Tracing a student’s covariational reasoning in constructing the diameter-circumference relationship

This study examines how a seventh-grade student coordinated circumference and diameter while constructing the relationship between these quantities. Conducted in two phases, a clinical interview and a task-based interview, the study drew on the student’s verbal responses, actions, and gestures. Clinical interview data were analysed descriptively, and task-based interview data through retrospective analysis. Findings showed that, although the student could carry out procedures involving circumference, he could not explain the reasoning underlying the formula π × d. During the task, he initially considered circumference and diameter separately, but later coordinated their corresponding changes. We recommend tasks that engage students in coordinating diameter and circumference as related quantities when making sense of this relationship.