Visual Representation of Arithmetic Properties

Abstract

Quantitative graphs use a spatial metaphor in which spatial features represent numerical amounts. Tally number systems (used in ancient civilizations) also made use of the spatial feature of length. Arithmetic properties, such as the commutative properly of addition, can also be represented spatially. An experiment trained college students about 11 basic arithmetic properties either using numerical examples or spatial/graphical examples. Both groups were tested using arithmetic problems based on the arithmetic properties both prior to and following the training. The Spatial Training Group improved response time more from the pre- to the post-test than did the Numerical Training Group. The discussion focuses on the cognitive representation of numbers and arithmetic operations by means of spatial representation, evidence from neurophysiology, and the historical development of number systems.