The author uses Stella the Spider as the main character in a number of three-dimensional geometry problems. Eight of these problems are discussed, with solutions. (MNS)

A problem-solving approach involving systematic experimentation, one of the most-used problem-solving strategies, is advocated since it is useful beyond mathematics problems. Examples of its use are given, with two problems explored and four others noted. (MNS)

Discusses geometric construction problems. Presents four ways to construct a regular octagon using different conditions. Provides drawings showing the constructions. (YP)

To help mathematics teachers introduce and reinforce concepts and processes by using relevant problems, several such problems are presented and discussed. (MNS)

Five basic skill areas needing more attention in standard high school geometry are discussed. Levels of student mental development in geometry and a need for less emphasis on formal proofs are reviewed. (MP)

Presents two ancient problems, trisecting any angle and dividing a circle into any number of equal parts. Illustrates how to use these problems to prompt students to think broadly and creatively about problems instead of letting the apparent boundaries of the problem limit their thoughts. Combines three-dimensional solutions to the problems to…

From 1984 through 1988, the authors worked with teachers using an inquiry approach to teach high school geometry courses with the aid of the "Geometric Supposers." Problems are a critical component of the approach because they focus attention and energy and guide students in the application, integration, and extension of knowledge.…

A three-dimensional classification system of mathematical problems is given. A background philosophy is constructed through an analysis of different approaches to problem-solving research, leading to the statement of 5 theses and the objectives for the study. An exploratory study of mathematical problem-solving processes is conducted within this…