Two non-verbal cognitive systems, an approximate number system (ANS) for extracting the numerosity of a set and a parallel individuation (PI) system for distinguishing between individual items, are hypothesized to be foundational to symbolic number and mathematics abilities. However, the exact role of each remains unclear and highly debated. Here…

Examines some of the issues that underlie the conceptual structure of the computational approach to cognition. Finds that this approach construes symbolization too narrowly, thereby blocking more adequate treatments of learning and acquisition of skills. Discusses the notion of symbol and symbolization and suggests an alternative approach to the…

Examines Kolers and Smythe's 1984 paper on the computational approach to cognition. Considers: (1) five specific criticisms of the computational approach, (2) their analysis of the conceptual basis of symbolization, and (3) their proposed alternative approach. Summarizes their position and discusses its shortcomings. (SED)

Discusses Kolers and Smythe's 1984 paper on the computational approach to cognition. Suggests some factors that support the continued emphasis on the analytic approach of the psychological representation of knowledge, but also acknowledges that they have provided a useful set of distinctions and at least one vocabulary for describing them. (SED)

Many of the difficulties that students have with mathematical symbolism seem to stem from the use of a horizontal form for an equation and a vertical form for computation. The differences between these two forms are discussed. (JT)

Computation can have a profound intellectual impact, like the alphabet thousands of years ago. Using computation, people can begin to outline cognitive structures that will revolutionize the way they learn, although, especially at universities, the dreams must sometimes lag behind their potential due to limited funding. Ultimately, however, the…

Explores two hypotheses about the effect of symbolic systems on psychological functions: (1) culturally elaborated systems of signs affect psychological functioning in a general way; and (2) systems of signs, when used to support skilled action, affect the organization of human activity. Reviews research that supports the second hypothesis. (LB)

This paper examines sixth-grade children's thinking related to solving ratio and proportion problems before these children had received any instruction in the domain. It explores unitizing and norming, one of the processes identified by both content analyses (Behr, Harel, Post, & Lesh, 1990); Harel, Behr, Post & Lesh, 1990) and research in…