Strategies for Finding Sums and Differences Brenda, Tarus, and James

From our point of view, strategies for finding sums and differences involve the coordination of arithmetic symbols that signify systems of integration operations and their products. Moreover, because mental operations (including integration operations) can be expressed in terms of action, the coordination of symbols implies a corresponding coordination of action that need not be carried out unless the need arises (Piaget, 1974b, p. 238). In general, a symbol can figure in a re-presentation and “point to” a signified structure, without the need to realize that structure through either sensory-motor action or re-presentation (von Glasersfeld, 1982a). At the level of operative thought, Piaget suggested that figural re-presentations are, in fact, nothing but “illustrations” that may accompany the performance of mental operations.