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Abstract

In Piaget's theory, cognitive behavior in sonic problem situations can be likened to a four-group—a mathematical group whose elements consist of four transformations. These four transformations are represented as follows: I (identity), N (negation), R (reciprocal), C (correlative). The INRC group has logical and physical “realizations,” i.e., different systems which exemplify its properties. Piaget holds that the INRC group and combinatorial structures can only be found at the stage of formal operations. In the snail problem, referred to by Easley, a snail is placed on a board which rests on a table. The snail can move from left to right or right to left while the board is stationary. Likewise, the board can move in either direction while the snail is stationary. Finally, the snail and the board can move simultaneously in either direction. In the following note Easley presents an analysis of the snail problem in terms of the INRC group.