Math Visualizations in VR

Abstract: Visualization of linear algebra with virtual reality (VR) can be helpful for math teachers. A study has shown more engagement, focus, and active learning through immersion and interactivity, supplementing opportunities for visualizing abstract concepts. This project aims to provide math teachers with an accessible tool for linear algebra concepts in VR. The focus will be on abstraction for the coding by providing a graphical user interface (GUI) as a middle ground, premade virtual objects to reuse, and a manual with linear algebra examples. Furthermore, there are several math visualization tools available for VR. However, there is currently no information about a tool made specifically for math teachers focusing on linear algebra to prepare lessons for VR environments. Unity is the preferred game engine for this project. The object-oriented design used in this project is polymorphism, Model-View-Controller (MVC), and the commandpattern. The system development methodology is extreme programming (XP). The system development methodology is extreme programming (XP). Unit tests are used to drive development; integration tests are used to test between classes; paired t-testis used to test the student’s learning with the tool and, additionally, test the experience of using the tool with a usability test. Furthermore, integration tests, usability tests, and paired t-test are used to analysis the result. Moreover, the linear algebra objects is created as data models. A controller uses linear algebra objects to update the GUI and the handles for visual manipulation. Undoing and saving are handled in the controller. Two simple linear algebra lessons are created by two teachers. The student access the saved lessons in VR and uses handles to interact with the VR world. Moreover,linear algebra expressions of the objects manipulated are shown to the student. Thetest results showed positive results.This framework can assist in empowering the creation of three-dimensional (3D) worlds and VR experiences, making them more accessible to a wider variety of educators by removing the requirement that teachers possess coding abilities. As aconcept, it can be promising for math teachers to have control over the design of their own VR world without caring about the data science behind it.