Author(s):
(Need) Many STEM students struggle to develop a deep understanding of the theoretical aspects of linear algebra and prefer to employ a practical approach when they conceptualize and process tasks. In this practical approach, language emerges from physical actions and tends to be goal-oriented, informal, colloquial, and not precise (versus formal, logic-supported, and structured), objects are natural (versus discursive) and terms are known through their reference to objects (versus property-driven), examples serve as models of concepts and definitions (versus models for concepts and definitions), and reasoning and visualization tend to be holistic and nondiscriminatory (versus analytic) and are primarily employed to deal with situations (versus concepts). Our project will improve students’ mathematical experiences in undergraduate linear algebra courses by developing, testing, and implementing a suite of virtual-reality (VR) mediated linear algebra tools and activities that can support students to successfully transition from practical to theoretical thinking about concepts and relationships. (Guiding Questions)We will employ design-based research implementation research (DBIR), which relies on well-articulated hypothetical learning trajectories and different conceptualizations of key topics in linear algebra, to (i) develop, test, and refine the VR-mediated linear algebra tools in the first two years of the project and (ii) implement classroom teaching experiments during the proof-of-concept study phase in the third year. Our VR-mediated introductory Linear Algebra course will provide all STEM students with every opportunity to deepen their visual and theoretical understanding of related concepts and relationships in a virtual environment. Our VR tools are computer-generated and fully immersive representations that enable all students to experience constructing and manipulating linear algebra objects beginning in R3. Our guiding questions are: To what extent does a visual-geometric and action-oriented VR-mediated intervention support and enhance a deep theoretical understanding of linear algebra concepts? What is the nature of student reasoning elicited in a VR-mediated environment for learning linear algebra? (Outcomes)Our exploratory Level 1 study will establish a relationship between the use of VR-mediated linear algebra tools (as a malleable factor) and depth of linear algebra knowledge (as a learning outcome) from an enactivist, embedded, embodied, and extended perspective (as a theoretical framework). Our deliverables include VR-mediated tools and resources, which provides a potentially transformative approach for increasing student engagement and improving instruction and learning in an introductory linear algebra course, and a model of student learning in VR-mediated learning environments, which can deepen conversations about how to support growth in theoretical thinking in linear algebra. (Broader Impacts)Our project is situated within the broader concern of how universities and mathematics departments can effectively prepare STEM students for the “society of the future” that employs 21st century representational tools and mathematical skills and high-level conceptual understanding. Our project will support student growth by building VR tools that assist in democratizing access to fundamental theoretical knowledge in linear algebra. Project results will be disseminated through publications, presentations, professional development workshops, articulation sessions with colleagues, maintenance of a public project website, and public demonstrations in science and technology museums. The VR tools will also be made freely available online.
Coauthors
Plamen Koev, San Jose State University, and Yingjie Liu, San Jose State University
