Developing Virtual Reality-Mediated Representational Tools for Supporting and Enhancing Deep Mathematical Understanding of Linear Algebra Relationships

This project at San Jose State University, a Native American Pacific Islander Serving Institution (AANAPISI) and Hispanic Serving Institution (HSI), aims to serve the national interest by improving student's mathematical experiences in undergraduate linear algebra courses. Linear algebra subject matter provides important content and concepts that are pertinent to undergraduate majors across several STEM disciplines, including, but not restricted to, mathematics, computer science, physics, and most engineering disciplines.

The project will develop, implement, investigate, refine, and disseminate a suite of virtual reality (VR) tools and resources that will be designed to support student growth with 21st century mathematical skills and competencies. These tools and resources will be practical, and also will be focused on promoting deep thinking and understanding. The VR tools will be computer-generated and will provide fully immersive representations that enable students to gain equitable access to experience constructing, manipulating, simulating, and understanding objects and concepts, primarily in two-dimensional and three-dimensional frameworks.

It is through these efforts that results will then be extended to include higher-dimensional settings. The first two years of the project involve developing, testing, and refining the VR tools and supplemental instructional resources. The third year of the project will involve implementing a proof-of-concept study of the impact of the VR tools and resources.

An underlying outcome will be to enhance students' 21st century mathematical skills, critical and analytical thinking, and high-level conceptual understanding to meet the demands of the society of the future.

This project will pursue several goals related to improving student experiences and successes in mathematics, in general, and linear algebra, in particular. Goal 1 is to develop tools and resources to implement an innovative VR-mediated learning environment to capture the interest and enhance the engagement of students. A second goal is to study this setting to increase the knowledge base on how to better support students in developing skills and a deep comprehension of linear algebra concepts, calculations, applications, and theoretical underpinnings.

Too often, students only realize a peripheral understanding related to these features. A third and related goal is to advance the current state of knowledge on how to capitalize on the central role of imagery and visual representations in communicating about and reasoning in mathematics, particularly linear algebra. Goal 4 is to provide research-based findings on the potentially transformative power of VR for deep learning of mathematical concepts and processes.

A fifth goal is to disseminate outcomes and research findings while making project tools and resources available to the STEM education community. An initial impetus will be to examine topics such as vectors, matrices, linear transformations, and linear algebra simulations in two- and three-dimensional Cartesian Coordinate systems. The setting will then be extended to more general n-dimensional systems by establishing a relationship between the use of VR tools and, for example, projections, lower dimensional approximations, dimensional reduction, and data compression.

The project will be guided by the following two research questions (RQs): (RQ1) To what extent does a visual-geometric and action-oriented VR-mediated intervention support and enhance a deep learning of linear algebra concepts and the ability to manipulate within this context? (RQ2) What is the nature of student reasoning elicited in a VR-mediated environment for learning linear algebra? This project will utilize a design-based mixed-methods research implementation in establishing and refining the VR tools and in implementing and investigating classroom teaching experiments.

Project assessment items will be used to compare the post-test performance across control and treatment groups. In addition, students' responses in video recorded clinical interviews, assessments, and surveys will be coded and analyzed. Project results will be proactively disseminated through publications in high-impact peer reviewed education journals, presentations at conferences and annual meetings, webinars, colloquia, professional development workshops, articulation sessions with colleagues, maintenance of a public project website, and public demonstrations in science and technology museums.

In concert with this dissemination plan, tools, materials, and resources that emanate from the project will be made freely available online. The NSF IUSE:EDU Program supports research and development projects to improve the effectiveness of STEM education for all students. Through the Engaged Student Learning track, the program supports the creation, exploration, and implementation of promising practices and tools.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.