Mathematical Symbolism

Abstract

One of the essential distinguishing features of mathematics is its eventual dependence upon symbols and symbolic expression. Few attempts to determine those processes, activities, or contents which uniquely identify mathematics have succeeded. It is indeed questionable whether human knowledge can be classified into such self-contained categories. The many diverse activities of mathematicians do, however, have symbolic expression as their common feature, and the extent to which modern disciplines depend upon mathematics could be measured by their growing reliance on symbols. It is reasonable to surmise that much of the difficulty experienced by children in mathematics, and the lack of popularity of physical as opposed to biological sciences in higher education, could be traced to the problem of symbolization. It will be interesting to watch the effect on, say, geography as the school syllabuses move toward mathematical as opposed to descriptive aspects. There is surprisingly little apparent research into the use and learning of symbols, except for the many investigations into both the problem of how children learn to read and adult perceptual experiences with words (e.g., Coltheart 1972). There is, however, a real distinction between the use of symbols as a verbal language (spoken or written) and the use of symbols in the mathematical sense. It will indeed be suggested below that one activity interferes with the other.