Fourth-graders’ justifications in early algebra tasks involving a functional relationship

Abstract

In the context of early algebra research and as part of a classroom teaching experiment (CTE), we investigated fourth grade (9- to 10-year-old) students’ justifications of how they performed tasks involving the functional relationship y = 2x. We related their written justifications (part of the task) to the task characteristics, which included various semiotic systems (verbal, numerical and alphanumeric, among others) and the demand of different type of justifications. The role of classroom discussion in helping express the functional relationship orally in more sophisticated terms was also investigated. The findings showed that students’ written justifications changed with the semiotic system involved in the task. Oral discussion helped students generalize in more sophisticated terms than in their written justifications, in which they omitted information or used less precise language.