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…

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…

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…

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…

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 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…

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…

Many novice teachers learn to teach "on the job," leading to burnout and attrition among teachers and negative outcomes for students in the long term. Preservice teacher education is tasked with optimizing teacher readiness, but there is a lack of causal evidence regarding effective ways to prepare new teachers. In this paper, we use a…

Findings synthesized across five empirical, laboratory-and classroom-based studies of high school and college students engaged in geometric reasoning and proof production during single and multi-session investigations (346 participants overall) are presented. The findings converge on several design principles for embodied mathematical thinking and…

Extended Reality (XR) experiences for mathematics teachers can allow them to understand both pedagogy and the mathematics itself in new ways. In this study, we explore a virtual reality (VR) simulation for learning about geometric shapes where teachers could engage in joint, shared manipulation of holograms in three dimensions. We examine what…

This study describes the role that Rasch measurement played in the development of assessments aligned to the "Next Generation Science Standards," tasks that require students to use the three dimensions of science practices, disciplinary core ideas and cross-cutting concepts to make sense of energy-related phenomena. A set of 27…

Developing models and using mathematics are two key practices in internationally recognized science education standards such as the Next Generation Science Standards (NGSS, 2013). In this paper, we used a virtual performance-based formative assessment to capture students' competencies at both "developing" and "evaluating"…