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…

The research question addressed by this study is whether or not students made effective use of dynamic geometry software to explore the validity of a geometrical statement. Particular attention was paid to the use of definitions and the types of justifications students employed. Interviews conducted with six secondary mathematics preservice…

Readers will find several papers that address high-level issues in the use of technology in education, for example architecture and design frameworks for building online education materials or tools. Several other chapters report novel approaches to intelligent tutors or adaptive systems in educational settings. A number of chapters consider many…

Purpose: The purpose of this scientific monograph is to show new and creative approaches to different school subjects in primary and secondary level. Methodology: Interdisciplinary and international comparative approaches were used. Now according to the 7th Framework Program, the preferred form of Science Education (www.scientix.eu) is preferred…

Presents 5 activities for the K-1, 2-3, 4-5, 6-8 grade levels and for in the home in which students explore the concept of triangle through cooperative open-ended investigations. Provides related reproducible worksheets. (MDH)

This article explores the concept of the center of gravity and the geometry involved in locating the center of gravity of an object. (Contains 15 figures.)

This paper describes a possible dragging experiment in a dynamic geometry environment (DGE) that explores a necessary and sufficient condition for cyclic quadrilateral. The dragging modalities identified by Arzarello, Olivero, Paola, and Robutti (2002) and the functions of variation realized in DGE discussed by Leung (2003) will be used as tools…

In this article we examine students' perspectives on the customary, public work of proving in American high school geometry classes. We analyze transcripts from 29 interviews in which 16 students commented on various problems and the likelihood that their teachers would use those problems to engage students in proving. We use their responses to…

Technological tools have the potential to offer students the possibility to represent information and relationships embedded in problems and concepts in ways that involve numerical, algebraic, geometric, and visual approaches. In this paper, the authors present and discuss an example in which an initial representation of a mathematical object…

If we look into the past we will discover that the teachers of thermodynamics were always trying to interpret an important part of their science by using geometry. The relation between geometry and thermodynamics is of great interest and importance in teaching thermodynamics. This article examines the way undergraduate students of thermodynamics…

This article describes a classroom activity in which a solar eclipse is simulated and a mathematical model is developed to explain the data. Students use manipulative devices and graphing calculators to carry out the experiment and then compare their results to those collected in Koolymilka, Australia, during the 2002 eclipse.

This study focuses on the constructions in terms of area and perimeter in equivalent triangles developed by students aged 12-15 years-old, using the tools provided by Cabri-Geometry II [Labore (1990). "Cabri-Geometry (software)," Universite de Grenoble]. Twenty-five students participated in a learning experiment where they were asked to construct:…

These excerpts from the National Council of Teachers of Mathematics (NCTM) Standards support the Third International Mathematics and Science Study (TIMSS) Resource Kit by offering some context for discussing the teaching of algebra and geometry seen in the videotapes that are also part of the kit. The Standards describe the mathematics content…

The main focus of the study was to describe how students of various ages established the truth of their ideas in school geometry. Thirty-two students in grades 2, 5, 7, and in a high school geometry class were interviewed. Formal proof was used in less than 1% of the student arguments. Second and 5th graders were most likely to convince themselves…

This document lists mathematics objectives for Boston high school students. All objectives are presented in two columns. The left-hand column states each objective in general terms and gives an idea of its scope. The right-hand column gives a specific example of what students should be able to do when the objective is achieved. Objectives are…