Presents a model for representing and storing binary topological and directional relationships between 2-dimensional objects that is used to provide a basis for fuzzy querying capabilities. A data structure called an abstract spatial graph (ASG) is defined for the binary relationships that maintains all necessary information regarding topology and…

Shares how students worked on a geometry activity that emphasizes patterns featured in this journal. (ASK)

This article reviews some of the research on indirect proof, discusses implications of the research for teaching, and offers some specific examples and strategies that can increase students' success with this important proof technique. (AIM)

Integrates different geometries and blends several topics that have important applications in both higher mathematics and other disciplines. Aims to make these topics more attractive and understandable to high school students in a way that reinforces logical thinking with visual understanding obtained through computer usage. Contains 28…

Created two geometric inductive reasoning matrix tests by manipulating four sources of complexity orthogonally. Results for 313 undergraduates show that fluid intelligence is most strongly associated with the part of the central executive component of working memory that is related to controlled attention processing and selective encoding. (SLD)

Discusses reflections on a videotaped geometry lesson from a Japanese classroom. Contrasts the lesson with the work of a group of teachers on a B.Ed. program who were given the same problem-solving task as the Japanese pupils. (MM)

Offers a tangible suggestion for how dot paper can be used to implement an exploratory approach to problem solving in middle school geometry. Presents some intriguing mathematical tasks that demonstrate the elegance of mathematics, the usefulness of dot paper as a teaching tool, and the value of divergent thinking approaches to problem solving.…

Proposes that a mathematical treatment of Strong Inequality Triangles (sum of any two sides is greater than the third) within the reach of high school and college students is possible. Invites further explorations of other properties of Strong Inequality Triangles. (ASK)

Presents a study that is interested in the teaching of geometry to primary school teachers. Defines a priori a conceptual frame that organizes geometry into three kinds of knowledge: (1) intuition; (2) experience; and (3) deduction. Illustrates this conceptual frame with examples of teaching geometry. (Contains 31 references.) (Author/ASK)

Discusses a town called Chartres and its cathedral which features the figure of Pythagoras. Discusses the Pythagorean theorem and his mathematical contributions to music. (ASK)

Introduces a place of mathematics using a town called Amiens and its Cathedral whose overall floor plan was based on the Greek cross using proportions matching that of the ideal human body, the figures in the shape of an octagram or star octagon, and the symbols in the design. (ASK)

Presents discovery mathematics activities involving sporting equipment. (ASK)

Students should be given an opportunity to explore and conjecture with the help of new technology to become good problem solver. Ron Mclister, while using the Geometer's Sketchpad to explore the Pythagorean theorem, came upon a nice result about the relationship of some geometrical patterns.

Students solve a geometric problem of measuring polygons with the help of proportional reasoning. Thus the importance of conceptual reasoning is emphasized as a highly efficient technique for teaching and strengthening mathematical content.

A Mandelbrot mathematical set is an object with endless borders, and in the present exercise a graphing calculator is used to identify and examine the set points. The significance and power of technology is also displayed in the understanding and solving of problems.