We previously observed students gesturing during a symmetry and group theory activity. This prompted additional interviews, wherein we attempted to understand the semiotic function of these gestures. We report here on the gestures that students used in this context to represent symmetry elements, symmetry operations, and other related ideas. In…

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…

Spatial ability is a multifaceted construct with demonstrated ties to success in mathematics and gesture production. Recent empirical work has also begun investigating whether targeted interventions for spatial ability can transfer to mathematics but are often limited to specific populations and specific math outcomes. Spatial anxiety has been…

Geometry and spatial reasoning form the foundations of learning in mathematics. However, geometry is a subject often ignored by curriculum writers and teachers until high school, leading to students lacking in critical skills in geometric reasoning. As the United States moves into a new curriculum epoch, heralding the commencement of the national…

This study aims to describe the abstraction of epistemic action, which includes recognition, building-with and construction in junior high school students with low spatial ability in constructing cube nets. The research method used in this study is an exploratory qualitative method with the primary data in the form of interviews with two junior…

We report on a group theory activity in which learners explored dihedral symmetries through a tangible geometric model. This approach has historical roots in the work of Felix Klein's Erlangen Program and his "Elementary Mathematics from an Advanced Standpoint." We situate our study with respect to this history as well as current…

Angularity is a persistent quantity throughout K-12+ school mathematics, and many studies have shown that individuals often conflate angularity with linear attributes (e.g., the length of an angle model's sides). However, few studies have examined the productive ways in which students might reason about angularity while attending to linear…

By the end of primary school, children are expected to acquire a range of mathematical skills that progressively develop. This study aimed to gain insight into how a large number of numerical and geometrical measures are grouped and whether the structures shift or remain invariant along child's development based on the data obtained from a sample…

Geometry learning has a long history with the connection to human cognitive development. The ability to mentally or physically orient 2D shapes or 3D objects in space is believed to support achievement in science, technology, engineering, and mathematics (STEM) disciplines. Thus, geometry by its description is characterised by space; hence its…

In learning during the current epidemic, students cannot meet face to face on campus, and learning geometry in universities is a dreadful lesson before the pandemic. Both at UPGRIS and other private universities so far, students are required to use a compass and ruler in making flat shapes and building spaces so they have to face to face with the…

Spatial geometry is one of the multi-purpose fields of mathematics and is tightly linked to the development of mathematical and intellectual thinking. Spatial thinking is necessary in various areas of life such as civil engineering, mechanical engineering, interior design, graphic design and other. At present, teaching spatial geometry is mainly…

This study investigates whether Vietnamese students face specific challenges when visualizing skew versus intersecting lines and whether using the anaglyph feature of GeoGebra can help overcome these difficulties. Employing a design-based research approach over four phases with 12th-grade students, the study involved tasks in traditional…

Aim/Purpose: This study aims to assess the effectiveness of a tessellation-based instructional program supported by digital technologies for enhancing geometric learning in primary school pupils. Background: Digital education offers various benefits, including increased motivation and engagement, and has been shown to be effective in teaching…

It is well established that spatial reasoning skills (i) support mathematics achievement, (ii) are malleable, and (iii) can be improved through training. More recently, there has been interest in using spatial training to causally support corresponding improvements in mathematics achievement; however, findings so far appear to be mixed. The…