Structure recognition and generalization by second-graders in direct and inverse forms of a linear function

Abstract

Within the context of the functional approach inherent in early algebra education, this paper reports the structures recognized and the generalizations shown by second-grade students (aged 7–8 years). Semi-structured interviews were conducted with 4 students selected from a cohort participating in a previous classroom teaching experiment. These students were tasked with solving word problems that required understanding of both the direct and inverse forms of linear functions. This paper details the structures recognized by the students both when working with specific cases and when attempting generalization. All students successfully identified the structures involved in both the direct and inverse forms of the function. Differences in the generalized structures were observed depending on the function and its form. A greater number of students was able to generalize structures for the inverse form than for the direct form of the functions examined. This study is presented as part of a broader research project at XXXX.