This article describes an investigation of Buffon's coin problem and related problems with the aid of an applet. The problems are accessible at a variety of grade levels and facilitate making connections between geometry and probability.

Truly flower-naive bumblebees, with no prior rewarded experience for visits on any visual patterns outside the colony, were tested for their choice of bilaterally symmetric over asymmetric patterns in a radial-arm maze. No preference for symmetry was found. Prior training with rewarded black and white disks did, however, lead to a significant…

Descriptions of methodologies that can be used to create items for assessing teachers' "professionally situated" knowledge are lacking in mathematics education research literature. In this study, researchers described and used the Delphi method to design an instrument to measure teachers' pedagogical content knowledge. The instrument focused on a…

This paper presents findings from a comparative analysis of three similar secondary geometry texts, one critical unit, one standards-based reform unit, and one specialist chapter. I developed the critical unit as I took the tenets of critical mathematics (CM) and substantiated them in printed curricular materials in which to teach as part of a…

In providing a continued focus on tasks and activities that help to illustrate key ideas embedded in the new Australian Curriculum, this issue the authors focus, on Geometry in the Measurement and Geometry strand with strong links for an integrated focus on the Statistics and Probability strand. The small unit of work on the sorting and…

Exploring mathematical symmetry is one way of increasing students' understanding of art. By asking students to search designs and become pattern detectives, teachers can potentially increase their appreciation of art while reinforcing their perception of the use of math in their day-to-day lives. This article shows teachers how they can interest…

This article presents a way of studying the rationality that mathematics teachers utilize in managing the teaching of theorems in high-school geometry. More generally, the study illustrates how to elicit the rationality that guides teachers in handling the demands of teaching practice. In particular, it illustrates how problematic classroom…

An outbox of a quadrilateral is a rectangle such that each vertex of the given quadrilateral lies on one side of the rectangle and different vertices lie on different sides. We first investigate those quadrilaterals whose every outbox is a square. Next, we consider the maximal outboxes of rectangles and those quadrilaterals with perpendicular…

The present study examined the effectiveness of three instructional treatments which had different combinations of mathematical elements regarding 2-dimensional (2-D) geometry and area measurement for developing 4th-grade children's understanding of the formulas for area measurement and their ability to solve area measurement problems.…

The papers in the monograph address different topics related to mathematics teaching and learning processes which are of great interest to both students and prospective teachers. Some papers open new research questions, some show examples of good practice and others provide more information about earlier findings. The monograph consists of six…

Previous studies have shown that several key variables influence student achievement in geometry, but no research has been conducted to determine how these variables interact. A model of achievement in geometry was tested on a sample of 102 high school students. Structural equation modeling was used to test hypothesized relationships among…

The present study investigated (a) whether the perceived cognitive load was different when geometry problems with various levels of configuration comprehension were solved and (b) whether eye movements in comprehending geometry problems showed sources of cognitive loads. In the first investigation, three characteristics of geometry configurations…

The activity of posing and solving problems can enrich learners' mathematical experiences because it fosters a spirit of inquisitiveness, cultivates their mathematical curiosity, and deepens their views of what it means to do mathematics. To achieve these goals, a mathematical problem needs to be at the appropriate level of difficulty,…

Determining how to provide good tutoring functions is an important research direction of intelligent tutoring systems. In this study, the authors develop an intelligent tutoring system with good tutoring functions, called "FUDAOWANG." The research domain that FUDAOWANG treats is junior middle school mathematics, which belongs to the objective…

Gabriel's Horn is a solid of revolution commonly featured in calculus textbooks as a counter-intuitive example of a solid having finite volume but infinite surface area. Other examples of solids with surprising geometrical finitude relationships have also appeared in the literature. This article cites several intriguing examples (some of fractal…