Bialystok, E. (1986). Frames of reference for coding spatial relations. Cirade (Université du Québec à Montréal), 13.

(Introduction.) The development of children's ability to mentally transform spatial displays has long been a central measure of cognitive growth. The two major types of spatial transformations that have been examined are perspective changes, first studied by Piaget and Inhelder (1956) in the three-mountain task, and rotation changes, the earliest systematic studies being those of Ghent (1961). In the decades following, a great deal of evidence has accumulated concerning the types of problems most easily solved by children, the course of development for each, and the relationship between ability in these tasks and other cognitive abilities. What has been less well examined, however, is the nature of the mental representation that the child uses to permit the solution to these problems and the development of those representations. What, in other words, are the mental processes involved in carrying out spatial transformations and how do they develop?

The major controversy in this area is whether the mental representations underlying the solution are best construed analogically as images or digitally as propositions. The mental transformations associated with imagistic representations are assumed to function much like the physical transformations of real objects, moving smoothly through continuous space, in three dimensions corresponding to the angles and distances that describe physical movement. For propositional representations, transformations are achieved by computing positions and distances in a stepwise fashion, using categories such as half-turn, top, etc. The argument about analogue visual versus computational propositional codings is discussed by Anderson (1978), Kosslyn (1983), Mandler (1983), Pylyshyn (1981), Johnson-Laird (1980) and others.

Johnson-Laird (1980) claims that four features differentiate propositional from imagistic descriptions but that only one of the four is critical in distinguishing these explanations. This feature is the nature of the correspondence between the representation and the world: images represent objects in that the structural relations of the object and the image are isomorphic; propositions are abstractions that are true or false of objects and resemble neither pictures nor words. In some view, such propositional representations are capable of encoding analogical information (e.g. Palmer, 1975) and so can provide the richly detailed descriptions usually associated with imagery.

Following Johnson-Laird, then, representations that are imaginal or propositional would result in different types of errors as a function of the presence or absence of structural isomorphism. Specifically, an image-like representation whould preserve the structure of the display, although the operation of rotating may have been carried out through an incorrect distance. These incorrect distances would likely involve small errors in linear distance but not be systematically related to the display structure. A propositional representation of the display, however, should relate only critical features of the display to a reference and thus indicate critical aspects of the transformation but not necessarily preserve the internal structure of the display nore necessarily all of its features. Similarly, errors in the transformation would involve confusion of features of the display structure, rather than miscalculations of linear distance. These predictions were tested in the present study.