Augmented Reality (AR) technologies allow for holograms to be layered over the real-world, "augmenting" human vision by overlaying illustrations onto 3D space. Here we explore the question: What affordances does AR in a collaborative environment have for the future of mathematics education in uncertain times? We conducted a study where…

In this chapter, we explore the use of Augmented Reality (AR) and Virtual Reality (VR) in geometry courses for teachers. There is increasing use of AR and VR technologies, such as AR and VR goggles, in K-12 schools, providing new opportunities for learners to interact with geometry in three-dimensional (3D) environments. These opportunities lead…

Recent developments in Augmented Reality (AR) headset technologies have allowed for users to see and manipulate the same 3D hologram at the same time, allowing for collaborative, embodied interactions using gestures and actions. Three-dimensional geometry has traditionally been taught largely through 2D projections of 3D figures on pages or…

The emergence of immersive digital technologies, such as shared Augmented Reality (shAR), Virtual Reality (VR) and Motion Capture (MC) offers promising new opportunities to advance our understanding of human cognition and design innovative technology-enhanced learning experiences. Theoretical frameworks for embodied and extended cognition can…

Augmented Reality (AR) technologies allow for holograms to be layered over the real-world, "augmenting" human vision by adding technical information or illustrations onto 3D space. Although AR-based applications are showing positive effects in many systematic reviews and meta-analyses, well-designed, rigorous studies with strong control…

Augmented reality (AR), where digital holograms are layered over the real world, is rapidly being applied to different educational domains, including mathematics education. However, little is known about how AR can be effectively designed for collaborative use. There are both practical and theory-based reasons to set up collaboration in AR in…

Contextual multi-armed bandits have previously been used to personalize student support messages given to learners by supplying a model with relevant context about the user, problem, and available student supports. In this work, we propose using careful feature selection with relevant domain knowledge to improve the quality of student support…

Dynamic geometry software (DGS) has long been studied in mathematics education as a way for students to explore and interact with geometric objects and figures. Recent advances in Augmented Reality (AR) technologies that allow dynamic three-dimensional mathematical objects to appear in students' environment as holograms have changed the nature of…

Virtual experiments offer opportunities for students to engage in the scientific process and observe scientific phenomena. However, virtual experiments are not always effective for learning. The current study examined how two small manipulations might support better learning from virtual experiments and the extent to which this varied across…

Composite scores are an exceptionally important psychometric tool for behavioral science research applications. A prototypical example occurs with self-report data, where researchers routinely use questionnaires with multiple items that tap into different features of a target construct. Item-level missing data are endemic to composite score…

This study investigates how learners collaboratively construct embodied geometry knowledge in shared VR environments. Three groups of in-service teachers collaboratively explored six geometric conjectures with various virtual objects (geometric shapes) under the guidance of a facilitator. Although all the teachers were in different physical…

This article explores the use of Extended Reality (XR) technologies, such as Augmented Reality (AR) and motion capture, in mathematics instruction, specifically focusing on geometry learning. Our research highlights the challenges students face in learning geometry due to its abstract nature and the potential of XR technologies to create…

Missing data are exceedingly common across a variety of disciplines, such as educational, social, and behavioral science areas. Missing not at random (MNAR) mechanism where missingness is related to unobserved data is widespread in real data and has detrimental consequence. However, the existing MNAR-based methods have potential problems such as…

This study investigates the use of GeoGebra, a Dynamic Geometry Software (DGS) for math learning in Virtual Reality (VR) using head-mounted displays. We conducted a study with n = 20 middle school students receiving a mathematics tutoring intervention over time in a VR environment. Using theories of embodied cognition and playful mathematics, this…

Augmented Reality (AR) and Virtual Reality (VR) platforms now support shared, immersive experiences that enable people to directly physically and perceptually engage with mathematical objects, including shared objects. These new forms of AR/VR technology -- which we call "shared holographic AR/VR" (shAR) -- enable multiple learners to…