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…

The use of dynamic geometry software (DGS) is becoming increasingly familiar among teachers, but letting students conduct inquiries using computers is still not a welcome idea. In addition to logistics and discipline concerns, many teachers believe that mathematics at the lower secondary level can be learned efficiently through practice alone.…

Metaphors are regularly used by mathematics teachers to relate difficult or complex concepts in classrooms. A complex topic of concern in mathematics education, and most STEM-based education classes, is problem solving. This study identified how students and teachers contextualize mathematical problem solving through their choice of metaphors.…

The most recent Kindergarten Common Core Mathematics State Standards include an emphasis on teaching geometry skills, such as recognizing, describing, naming, and composing shapes. This article provides five effective ideas for teachers of young children as they introduce and teach shapes.

This article is written to share teaching ideas about using commonly available computer applications--a spreadsheet, "The Geometer's Sketchpad", and "Wolfram Alpha"--to explore three classic and historically significant problems from the probability theory. These ideas stem from the authors' work with prospective economists,…