Since ancient times mathematicians and geometricians have used visualisations to describe, discuss, study and teach mathematics. In mathematics education, visualisations are still used whenever possible to support teaching, to inspire students and feed their need to actually see abstract mathematical facts. In our times, virtual reality presents a…

In this study, we examine a large set of student responses to a constructed-response geometry item on the National Assessment of Educational Progress (NAEP) administered in 1992 and 1996. The item asks students to name the similarities and differences between a parallelogram and a rectangle of equal area presented side by side on a grid. Through…

When geometry and career and technical education (CTE) are cotaught in the process of building a house, learning is enhanced, test scores improve, and there's a waiting list of students wanting in. Geometry in Construction is a class instructed by the authors--a CTE teacher (Scott Burke) and a mathematics teacher (Tom Moore). While Moore instructs…

Test anxiety and mathematics anxiety have been found to relate to mathematics performance in both children and adults. This study investigated mathematics anxiety in elementary teachers and whether those who experience mathematics anxiety also have professional anxiety about teaching mathematics. A researcher-developed instrument called the…

When properly implemented, the vision of "Beyond Crossroads" will result in classrooms where students are actively engaged and responsible for their learning. They are able to share their thinking and the teacher, in turn, can use the emerging understanding as a foundation for learning. According to "Beyond Crossroads," students will be expected…

The aim of this study is to compare the experimental teaching method (ETM) with the teacher centered traditional teaching method based on students' success. This study is conducted with 54 students, randomly divided into two groups; an experimental group and a control group. Experimental teaching method was used for the experiment group and…

This study compared the effects of worked example and problem-solving approaches in individual or group work settings on learning to solve geometry problems. One hundred and one seventh graders from Indonesia were randomly allocated to four experimental groups using a 2 (problem-solving vs. worked examples) x 2 (individual vs. group study) design.…

In the present study we explore changes in perceptions of our class of prospective mathematics teachers (PTs) regarding their mathematical knowledge. The PTs engaged in problem posing activities in geometry, using the "What If Not?" (WIN) strategy, as part of their work on computerized inquiry-based activities. Data received from the PTs'…

A cube is a solid in three dimensions, with three mutually perpendicular right angles evident at the vertices. In this article, the author describes how to create a four-dimensional cube. Before searching this extra dimension, she first reviews what people know about zero, one, two, and three dimensions, and certain shapes in each of these. She…

Common Core education standards establish a clear set of specific ideas and skills that all students should be able to comprehend at each grade level. In an effort to meet these standards, educators are turning to technology for improved learning outcomes. "Cases on Technology Integration in Mathematics Education" provides a compilation…

This study examines Indonesian primary teachers' mathematical knowledge for teaching geometry and what factors contribute to this knowledge. A translated and adapted version of the Learning Mathematics for Teaching measures and the Indonesian Educational Survey were used to gather information on teachers' knowledge for teaching geometry and their…

Purpose: To ascertain the amount of phase asymmetry of the vocal fold vibration in normophonic speakers via visualization techniques and compare findings for habitual and pressed phonations. Method: Fifty-two normophonic speakers underwent stroboscopy and high-speed videoendoscopy (HSV). The HSV images were further processed into 4 visual…

There are many interesting explorations that can be done in knot theory, the study of mathematical knots. This article offers some knot theory activities that are appropriate for elementary grade children. These activities teach some basic concepts from knot theory as a natural extension of commonly-taught geometric ideas. (Contains 10 figures.)

Research on navigation has shown that humans and laboratory animals recover their sense of orientation primarily by detecting geometric properties of large-scale surface layouts (e.g. room shape), but the reasons for the primacy of layout geometry have not been clarified. In four experiments, we tested whether 4-year-old children reorient by the…

Tangrams have sometimes been used as an extension activity intended only to keep faster students busy while others finished essential desk-work. Without adequate introduction, many find that tangrams are just an open-ended form of a jigsaw puzzle. Happily teachers have discovered that games provide an effective introduction to a new topic. In the…