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…

This study aims to examine the relation between spatial ability and creativity in Geometry. Data was collected from 94 ninth graders. Three spatial abilities were investigated: spatial visualization, spatial relations and closure flexibility. As for students' creativity, it was examined through a multiple solution problem in Geometry focusing on…

Immersive spatial diagrams (three-dimensional diagrams rendered with immersive stereoscopic displays) offer learners the opportunity to extend practices of diagramming in school geometry into a human-scale, spatial context. Learners can use two or more hands to inscribe simultaneously with digital spatial painting tools, a spatial analog of the…

This article is intended to contribute to greater knowledge regarding the importance of flow and the time used to perform an activity, with a focus on students' mathematical experiences of 3D bodies. Thirty-one 9th-grade students took part in the study. Flow and variation theory was used in the analysis of lesson observations, submission tasks,…

Understanding fraction as a quantity has been identified as a key developmental understanding. In this study, students in Grades 5, 8, and 11 were asked to compare the areas of two halves of the same square--a rectangle and a right triangle. Findings from this study suggest that students who understand fraction as a quantity use reasoning related…

Video game use is widespread among all age groups, from young children to older adults. The wide variety of video game genres, which are adapted to all tastes and needs, is one of the factors that makes them so attractive. In many cases, video games function as an outlet for stress associated with everyday life by providing an escape from reality.…

A growing body of research suggests that children's understanding of mathematical language is critical for their mathematical abilities. Most of this work has been restricted to single language learners (i.e., SLLs), and used dual language learners (i.e., DLLs) as an exclusion criterion, raising questions about the generalizability of these…

Current reforms in geometry seek to challenge prevailing ideas about "what it means to do mathematics" (p. 139) by engaging learners in "the grasping of space" (p. 241). This study takes up this challenge by investigating problematizing activity as an embodied phenomenon among 21 eighth-grade learners who engaged with spatial…

This article details the design and implementation of a professional development model called Learning Trajectory-Based Lesson Study focused on issues of equity, identity, and agency. We developed the Vertical Articulation to Unpack the Learning Trajectory (VAULT) tool to orient teachers' instructional planning toward an asset-based view of…

Twenty students who earned A or B course-grades in the proof unit(s) of a secondary course that addressed proof in geometry were asked to work on two proof tasks while sharing their thinking aloud and using smartpens. Students were classified into two categories: those who were successful with both proofs and those who were unsuccessful with both…

Digital simulators have an interesting potential to explain the relationships between two or more variables in a system, facilitating the activation of learning processes and favoring the occurrence of meaningful learning with positive impact on academic performance. To study the impact of the use of digital simulation on learning and academic…

Block building activities help develop students' spatial reasoning, but few studies focus on the development of block building skills beyond preschool. We worked with four kindergarten, four first grade, and four second grade students to learn more about their Lego block building. We compared students' accuracy, building strategies, and spatial…