Structures and representations used by 6th graders when working with quadratic functions

Abstract

This study lies within the field of early-age algebraic thinking and focuses on describing the functional thinking exhibited by six sixth-graders (11- to 12-year-olds) enrolled in a curricular enhancement program. To accomplish the goals of this research, the structures the students established and the representations they used to express the generalization of the functional relationship were analyzed. A questionnaire was designed with three geometric tasks involving the use of continuous variables in quadratic functions. The students were asked to calculate the areas of certain figures for which some data were known, and subsequently to formulate the general rule. The results show that the participating students had difficulties expressing structures involving quadratic functions. However, they displayed the potential to use different types of representations to establish the functional relationship. The originality of this study lies in the differences observed in the process of generalization with discrete variables, since, in the case of continuous variables, students could recognize the general expression from analyzing the set of values that can be attributed to the variables in an interval.