Symbols, Icons, and Mathematical Understanding

Abstract

Extracts are taken from the biographies of Hobbes, Rousseau, Darwin, and Russell which refer to their mathematical education. The common feature of an attraction toward geometry and an aversion to elementary algebra is noted. These experiences are analyzed using theoretical positions promulgated by Davis, Hersh, Skemp, and Bruner. The central thesis is that these men probably have had difficulty learning elementary algebra because they had failed to develop a strong image or iconic representation of the concepts involved. This thesis is developed in relation to "squaring a binomial," the concept which troubled both Rousseau and Russell.