Generalization in fifth graders within a functional approach

Abstract

This article discusses evidence of 24 fifth graders’ (10-11 year olds’) ability to generalize when solving a problem which involves a linear function. Analyzed in the context of the functional approach of early algebra, the findings show that three students generalized both when solving specific instances and when asked to provide the general formula; while 16 students generalized only when asked to define the general formula. The results are described in terms of the functional relationship identified, the types of representation used to express them, and the type of questions in which students generalized their answers. Most of the pupils who generalized did so based on the correspondence between pairs of values in the function at issue.