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)

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…

Using license plates to generate random number pairs, students can calculate an approximate value for pi. The author views this approach as easier to understand than Buffon's needle. (SD)

An activity involving comparison of boxes constructed is described. (SD)

Describes a theory concerning the formation of soap films which enables this technique to be applied to problems requiring the minimization of the surface area between fixed boundaries. (Author/CP)

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)

The isometric grid geoboard can be used to demonstrate the nine-point circle theorem. (SD)

Similarity of parabolas and other conic sections is discussed. The theorem "Any two parabolas are similar" is deduced. (SD)

The converse of a familiar construction problem is explored, and a partial solution presented. The general problem is "Given a segment with length whose square is x, construct a segment with length 1." (SD)