This paper describes aspects of 13 year-olds activity in mathematics as emerged during the implementation of proportional geometric tasks in the classroom. Pupils were working in pairs using a piece of software specially designed for multiple representation (symbolic and graphical) of the variation in parametric procedures with dynamic…

This essay contains some reflections and questions arising from encounters with the text of Euclid's Elements. The reflections arise out of the teaching of a course in Euclidean and non-Euclidean geometry to undergraduates. It is concluded that teachers of such courses should read Euclid and ask questions, then teach a course on Euclid and later…

This study extended over three months and involved 344 subjects. It compared the performance and attitudes of seventh-grade students taught geometry using the TI-92 calculator and a supplementary activity manual written to be used with the TI-92 calculator with the performance and attitudes of students using the traditional approach. On a…

The goals, objects, materials and grade levels are specified in this description of a laboratory activity involving analytic geometry concepts. Students mark out bicycle gymkhana courses in which directions to participants are given by Cartesian coordinates. (JP)

Given two interesecting lines, the "pencil" of this interesection is the family of all lines passing through the point of intersection. Presented is a characterization of all lines both in the plane and lying in opposite sectors of the plane as determined by one of the original intersecting lines. (JP)

Paper shows that an obvious generalization of the subjective metrics model by Bloxom, Horan, Carroll and Chang has a very simple algebraic solution which was previously considered by Meredith in a different context. (Author)

Activities designed for levels 1-4 give experience in recognizing shape and form after standard transformations are applied to geometric figures. The activities for the upper levels use a physical projection to provide experience with the properties of similarity. (DT)

Creation of materials for a geometry course using transformations is briefly summarized, then research on its effect upon student learning of geometry concepts and student attitudes towards mathematics is discussed. Implementation and other related questions are considered informally. (DT)