A Learning Trajectory to the Understanding of the Curve Length Concept

In this article, we present results of a research study focusing on the analysis of a hypothetical learning trajectory carried out with students taking a mathematics teaching degree. The aim of this study was to examine students’ understanding of the concept of curve length. The qualitative research was carried out with nine students participating in a course on Differential and Integral Calculus discipline of a private university in which that content was approached. The data were obtained through records of the students’ worked out solutions, notes from observation recorded in the teacher’s field diary and audio recordings made during the course development. From the analysis of the results, it can be inferred that the students showed gaps in their previous knowledge and difficulties on how to use that knowledge in the construction of new concepts; however, evidence was observed that the planned hypothetical learning trajectory facilitated, in part, the understanding of the concept of curve length.