Rates of Change and an Iterative Conception of Quadratics

Abstract

Investigating students' conceptions of covariation patterns between quantities situated within contextual settings engenders enriched, deep understandings of functional relationships. This paper presents data from a case study of a student (Mary) who solved quadratic contextual problems. Mary's schemes, constructed from quadratically related quantities and patterns of additive rates, fostered the development of an iterative, summative conceptualisation of quadratics in contrast to the product view. Findings support the use of contextual problems to motivate students to think reflectively and mathematically.