Shows a series of Euclidean equations using the Euclidean algorithm to get the greatest common divisor of two integers. Describes the use of the equations to generate a series of circles. Discusses computer generation of Euclidean circles and provides a BASIC program. (YP)

Describes a unit in which students design a space station. Provided are a timetable for the unit, requirements for space-station manufacturing, and an outline of the unit. Lists nine references. (YP)

Presented is an alternative method for analyzing the van Hiele level of students' geometrical reasoning. The accuracy of students' answers may afford a description of acquisition and/or expertise for each of the van Hiele levels simultaneously rather than the traditional assignment and evaluation of one level at a time. (JJK)

Draws on the new field of mathematical study called fractal geometry. Illustrates the pervasiveness and constraining tendencies of classical geometries. Suggests that fractal geometry is a mathematical analogue to fields such as post-modernism, post-structuralism, and ecological theory. Examines how fractal geometry can complement other emergent…

"The Simpsons" is an ideal source of fun ways to introduce important mathematical concepts, motivate students, and reduce math anxiety. We discuss examples from "The Simpsons" related to calculus, geometry, and number theory that we have incorporated into the classroom. We explore student reactions and educational benefits and difficulties…

Designing successful learning environments entails drawing on theoretical perspectives on learning while, at the same time, being cognisant of the affordances and constraints of the technology. This paper reports on the development of a software environment called "3DMath", a dynamic three-dimensional geometry microworld aimed at enabling learners…

A heuristic description is given of the rediscovery with "Sketchpad" of a less-well-known, but beautiful, generalization of the nine-point circle to a nine-point conic, as well as an associated generalization of the Euler line. The author's initial analytic geometry proofs, which made use of the symbolic algebra facility of the TI-92 calculator,…

Teachers assume that by the end of primary school, students should know the essentials regarding shape. For example, the NSW Mathematics K-6 syllabus states by year six students should be able manipulate, classify and draw two-dimensional shapes and describe side and angle properties. The reality is, that due to the pressure for students to…

In this narrative of teacher educator action research, the idea for and the context of the lesson emerged as a result of conversations between Shelly, a mathematics teacher educator, and Lisa, a quilter, about real-life mathematical problems related to Lisa's work as she created the templates for a reproduction quilt. The lesson was used with…

This book describes how teachers have taught students to behave like working mathematicians who conjecture and prove within a community of learners through the use of microcomputers and the "Geometric Supposers" software. The first section discusses the definition and importance of the conjecture, describes inquiry skills and understandings…

Discusses the geometry, algebra, and logic involved in the solution of a "Mindbenders" problem in "Discover" magazine and applies it to calculations of satellite orbital velocity. Extends the solution of this probe to other applications of falling objects. (JM)

PROLOG is a relatively new programing language with graphics capability. In addition, the language has a declarative rather than a procedural structure. Two programs illustrating use of the language in the mathematics classroom are presented. (JN)

Seymour Papert, creator of LOGO, explains how he came to create this important problem-solving language and how he intended it to be used to foster learning among children. What children can do with turtle geometry (indicated to be a natural approach to mathematics) is one topic considered. (Author/JN)

In this paper there is a description of a case in which mathematical argumentation emerge and develop between 7th grade students working in an interactive computerized environment without a deliberate mentoring. The computerized environment has its influence on the characteristics of this argumentation which include mathematical regularities based…

Describes techniques intended to provide the teacher (or student) with insights to the solution of the problems of constructibility of squares of area c and determination of the numbers of squares, and a method for the construction of constructible integers of area c. (DS)