Modeling reasoning. (English)

Gravemeijer, Koeno (ed.) et al., Symbolizing, modeling and tool use in mathematics education. Dordrecht: Kluwer (ISBN 1-4020-1032-X). Mathematics Education Library 30, 295-304 (2003).

The three chapters in this section approach modeling from very different yet consistently intriguing points of view. Nemirovsky focuses on how people generalize; he argues that generalizations are intimately grounded in situations and only exceptionally take the form of ’For all x, the following holds...’ He illustrates his view through a detailed analysis of how a student creates representations to model the passage of a train through a tunnel. Verschaffel, Greer, and De Corte review their program of research about how students and teachers interpret mathematical word problems. They argue that classroom cultures tend to encourage students to ignore real-world constraints and considerations crucial to problem solving in out of school settings. Further, they claim that for mathematics to be useful in modeling problems of a practical nature it is important that mathematics education give due regard to realistic considerations in modeling. Kaput and Shaffer discuss human reasoning, including modeling, from an evolutionary perspective. They adopt Donald’s theory that human representational competence has gone through stages marked by radically new means of using symbols. And they propose that human cognition is presently moving toward a fifth stage, where computer technology augments people’s ability to represent scientific and mathematical problems.