The small angle approximation sin[theta approximately theta] is central to all treatments of the simple pendulum as a harmonic oscillator and is typically asserted as a result that follows from calculus. Here, however, we show that the geometry of the pendulum "itself" offers a route to understanding the origin of the small angle…

There has been little written about the ways in which teachers understand draggable geometric objects in a dynamic geometry environment with respect to variance and invariance--two important mathematical ideas related to the development of spatial perception and geometric reasoning. In this article, we investigated such understanding from two…

Spatial updating based on self-motion cues is important to navigation in the absence of familiar landmarks. Previous studies showed that spatial updating without vision was automatic. The goal of the current study was to investigate whether ambiguous orientations indicated by visual cues affect spatial updating based on self-motion. Participants…

Research on geometric transformations suggests that early learners possess intuitive understandings grounded in motion metaphors, transitioning to mappings. The processes through which students transition between these two conceptions are not fully understood. We propose that Vygotskian hybridizing (related to Vygotsky's articulation of everyday…

How might a 4-year-old pupil come to conceive a line, created by himself with a continuous gesture, as constituted by a series of points? In this paper, we theoretically introduce and discuss a design study of the educational path in which this possibility emerged. The path aimed at leading pupils to "experience," in the sense of the…

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…

A solid ball placed on a rotating turntable is known to roll slowly around a circular path, at a speed 3.5 times slower than the turnable itself. If the ball is located in a straight track across a diameter of the turntable, then it accelerates rapidly to the edge. Both effects were filmed in slow motion using a video camera and a cake decoration…

In this article, we examine spatial inscriptions marked in real or rendered spaces, rather than on two-dimensional surfaces, conceptualize spatial inscriptions from an inclusive materialist perspective and consider realizations of spatial inscriptions that are possible with emerging technologies (e.g. 3D pens, immersive virtual reality). We then…

Collaborative learning, driven by knowledge co-construction and meaning negotiation, is a pivotal aspect of educational contexts. While gesture's importance in conveying shared meaning is recognized, its role in collaborative group settings remains understudied. This gap hinders accurate and equitable assessment and instruction, particularly for…

This study looks at how students embody their ideas about geometry conjectures and how those ideas travel within and between student groups. In one classroom of a Title 1 high school, students participated in a three-part program in which they: (1) played "The Hidden Village," a motion-capture video game where they assess the veracity of…

Despite the rapid development of motion-based technologies, their role in embodied learning remains ambivalent. This study aimed at investigating the potential added value of motion-based technologies in the context of geometry elementary education. An explanatory sequential design was adopted, composed of two phases. First, an experiment was…

In this study, we devised research design that provides pre-service teachers to effectively experience embodied geometric thinking with the goal that it will impact teachers' instruction to students in their classrooms. Using a motion-capture video game and design tool, we offered opportunities for pre-service teachers to experience of performing…