Facilitating Mathematical Competencies Development for Undergraduate Students During the Pandemic Through ad-hoc Technological Learning Environments

Abstract

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.

Enhancing mathematical education with spatial visualization tools

“…Additionally, qualitative feedback from students suggests a heightened sense of engagement and enthusiasm when participating in activities involving 3D tools, indicating their potential to enhance the overall learning experience (Medina Herrera et al, 2019). Overall, the literature supports the notion that the integration of 3D tools and methodologies holds promise for improving spatial visualization skills, problem-solving abilities, and overall mathematical proficiency among students (Hake, 1998;Hegarty and Kozhevnikov, 1999;Delahunty et al, 2016;Ruiz Loza et al, 2022).…”

“…Researchers have proposed various activities and approaches to develop spatial skills in mathematics. Some of these proposals include the use of blocks in different forms, such as flat images or augmented reality images, to aid students in visualizing and manipulating objects in space (Sorby, 2009;Ruiz Loza et al, 2022). Augmented reality has been employed as a tool to virtually model objects, enabling students to visualize vertices, edges, and object projections, thereby enhancing their ability to form mental images and comprehend spatial relationships (Medina Herrera et al, 2019;Buentello Montoya et al, 2021).…”

“…Individualized instruction: VR and AR could adapt to individual students' needs, offering individualized learning experiences. These technologies can provide interactive tutorials, adaptive exercises, and customized feedback based on students' progress and performance, catering to their unique learning requirements (Ruiz Loza et al, 2022). When incorporating VR and AR into mathematics education, it is crucial to provide proper guidance, establish clear learning objectives, and ensure that the technology serves to enhance mathematical comprehension.…”

“…Spatial skills have a vital significance in the acquisition of mathematical knowledge, particularly in the realms of geometry and calculus (Arcavi, 2003;Battista, 2007;Medina Herrera et al, 2019). Proficiency in spatial visualization, encompassing the manipulation of figures in three-dimensional space, recognition of patterns, projections, and the ability to describe concepts using both natural and mathematical language, are essential attributes sought in promoting mathematical learning (Gilligan et al, 2022;Ruiz Loza et al, 2022). Research shows that throughout development, there is a consistent, predictive, and strengthening relationship between spatial reasoning and mathematical achievement (Resnick et al, 2020).…”

“…We present various technological tools designed for this purpose, including three developed by our team: AVRAM (Spanish acronym for Remote Virtual Environments for Mathematics Learning), which utilizes virtual environments, and ARC (Augmented Reality Calculus), which harnesses augmented reality (Medina Herrera et al, 2019). Additionally, we introduce LUMEN (Learning in Unified Mathematics Environments) (Ruiz Loza et al, 2022), a recent platform that seamlessly integrates both virtual and augmented reality capabilities. Furthermore, we incorporate other valuable tools in our research, such as GeoGebra 3D (GeoGebra 3D, 2018) and CalcPlot3D (Seeburger, 2011).…”