From Coefficients to 3D Planes: A VR Mathematics Module for Teaching Systems of Linear Equations with 3D Interaction

Adam Nowak, Anita Dabrowicz-Tlalka, Magdalena M. Musielak, Katrzyna Kujawska, Zuzanna Partyka, Dorota Krawczyk-Stando, Anna Laska-Lesniewicz, Nina Szczygiel, Jacek Stańdo

2025

Abstract

Traditional approaches to teaching systems of linear equations frequently fail to connect abstract algebraic principles with students’ spatial reasoning, resulting in recurring errors in solution determination. To address this, we developed a virtual reality (VR) application for Meta Quest headsets that enables immersive interaction with 3D graphical representations of systems of linear equations. The application allows users to manipulate equations as interactive planes in virtual space, adjust coefficients and visualize intersections in real time. In a study of 38 students, participants were tasked with identifying valid solutions (empty set, point, line, plane) in a paper-based exercise. Results indicated that students frequently misidentified solutions, selecting incorrect options such as two lines, three lines, several points, lines, and two triangles. Furthermore, correct solutions were not consistently identified (empty set: 60%, point: 44%, line: 51%, plane 68%). After a VR session, all students correctly recognized proper solution types (empty set, point, line, plane) in post-test scenarios, demonstrating improved conceptual mastery. Qualitative feedback highlighted heightened engagement and reduced cognitive load during VR tasks. These findings suggest that VR presentation can significantly improve algebraic problem-solving skills compared to static, paper-based methods. This study underscores the potential of immersive technologies to transform mathematics education while emphasizing the need for teacher training to integrate such tools effectively.

Paper Citation

in Harvard Style

Nowak A., Dabrowicz-Tlalka A., Musielak M., Kujawska K., Partyka Z., Krawczyk-Stando D., Laska-Lesniewicz A., Szczygiel N. and Stańdo J. (2025). From Coefficients to 3D Planes: A VR Mathematics Module for Teaching Systems of Linear Equations with 3D Interaction. In Proceedings of the 17th International Conference on Computer Supported Education - Volume 1: ERSeGEL; ISBN 978-989-758-746-7, SciTePress, pages 874-881. DOI: 10.5220/0013500000003932

in Bibtex Style

@conference{ersegel25,
author={Adam Nowak and Anita Dabrowicz-Tlalka and Magdalena Musielak and Katrzyna Kujawska and Zuzanna Partyka and Dorota Krawczyk-Stando and Anna Laska-Lesniewicz and Nina Szczygiel and Jacek Stańdo},
title={From Coefficients to 3D Planes: A VR Mathematics Module for Teaching Systems of Linear Equations with 3D Interaction},
booktitle={Proceedings of the 17th International Conference on Computer Supported Education - Volume 1: ERSeGEL},
year={2025},
pages={874-881},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013500000003932},
isbn={978-989-758-746-7},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 17th International Conference on Computer Supported Education - Volume 1: ERSeGEL
TI - From Coefficients to 3D Planes: A VR Mathematics Module for Teaching Systems of Linear Equations with 3D Interaction
SN - 978-989-758-746-7
AU - Nowak A.
AU - Dabrowicz-Tlalka A.
AU - Musielak M.
AU - Kujawska K.
AU - Partyka Z.
AU - Krawczyk-Stando D.
AU - Laska-Lesniewicz A.
AU - Szczygiel N.
AU - Stańdo J.
PY - 2025
SP - 874
EP - 881
DO - 10.5220/0013500000003932
PB - SciTePress