is placed between A and B. The child's understanding progresses from (1) looking only at the distance from A or from B to the screen, but ignoring the overall (AB) distance, to (2) believing the distance is shortened since the screen seems to absorb space, and then to (3) understanding that the distance from A to B is the same regardless of objects placed in between the two points.
Children understand properties of length when they can agree that two lines are equal in length, even when they appear to be different. For example, a child can be asked to compare a straight line to a zigzag line of the same overall length (figure 4). In the earliest stage, the child focuses on the end points and, therefore, believes the straight line is longer. The child makes inconsistent responses during the next stage, but eventually the child realizes that both lines are equal in length.
The concept of elevation can be defined as "vertical distance." In contrast to horizontal distance, elevation is represented (1) in intervals rather than exact measurements, (2) in feet or meters rather than miles or kilometers, and (3) in color rather than by shape symbols.
A measurement task (Piaget, Inhelder, and Szeminska 1960) determines if a child understands the relationship between vertical distance and a base level (figure 1c). In this task, children are instructed to duplicate a model building using materials that vary in size (e.g., different size blocks) and on bases (e.g., tables) that vary in height. At first, children construct the new building using the same number of blocks as the model, regardless of their size. Next, they use measurement, but they fail to take into account the difference in base levels. Finally, they spontaneously select standard or nonstandard measuring tools and apply them solely to the building, irrespective of its base.
The concept of relief involves topography or contour. Understanding relief when reading a one-dimensional map involves distinguishing between horizontal and vertical space in concave and convex areas. Two tasks assess that distinction (Piaget and Inhelder 1948). A verticality task determines if a child understands the vertical plane. The original task asked the child to draw a plumb line in a bottle that is tilted to the left and then to the right. The exercise is easily adapted by observing a child draw trees on a mountain (figure 1d). In the first stage, the child believes the trees tilt with the mountain's slope. Later, the child visualizes inconsistent relationships. Finally, the child consistently places trees perpendicular to an unseen baseline. The horizontality task requires a child to hypothesize how the water level would change if a glass that sits upright were tilted to the left or to the right (figure 1e). At first, the child imagines the water line to be parallel either to the bottom or to the sides of the bottle. Next, the imagined view is independent of the bottle's perimeters, but the lines are diagonal. Finally, the child correctly imagines the water as perpendicular to ground level.
Scale refers to the size of a map's reproduction. A child who comprehends the concept of ratio, or the relationship between two units, recognizes the difference between an area's actual size in space and its reduced size on a map. Towler and Nelson (1968) devised a task involving scale that used a three-dimensional model and a small map of the model's area. Given symbols of various size, the child selects those that are most appropriate to use on the map.
Maps that contain insets at different scales require an understanding of proportion. In this case, children must understand the relationship between an area's actual and reduced, or map, size when compared to the actual and reduced size of the second scale. Karplus and Peterson's (1970) Mr. Short-Mr. Tall activity analyzes the understanding of proportion. The child uses small and large paper clips to measure the height of a stick figure. Later, the task administrator provides only one measurement in small paper clip lengths; and asks the student to determine the height of an unseen figure if he or she used large paper clips. In the first stage, the child is unable to predict the figure's height. In the second stage, they apply addition. Only in the final stage does the child multiply by the correct factor.
Assessment of spatial abilities is integral to designing instruction for children in making or reading maps. Total success on the tasks described in this article is not a prerequisite for instruction; moreover, it is unrealistic to expect teachers to administer each task to every child. It is realistic, however, to use these tasks to analyze the difficulties certain children have with maps to determine if the activities are appropriate to their spatial development. Both teachers and curriculum developers can gain insight into the learning process by interviewing children as they perform these manipulative exercises. As teachers become increasingly aware of children's misunderstandings and difficulties, they are relieved of the guilt that their teaching method is to blame for those problems, and they become aware of the extent to which an existing curriculum is or is not developmentally appropriate. In turn, curriculum developers can implement the findings from teachers' observations, resulting in more effective instruction.
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