LAYERS OF GENERALITY AND TYPES OF GENERALIZATION IN PATTERN ACTIVITIES

Abstract

Pattern generalization is considered one of the prominent routes for introducing students to algebra. However, not all generalizations are algebraic. In the use of pattern generalization as a route to algebra, we —teachers and educators— thus have to remain vigilant in order not to confound algebraic generalizations with other forms of dealing with the general. But how to distinguish between algebraic and non-algebraic generalizations? On epistemological and semiotic grounds, in this article I suggest a characterization of algebraic generalizations. This characterization helps to bring about a typology of algebraic and arithmetic generalizations. The typology is illustrated with classroom examples.