Geometry students have few opportunities to apply geometric concepts and solve geometry problems in authentic contexts. We developed a Ubiquitous Geometry (UG) system to teach geometry to elementary students by using it to measure common objects in authentic contexts. The instant study investigates the effects of UG on student geometry estimation…

This report summarizes the findings across two case studies conducted as part of WestEd's evaluation of the California Statewide Early Math Initiative (CAEMI). The case studies aimed to understand the planning and implementation of professional learning and coaching in local communities. They also examined changes in educators' math knowledge,…

Practical problems that use mathematical concepts are among the highlights of any mathematics class, for better and for worse. Teachers are thrilled to show applications of new theoretical ideas, whereas most students dread "word problems." This article presents a sequence of three activities designed to get students to think about…

This article addresses the use of the fifth position in historical and current dance training practices with particular emphasis upon examining the 180° aesthetic and its hegemonic, idealized persistence in dancing bodies, as a marker of perfection and "beauty". Historical research is interwoven with practice-based experience and dance…

Students' experiences with pattern blocks begin as early as preschool. At that time, they begin to develop an understanding of repetition by alternating the colored shapes to create AB, AAB, or ABC patterns. They experiment with area and symmetry by covering polygonal spaces using the fewest (or the greatest) number of pattern blocks possible or…

The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…

This study presents an analysis of whether geometry teachers create opportunities for student discussion when engaging students in proving as revealed through the use of a multimedia survey instrument. We presented 42 secondary mathematics teachers with 8 multimedia narratives set in the situation of doing proofs in high school geometry and asked…

During spatial reorientation, the use of local geometric cues (e.g., corner angles) and global geometric cues (e.g., principal axis) is differentially influenced by enclosure size. Local geometric cues exert more influence in large enclosures compared to small enclosures, whereas the use of global geometric cues is not influenced by changes in…

In the present study we aimed to develop a multidimensional test assessing high school students' knowledge about triangles, and then to determine the validity evidence for it based on the internal structure and relations to another variable and its reliability. The test developed was administered to 557 tenth grade students. To assess the validity…

Introduction: Visually impaired students (that is, those who are blind or have low vision) have difficulty accessing curricular material in mathematical textbooks because many mathematics texts have visual images that contain important content information that are not transcribed or described in digital versions of the texts. However, little is…

This paper reports on an aspect of a larger research study conceptualised within a teacher development project in Mthatha, Eastern Cape Province. The project was initiated with the objective to develop appropriate skills to use dynamic geometry software (DGS) effectively and strategically as a teaching and learning tool for mathematics. The study…

Solution of problems in mathematics, and in particular in the field of Euclidean geometry is in many senses a form of artisanship that can be developed so that in certain cases brief and unexpected solutions may be obtained, which would bring out aesthetically pleasing mathematical traits. We present four geometric tasks for which different proofs…

This study aims at analyzing how Pythagoras' theorem is handled in three versions of Taiwanese textbooks using a conceptual framework of a constructive-empirical perspective on abstraction, which comprises three key attributes: the generality of the object, the connectivity of the subject and the functionality of diagrams as the focused semiotic…

In fall 2013 the author taught a graduate course entitled Topics in Geometry for Middle and High School Teachers. The majority of the participants had extensive experience teaching mathematics in middle school or high school. The fact that participants were rather comfortable with the basic concepts of school geometry made it both possible and…

One goal of a mathematics education is that students make significant connections among different branches of mathematics. Connections--such as those between arithmetic and algebra, between two-dimensional and three-dimensional geometry, between compass-and-straight-edge constructions and transformations, and between calculus and analytic…