Mitchell J. Nathan

This paper identifies the affordances and constraints teachers experienced using an augmented reality (AR)-based geometry learning simulation—GeoGebra-MR. The study operationalizes these constructs within the context of AR-based learning and introduces a subcategorization framework. AR-based dynamic geometry software (DGS) facilitates geometric reasoning by visualizing 3D geometric objects and providing real-time interactive feedback in a collaborative networked space. Researchers developed a coding scheme and decision tree to systematically classify usability issues and underlying needs to improve the design of the platform to make it more intuitive. Video recordings of K-12 geometry teachers’ geometric reasoning using the AR environment along with post-interviews highlighted several issues related to sensory, physical, cognitive, and functional affordances, and the corresponding needs linked to physical, logical, and cultural constraints. This study provides design recommendations for optimizing AR-based geometry learning environments, emphasizing that usability challenges are not solely technological but also shaped by teachers' perceived affordances and their attunement to constraints. By highlighting these factors, this paper offers valuable insights for researchers and educators seeking to enhance the design and implementation of AR in mathematics education.

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 conditions are lacking. Further, many experimental studies lack process data to illuminate what is happening as students engage with AR. In this pre-registered study, we conducted an experiment where n = 120 high school students were assigned to reason about identical geometry simulations collaboratively either using tablets or AR head‐mounted displays (HMDs). We look at their learning and how it was impacted by the dimensionality (2D or 3D) of the shapes they explored, as well as how they engaged with virtual objects using gestures and epistemic actions. AR HMDs were more effective for students getting an initial sense of 3D shapes, but less effective for 2D shapes. For gaining insights into the workings of shapes and formulating justifications of conjectures, we see no evidence AR is more effective, and trends indicating AR may be detrimental to eliciting generalizations. Further, process data showed that students using tablets are more likely to manipulate the geometric shapes in the simulations, while students using the AR HMDs are more likely to use dynamic gestures that simulate these manipulations, which are less constrained by the objects’ actual properties. Implications for the future design and use of AR in education are given.

Spatial skills can predict mathematics performance, with many researchers investigating how and why these skills are related. However, a literature review on spatial ability revealed a multiplicity of spatial taxonomies and analytical frameworks that lack convergence, presenting a confusing terrain for researchers to navigate. We expose two central challenges: (1) many of the ways spatial ability is defined and subdivided are often not based in well-evidenced theoretical and analytical frameworks, and (2) the sheer variety of spatial assessments. These challenges impede progress in designing spatial skills interventions for improving mathematics thinking based on causal principles, selecting appropriate metrics for documenting change, and analyzing and interpreting student outcome data. We offer solutions by providing a practical guide for navigating and selecting among the various major spatial taxonomies and instruments used in mathematics education research. We also identify current limitations of spatial ability research and suggest future research directions.

Among Walter Kintsch’s astounding insights about human cognition was realizing that reading comprehension and learning from text emerge from an interactive process between the reader and the text. ...