We investigate three 8th-grade students' mathematical meanings developed in the context of using linked representations to generate animations of figural models tuned in musical rhythm in "MaLT2," a programmable Turtle Geometry in 3D resource affording dynamic manipulation of variable values. We adopted a modified version of the UDGS…

Incorporating visual representations, rather than strictly relying on symbolic representations, is a research-based strategy for supporting fraction learning. However, students must also make transitions between visual and symbolic fraction representations to apply the conceptual understanding they gained from visual representations to symbolic…

The concept of area measure is widely viewed as fundamental. It is both intrinsically important and also structurally significant, as a representative of the class of continuous multiplicative quantities. Operating flexibly in this context with meaning and conceptual understanding is thus a critical objective for elementary education. Meanwhile,…

Rich research evidence supporting the strong, positive connections between spatial ability and mathematical ability has been well documented. Spatial tools, such as computer-aided-design (CAD) software, have been increasingly utilized and researched for promoting mathematics learning in K--12 (kindergarten to 12th grade). Tinkercad, a free online…

This article presents the theoretical considerations leading to the design and development of a digital experience for teaching linear equations using a modified balance model for equation solving. We modified the balance to alter physics behaviour in a virtual reality (VR) experience, to strengthen students' schemes for solving linear equations…

Augmented reality (AR) and virtual reality (VR) have been noted to enhance student learning by supporting spatial reasoning and visualization, long-term memory, engagement, and increased motivation. The researchers situated the exploration of these tools for learning within the culturally responsive pedagogy (CRP) in mathematics education. The…

In this study, we report on the design and use of an apparently unbounded spatial diagram to explore shearing, an area-preserving transformation. Apparently unbounded spatial diagrams are realizations of geometric objects, such as lines, that appear to extend indefinitely. They can be rendered in virtual reality displays where users who are…

This article investigates how a computer simulator for human interactions and a dyadic system in a pencil-and-paper environment can contribute to helping students with poor motor co-ordination, notably those with dyspraxia, to learn geometry. The aim is to design an alternative way to teach the subject, and to explore its effects on the learning…