Think back to when you learned geometry. If you grew up in the United States, you probably explored some of the basics of elementary school. Then, in high school, you probably had an entire class devoted to geometry. Either way, you may remember studying two-dimensional diagrams intended to represent shapes, lines, planes, angles, curves, and other concepts displayed in textbooks or on an overhead projector screen. .

Justin Dimmel, an assistant professor of math education and instructional technology at the University of Maine, has long been interested in these diagrams and how they both facilitate and constrain the learning and teaching of math. geometry.

“My interest in diagrams started before college, when I was teaching geometry in high school,” says Dimmel. “I encouraged my students to draw, explore, and transform diagrams as mathematical thought experiments, and I was fascinated by the different diagrams they created to reason about a mathematical situation.”

When two-dimensional diagrams are used to represent three-dimensional figures, students and teachers must decode how the drawings would actually appear in the physical world. In other words, because the diagrams are flat, you can’t pan around them to see what they look like from different angles or where the edges and lines actually meet.

With the increasing availability and popularity of consumer virtual and augmented reality devices, Dimmel’s research is focusing on how such technology can be used to represent geometric diagrams in three dimensions rather than two. He recently received a National Science Foundation CAREER award of nearly $672,000 to support this work. This is the organization’s most prestigious award for early career faculty.

As Dimmel explains, there is nothing wrong with exploring two-dimensional geometric diagrams. It is a practice that has worked for thousands of years. But this has vast implications beyond the realm of geometry.

“People think about space all the time, about objects in space, and the relationships of those objects,” he says. “It’s fundamental for tasks ranging from repairing engines to moving furniture to multivariate calculus, linear algebra, and other advanced areas of math.”

A few years after joining UMaine in 2015, Dimmel started the Laboratory of Immersive Mathematics in Rendered Environments (IMRE), located in the Shibles room. With a team of graduate and undergraduate research assistants, the lab has developed VR educational tools that allow teachers and students to explore 3D geometric figures – spatial diagrams or inscriptions – in virtual environments. Dimmel led initial research in the affordances of these environments for teaching and learning geometry.

“We are at a time of transformation in terms of our ability to use these technologies for educational purposes,” he says. “Spatial inscriptions are largely free of material or physical constraints. You can study them at any size, in any orientation, in any position in space, and potentially realize a much more diverse set of mathematical concepts than is possible with physical models.

Dimmel’s five-year research plan includes two parallel and complementary strands focused on teaching and learning. The pedagogical component will seek to characterize the existing representations of three-dimensional figures and to analyze their place in the pedagogical practices of high school geometry teachers. For this part of the project, he will examine how three-dimensional figures are commonly represented in geometry textbooks, as well as the words, symbols, diagrams, models, and other means that high school geometry teachers use to communicate and represent these figures. .

The learning stream will explore the unique affordances of 3D diagrams in virtual and augmented reality. For this stream, Dimmel will use task-based interviews to collect data on students’ experiences with learning geometry in immersive spaces. The overall goal is to generate the first approximation of a theory that explains how motion-based interactions with spatial inscriptions can contribute to high school geometry learning and teaching. It aims to create a common language that can be used to discuss traditional and emerging representations of geometric diagrams.

“Before we can compare the effects of different representations, we need to understand what they are, how they work, the kinds of task situations they enable, and how they constrain students and teachers to engage in those tasks. “, explains Dimmel.

In addition to research, Dimmel says he has two broader impact priorities for the project. The first is improving STEM education and the development of educators at all levels. To that end, it will seek to create a multi-year professional development program for a dozen high school math teachers to help them use virtual and augmented reality in their schools.

Second, he hopes the award will lead to increased literacy and engagement in science and technology by the general public. He plans to launch an outreach program in rural Maine to create opportunities for the public to experience representations of mathematical ideas in immersive environments.

“I see this as an opportunity to have a meaningful impact in Maine, especially in rural areas, which have traditionally been underrepresented in terms of STEM access,” he says. “We could be a place that people across the country and even around the world look to as a model of what learning could look like in the 21st century.”

It is unique for an education faculty member to receive an NSF CAREER award, and Dimmel is believed to be a first for a faculty member at UMaine’s College of Education and Human Development. He is grateful to many colleagues and administrators at the college and university levels, as well as to Maine Research Center for STEM Education (RiSE Center), where he is an affiliate faculty member.

He collaborated with a doctoral student Camden Bock for several years, contributing to research and other projects of the IMRE laboratory. Staff members from the Office of Research Development and the Office of Research Administration also assisted in developing his research proposal.

“The process worked the way it was supposed to work,” says Dimmel. “I arrived as a new faculty member and received the support needed to develop a research program. This award is a reflection of the support I have received from many people along the way.

Contact: Casey Kelly, [email protected]