The cube is the most familiar and in many ways the simplest of the five regular polyhedra, and yet it is surprisingly rich mathematically. This article suggests a number of practical activities for the classroom which involve the cube and related polyhedra. (PK)

Interprets the philosophical concept of warrant in a mathematics education context and applies it to two central questions: (1) in what sense does mathematical proof warrant?; and (2) can there be warrants for mathematical knowledge other then deductive proofs? (Contains 36 references.) (Author/ASK)

Spatial tests involving the comparison of diagrams of interlaced ropes or knots at varying orientations were given to (n=21) subjects, mostly English college undergraduates, to determine an ordering in terms of complexity of tasks involving the mental manipulation of the knots. Certain knot shapes were processed faster than others and greater…

This report describes a program for increasing adolescent visualization and understanding of geometry problems. The targeted population consisted of high school students in two geometry classes in a growing middle-class community. The inability of students to adequately visualize and understand geometry problems was documented through teacher-made…

Discusses the need for three-dimensional ideas in geometry. Describes a three-year sequence of projects that help develop students' spatial skills. (ASK)

Explores the role of proof in mathematics education and provides justification for its importance in the curriculum. Discusses three applications of dynamic geometry software--heuristics, exploration, and visualization--as tools in the teaching of proof and as potential challenges to the importance of proof. (Author/MM)

Reports on a long-term teaching experiment carried out in the 9th and 10th grades of a scientific high school as part of a larger research project. Aims to clarify the role of a particular software, Cabri Geometry, in the teaching/learning process. Focuses on the social construction of knowledge. (Author/MM)

Presents interactive parabolas created from straight segments using a dynamic geometry software and its web component. (Author/KHR)

Investigated a secondary student's development of geometric thought during instruction using dynamic computer software. Clinical interviewing determined his predominant level of thought and highlighted the developmental process of geometric reasoning. Four learning stages were identified in terms of symbol, signal, and implicatory practices. Using…

Describes an enrichment activity based on the problem "Given a 2x2 square, and three colors, how many different ways can we shade the square?" (PK)

Presents three fundamental ideas of calculus and explains using the coordinate plane geometrically. Uses Cabri Geometry II to show how computer geometry systems can facilitate student understanding of general conic objects and its dynamic algebraic equations. (KHR)

Discusses the gap in France between institutional support for the use of technology in mathematics teaching and its weak integration into teacher practice. Identifies and analyzes steps in integration and indicates that the role played by technology in moving from being a visual to an essential constituent of the meaning of tasks affects student…

Presents activities where students visualize three dimensional figures, construct tables, discover patterns in the tables, and use the patterns to make predictions. (PK)

Identified are three obstacles which students must overcome when examining and interpreting diagrams. The resources of the Geometric Supposer, a set of microcomputer tools designed to aid students, are outlined. The advantages of the use of this software are emphasized. (CW)

Investigates gender differences and the role of spatial visualization in problem solving in high school geometry. Reports that, whereas males and females differed in spatial visualization and in their performance, they did not differ in logical reasoning ability or in their use of geometric problem-solving strategies. (Author)