This paper describes a study of the cognitive complexity of young students, in the pre-formal stage, experiencing the dragging tool. Our goal was to study how various conditions of geometric knowledge and various mental models of dragging interact and influence the learning of central concepts of quadrilaterals. We present three situations that…

This author relates how she used to hate bugs but a museum visit changed her perception about them. She realized that in her panic of shooing insects away, she failed to recognize them as living models of the elements and principles of design. It made her realize that insects can provide an opportunity to teach this important lesson to her seventh…

A point "E" inside a triangle "ABC" can be coordinatized by the areas of the triangles "EBC," "ECA," and "EAB." These are called the barycentric coordinates of "E." It can also be coordinatized using the six segments into which the cevians through "E" divide the sides of "ABC," or the six angles into which the cevians through "E" divide the angles…

The author looks at the image of the triangle and provides suggestions for teachers to expand children's perception of this geometric form. Studies have shown that when most children are asked to identify shapes, in particular triangles, they identify the equilateral triangle as the "true triangle." This article provides an overview of…

Modern geometry teaching in schools in Japan was modeled on the pedagogies of western countries. However, the core ideas of these pedagogies were often radically changed in the process of adaptation, resulting in teaching differing fundamentally from the original models. This paper discusses the radical changes the pedagogy of a German mathematics…

Beyond Crossroads is a call to action. Within this call, AMATYC has updated its 1995 Crossroads standards, developed a new set of guiding principles, and created a blueprint for implementing these revised principles and standards. The principles guiding Beyond Crossroads are a significant overhaul of their predecessors and are bold statements that…

Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…

Geometry students were randomly assigned to treatments in which they received (1) instruction in general problem solving procedures in addition to geometry or (2) regular geometry instruction. No significant differences attributable to treatments were found on a subsequent problem solving test. (SD)

Because of the extensiveness of the course outline for Math 201 (Manitoba Department of Education), schools would have had to purchase several different textbooks to cover the material adequately. Therefore, a set of materials to supplement the guide was developed. The exercises, projects, and reviews contained in this package are keyed to the 201…

The application of physical principles in solving mathematics problems have often been neglected in the teaching of physics or mathematics, especially at the secondary school level. This paper discusses how to apply the mechanical principles to geometry problems via concrete examples, which aims at providing insight and inspirations to physics or…

A carpenter's square can be used to introduce students to an alternative method of performing geometric constructions. (SD)

This problem solving strategy is illustrated by examples from the fields of algebra, trigonometry, geometry, and calculus. (MP)

Chemical bonding, for most simple complexes, is described in the Mulliken-Walsh Molecular Orbital (MO) theory. (CP)

Mathematical solutions to simple atomic structure problems involving (a) simple cubic, (b) body-centered cubic, and (c) face-centered cubic models are presented. (CP)