In analyzing any kind of thought, it is useful to distinguish representations from transformations—that is, data from manipulations performed on data or information from operations applied to the information. The distinction is not hard and fast; it is easy to argue that representations and transformations can be decomposed into finer levels of representations and transformations (Rumelhart, 1980). Spatial thinking rests on the interplay between mental representations that capture spatial features of the world and the transformations that can be applied to those representations. The transformations are similar to the perceptual transformations that are applied to the visuospatial world (Podgorny and Shepard, 1978). However, this statement, too, must be qualified because people can use spatialization to think about abstract concepts that are metaphorically spatial, a powerful feature of spatial thinking. Such uses are reflected in language; we say that someone is on top of the world or has fallen into a depression or become closer.

The committee proposes an organized catalog of elements of spatial thinking, beginning simply with the properties of representations, first static and then dynamic. It continues by describing the properties of transformations that can be performed on either external stimuli or mental representations. Then the committee turns to issues such as the process of complex spatial reasoning, the role of distortions in spatial thinking, using spatial thinking in abstract domains, and spatial thinking using external diagrammatic representations as opposed to internal mental representations. Finally, links between levels of expertise and the process of spatial thinking are discussed.

Representations: The Properties of Entities Representations, whether in the mind or external, map elements and their relations in the world to elements and their relations in the represented world. Thus, representations consist of elements and the spatial or conceptual relations among the elements with respect to a reference frame. An important component of spatial thinking, then, is encoding of the attributes of the spatial world. What follows is a partial list of the kinds of attributes that can be encoded and the processes that encode them. Saying that these attributes can be encoded does not say that they are encoded faithfully; indeed, there are systematic distortions in at least some of the encoding operations, distortions that appear to function to ease information-processing demands. For example, the location of an entity is encoded with respect to the locations of other entities or to a reference frame, and normalized to the reference frame so that entities are remembered as more aligned with the reference frame. Which attributes of entities are encoded will depend on the task and on the experience of the perceiver. Recognizing patterns, for example, may entail evaluating the shapes and sizes of the parts of the pattern.

Spatial thinking can be said to begin with distinguishing and encoding spatial features of the world (Hochberg, 1978). First, figures must be distinguished; then their features and their relations to each other and to their context can be encoded into mental representations. A partial list of encoding operations that establish mental representations follows; it is suggestive of the sorts of perceptual features that people encode, and it is ordered in terms of the importance of the process in terms of spatial thinking. Encoding processes are not atomistic in themselves; they result from prior information processing and, in turn, serve as components for more complex spatial judgments and inferences. Encoding processes include

  • distinguishing figures from ground;

  • recognizing patterns, both outline shapes and internal configurations;

  • evaluating size;

  • discerning texture;

  • recognizing color; and

  • determining other attributes.

For example, the process of distinguishing figures from ground occurs early in information processing, so early that we are rarely aware of it. However, on dark, foggy nights, it is sometimes

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