Mental Images and Arithmetical Symbols

Abstract

Experiments by psychologists have led to the conclusion that images play an indispensable, if subordinate, role in thought as symbols. An analysis is begun of the mental images that are judged to be properly evoked by certain number symbols in arithmetic. A variety of graphical models are suggested for use in linking these symbols to the desired mental construct. Some of these models have been found to be advantageous and may prove to be critically essential in certain mathematical contexts. Their assets and liabilities are discussed, and suggestions are made for modifications of conventional curriculum practice. A rich field of investigation exists in the visual imagery that can be associated with elementary mathematics. Progress here holds promise of extending mathematical competence to a larger portion of society.