A Context for Integer Computation

Abstract

The National Research Council (2001) notes that a variety of metaphors have been used to introduce negative numbers in school, “including elevators, thermometers, debts and assets, losses and gains, hot air balloons, postman stories, pebbles in a bag, and directed arrows on a number line” (p. 245). In addition, standard textbooks have typically employed either a chip model, where positive integers are represented by black chips and negative integers by red chips; a charged-field model, showing +/−; or a number-line model. Some contexts or models are not really metaphors because, for example, negative numbers do occur in temperatures, in accounting, and in some sports scoring (e.g., scores under par in golf). However, these contexts become metaphorical when they are used to model arithmetical operations with integers. Each model or context must construct a scenario that makes it plausible to explain, for instance, why subtracting an integer is the same as adding its opposite or why a negative times a negative is a positive.