A learning trajectory for university students regarding the concept of vector

Abstract

This paper presents and evaluates a hypothetical learning trajectory by which students bridge the transition from elementary to university-level instruction regarding the concept of vector. The trajectory consists of an instructional sequence of five tasks and begins with a problem in context. Each task is carried out with the support of a Virtual Interactive Didactic Scenario, accompanied by exploration and guided learning sheets, in which the problem is introduced through the simulation of the movement of a robotic arm. This proposal was implemented at the beginning of the SARS-CoV-2 pandemic using various digital media. Two teaching experiments were carried out with engineering students at a Mexican public university. We present the hypothetical learning trajectory that should be followed toward solving the task, and contrast it in each case with the students’ actual learning trajectory. The results show that more than 70 % of the students successfully transitioned from the geometrical vector representation of elementary physics to the algebraic one.