Facilitating mathematical competencies development for undergraduate students

In this article we show how to facilitate the development of mathematical skills using 3D surface visualization tools and virtual environments in an online, project-based learning context. The “Lumen” software is presented, which is an ad-hoc solution, designed and developed to visualize and combine mathematical surfaces in 3D, based on their associated equations. Several activities were designed with the use of Lumen, to measure the learning gain and problem-solving skills of the students, obtaining that a mean learning gain of 43% was observed on 242 students on the analysis of the pre- and post-tests for the first monitored activity, while a mean learning gain of 30% was observed on 210 students on the analysis of the second monitored activity. Based on these analyses, we make the point that although remote learning in the context of the COVID-19 pandemic poses difficult challenges for learners and professors, the use of ad-hoc technological applications is an important resource that supports the reinterpretation of the learning process, as it shifts the focus to the development of skills through active learning.