Lab

Immersive Mathematics in Rendered Environments (IMRE) Lab

Institution: University of Maine

About the lab

The Maine Immersive Mathematics in Rendered Environments (IMRE) Laboratory, directed and operated by Dr. Justin Dimmel, is a part of the College of Education and Human Development at the University of Maine.

The IMRE Lab designs math and science learning environments. Our mission is to investigate how virtual and augmented reality technologies can transform STEM education. Our vision is a world where all students have access to educational experiences that will deepen their interest in mathematical and scientific thinking.

Featured projects (2)

Project
A virtual reality room scale model of the earth to highlight geometric properties of our experiences of skylight.
Project
A rendering layer and SteamVR-based interface for a 3D geometry kernel focused on plane and sphere constructions

Featured research (3)

In this article, we examine spatial inscriptions marked in real or rendered spaces, rather than on two-dimensional surfaces, conceptualize spatial inscriptions from an inclusive materialist perspective and consider realizations of spatial inscriptions that are possible with emerging technologies (e.g. 3D pens, immersive virtual reality). We then describe two cases of immersive environments that allowed learners to make and interact with spatial inscriptions. Next, we analyze how movements of participant–environment–inscription assemblages realized diagrams. Our analysis highlights how varying scale and changing perspective can become resources for doing mathematical work with spatial inscriptions.
Mithala and Balacheff (2019) describe three difficulties with two-dimensional representations of three-dimensional geometrical objects: “it is no longer possible to confuse the representation with the object itself,” visually observed relationships can be misleading, and analysis of the representation requires the use of lower-dimensional theoretical properties. Despite these difficulties, students are routinely expected to learn about three-dimensional figures through interacting with two-dimensional inscriptions. Three-dimensional alternatives include diagrams realized through various spatial inscriptions (e.g., Dimmel & Bock, 2019; Gecu-Parmaksiz & Delialioglu, 2019; Lai, McMahan, Kitagawa & Connolly, 2016; Ng and Sinclair, 2018). Such diagrams are three-dimensional in the sense that they occupy real (e.g., 3D pen drawings) or rendered (e.g., Virtual Reality/Augmented Reality environments) spaces as opposed to being inscribed or displayed on surfaces. Digital spatial diagrams can be grasped and transformed by gestures (e.g., stretching, pinching, spinning), even though they can’t be physically touched (Dimmel & Bock, 2019). Spatial diagrams make it possible to use natural movements of one’s head or body to explore figures from new perspectives (e.g., one can stepinside a diagram), as they natively share the three-dimensional space. In this study I ask: How do learners use perspective to make arguments while exploring spatial diagrams? In particular, how do participants use perspectives outside and within geometric figures to make arguments while exploring spatial diagrams? To investigate this question, I designed a large-scale spatial diagram of a pyramid whose apex and base were confined to parallel planes. The diagram was rendered in an apparently unbounded spatial canvas that was accessible via a head-mounted display. The pyramid was roughly 1 meter in height and the parallel planes appeared to extend indefinitely when viewed from within the immersive environment. I created this diagram as a mathematical context for exploring shearing, a “continuous and temporal” measure-preserving transformation of plane and solid figures (Ng & Sinclair, 2015, p.85). I report on pairs of pre-service elementary teachers’ arguments about shearing of pyramids, using Pedemonte and Balacheff’s (2016) ck¢-enriched Toulmin model of argument. Shearing is a mathematical context that is likely novel to pre-service elementary teachers and provides an opportunity to connect transformations of plane and solid figures. Participants used perspectives outside and within the diagram to make arguments about the shearing of pyramids that would not be practicable with rigid three-dimensional models or dynamic two-dimensional representations. The results of this study suggest that the dimensionality of the spatial diagrams supported participants’ arguments about three-dimensional figures without mediation through projection or lower-dimensional components. The findings of this study offer a case that challenges the constraints of two-dimensional representations of three-dimensional figures, while maintaining theoretical constraints in a spatiographically accurate representation.
We report on the design and development of HandWaver, a mathematical making environment for use with immersive, room-scale virtual reality. A beta version of HandWaver was developed at the IMRE Lab at the University of Maine and released in the spring of 2017. Our goal in developing HandWaver was to harness the modes of representation and interaction available in virtual environments and use them to create experiences where learners use their hands to make and modify mathematical objects. In what follows, we describe the sandbox construction environment, an experience within HandWaver where learners construct geometric figures using a series of gesture-based operators, such as stretching figures to bring them up into higher dimensions, or revolving figures around axes. We describe plans for research and future development.

Lab head

Justin Dimmel

Members (2)

Camden Bock
  • University of Maine
Cody Emerson
  • University of Maine