Khushaal Kurswani, Edward Liao, Daniel Lorentz, and Ethan Mo
August 2022

[Capstone presentation: Slides]

Paper: K. Kurswani(*), E. Liao(*), D. Lorentz(*), E. Mo(*), R. Angotti, K. Sung, “Putting the ‘Fun’ in Functions: Engaging Students in Mathematical Functions Through VR,” in International Conference on Technology in Collegiate Mathematics (ICTCM 2023), Denver, Colorado, March 16.  Available:  Full Paper | Presentation Slides | Khushaal At the conference.

The concept of mathematical function is critical for student success at calculus, which is the gatekeeper for STEM fields. Unfortunately, many students have significant anxiety and can become disengaged with math, especially abstract concepts such as functions. These observations suggest that gamification, through exploration and experimentation with increased curiosity and decreased anxiety, may be an effective approach. Associating academic learning with videogames, especially in STEM related subjects, is nothing new. However, an interesting approach would be to design gameplay interactions based on strategized embodied cognition with the understanding that concept retention can be improved by utilizing or simulating bodily movements. The movements can act as a cognitive referent and help retrieve concepts from memory. Abstract function concepts such as graphs could be presented as tangible objects in an immersive environment with strategically designed play or interaction sequences. This may allow students to develop a concrete and tangible understanding of function concepts.

Over the summer of 2022, our team prototyped a system to support the building of a learning community to engage in friendly and fun interactions with mathematical functions. Instead of the more challenging objective of the potential for embodied learning, at this early stage, the goal is to verify the capabilities of integrating and interacting with bodily movements. Although the primary objective is immersive VR intersection, for affordability and accessibility all devices including mobile are supported. The delivered system supports multiple participant avatars collaborating and exploring functions in a rollercoaster experimenting the effects of steep slope under gravitational acceleration, walking or sliding down a function for fun, and changing the avatar size so as to examine the function from different perspectives.

Our user interface supports custom input template and analysis menus. A user can examine all relevant characteristics including at the selected marker positions on the function analysis menu. The displayed ribbons are color paired with the corresponding functions in the analysis menu. VR users can interact with a custom designed keyboard that facilitates the specification of typical functions, and customize an avatar via a menu.

Our prototype process went through two rounds of user testing for usability and assessment of engagement. Though only with eight testers, the feedback was uniformly positive. We have verified that the ability to interact with representations does indeed increase engagement and interest in experimentation. It is also the case that, as in all prototypes, many of the application states can be more clearly presented, e.g., avatar location and state. With the infrastructure developed and verified, it becomes possible to proceed with the next step of examining and associating appropriate gameplay interactions with specific concepts of mathematical functions.