The following HTML text is provided to enhance online
readability. Many aspects of typography translate only awkwardly to HTML.
Please use the page image
as the authoritative form to ensure accuracy.
Learning To Think Spatially
is a big city (St. Louis).” These children were thinking, and learning was an instrument for checking and improving the process. To at least a half dozen children in the class it is not a matter of indifference that no big city is to be found at the junction of Lake Huron, Lake Michigan, and Lake Superior. They were slightly shaken up transportation theorists when the facts were in. (Bruner, 1959, pp. 187–188)
The first group of children was practicing a vital form of thinking—spatial thinking—and their work was supported by a simple outline map. Hidden behind many of the daily operations of everyday life, the workplace, and science, spatial thinking is integral to successful problem solving. Section 1.2 defines spatial thinking and presents two examples of spatial thinking in epidemiology. Section 1.3 discusses the committee’s charge. The first group of children in Bruner’s study was successful in spatial thinking, and the purpose of this report (Section 1.4) is to foster a generation of students who are spatially literate, who can match the accepted norms for what should be known about space, representation, and reasoning. Fostering spatial literacy can be achieved only by systemic educational reform, and central to the reform process are members of the four audiences of this report (Section 1.5). Section 1.6 describes the structure of the report.
There are many forms of thinking: verbal, logical, metaphorical, hypothetical, mathematical, statistical, and so forth. They can be distinguished in terms of their representational system (e.g., verbal, using linguistic symbols; mathematical, using mathematical symbols) or their reasoning system (e.g., logic, metaphor). In any domain of knowledge, multiple forms of thinking are used: science, for example, uses linguistic, hypothetical, mathematical, logical, and many other thinking processes.
Spatial thinking, one form of thinking, is a collection of cognitive skills. The skills consist of declarative and perceptual forms of knowledge and some cognitive operations that can be used to transform, combine, or otherwise operate on this knowledge. The key to spatial thinking is a constructive amalgam of three elements: concepts of space, tools of representation, and processes of reasoning. It is the concept of space that makes spatial thinking a distinctive form of thinking. By understanding the meanings of space, we can use its properties (e.g., dimensionality, continuity, proximity, separation) as a vehicle for structuring problems, finding answers, and expressing and communicating solutions. By expressing relationships within spatial structures (e.g., maps, multidimensional scaling models, computer-assisted design [CAD] renderings), we can perceive, remember, and analyze the static and, via transformations, the dynamic properties of objects and the relationships between objects. We can use representations in a variety of modes and media (graphic [text, image, and video], tactile, auditory, kinesthetic, and olfactory) to describe, explain, and communicate about the structure, operation, and function of objects and their relationships. Spatial thinking is not restricted to any domain of knowledge, although it may be more characteristic, for example, of architecture, medicine, physics, and biology than of philosophy, business administration, linguistics, and comparative literature.
To think spatially entails knowing about (1) space—for example, the relationships among units of measurement (e.g., kilometers versus miles), different ways of calculating distance (e.g., miles, travel time, travel cost), the basis of coordinate systems (e.g., Cartesian versus polar coordinates), the nature of spaces (e.g., number of dimensions [two- versus three-dimensional]); (2) representation—for example, the relationships among views (e.g., plans versus elevations of buildings, or orthogonal versus perspective maps), the effect of projections (e.g., Mercator versus equal-area map projections), the principles of graphic design (e.g., the roles of legibility, visual contrast, and figure-ground organization in the readability of graphs and maps); and (3) reasoning—for example,