Proponents of a geometric module have argued that instances of young children's use of features as well as geometry to reorient can be explained by a two-stage process. In this model, only the first stage is a true reorientation, accomplished by using geometric information alone; features are considered in a second stage using association (Lee,…

Dispersive forces are a kind of van der Waals intermolecular force which could only be fully understood with the establishment of quantum mechanics and, in particular, of quantum electrodynamics. In this pedagogical paper, we introduce the subject in a more elementary approach, aiming at students with basic knowledge of quantum mechanics. We…

The objective of this study was to examine the use of the Geometer's Sketchpad on students' van Hiele level of geometric thinking. A total of 31 Year Three students from a primary school in Pahang, Malaysia, participated in this study which was carried out over two weeks. The experimental group (N=16) was given the intervention using Geometer's…

This paper describes a mentoring program designed to prepare novice instructors to teach a college geometry class using inquiry-based methods. The mentoring program was used in a medium-sized public university with approximately 12,000 undergraduate students and 1,500 graduate students. The authors worked together to implement a mentoring program…

This paper describes a mentoring program designed to prepare novice instructors to teach a college geometry class using inquiry-based methods. The mentoring program was used in a medium-sized public university with approximately 12,000 undergraduate students and 1,500 graduate students. The authors worked together to implement a mentoring program…

Despite a decade of reform driven by the NCLB legislation, there continues to be a significant gap in mathematics achievement between race/ethnicity and socioeconomic groupings of students. This study examines the practice of tracking and an effort to improve mathematics achievement by eliminating the general level mathematics track. The suburban…

We inspect the hypothesis that geometry students may be oriented toward how they expect that the teacher will evaluate them as students or otherwise oriented to how they expect that their work will give them opportunities to do mathematics. The results reported here are based on a mixed-methods analysis of twenty-two interviews with high school…

This study compared the effects of reading-oriented tasks and writing-oriented tasks on students' reading comprehension of geometry proof (RCGP). The reading-oriented tasks were designed with reading strategies and the idea of problem posing. The writing-oriented tasks were consistent with usual proof instruction for writing a proof and applying…

Geometer Sketchpad is far from a new innovation, but its potential in the classroom is probably still understated. The application described here can be replicated in any classroom, and the impact on learning is likely to be significant. The experiences documented are "real", and show how a software package can enhance an area of the mathematics…

Learners are all different and teachers are all different, so why do we often ignore this reality when trying to explain, or demystify, some aspect of mathematics in the classroom? Enabling learning can be challenging, demanding of creativity, and needy of alternatives if understanding is the real goal. Here the authors offer ideas that are aimed…

Proving and refuting mathematical claims constitute a significant element in the development of deductive thinking. These issues are mainly studied during geometry lessons and very little (if at all) in lessons of other mathematical disciplines. This study deals with high school students' perceptions of proofs in the geometry. The study explores…

The art gallery problem asks for the maximum number of stationary guards required to protect the interior of a polygonal art gallery with "n" walls. This article explores solutions to this problem and several of its variants. In addition, some unsolved problems involving the guarding of geometric objects are presented.

Conjectures, theorems, and problems in print often appear to come out of nowhere. Scott Fallstrom and Marion Walter describe how their thinking and conjectures evolved; they try to show how collaboration helped expand their ideas. By showing the results from working together, they hope readers will encourage collaboration amongst their students.…

Symmetry is found in the visual arts, architecture and design of artefacts since the earliest time. Many natural objects, both organic and inorganic, display symmetry: from microscopic crystals and sub-atomic particles to macro-cosmic galaxies. Today it features strongly in higher mathematics such as Linear and Abstract Algebra, Projective and…

The formula [image omitted] is closely related to combinatorics through an elementary geometric exercise. This approach can be expanded to the formulas [image omitted], [image omitted] and [image omitted]. These formulas are also nice examples of showing two approaches, one algebraic and one combinatoric, to a problem of counting. (Contains 6…