This paper deals with a set of geometrical problems for mathematical problem-solving at different difficulty levels. All of these are presented as national flags and one has to investigate invariant area proportions when changing the locus of any corner of the flag. This dynamic element suggests the usage of dynamical geometry environments.…

The author of this article, while recently working through some problem sets on determining volumes by triple integrals in cylindrical and spherical coordinate systems, realized that, although the textbook he was using included many interesting problems involving spheres, cylinders and cones and the increasingly complex solids that arose from the…

Another way to divide a line segment discovered by Nathan Besteman is described along with Euclid's and the GLaD construction. The related projects and problems that teachers of geometry can assign to their students are also presented.

This book helps teachers define good questions, offers tips on how to create their own good questions, and includes a wide variety of questions for use in the classroom. Each chapter of the book is organized by subject area and age group so that teachers can locate the topic their class is working on, then select probing, thought-provoking…

This booklet contains some 80 problems in mathematics suitable for computer solution. The problems range from very simple to complex. Problems have been included from most mathematic disciplines, including number theory, analytical geometry, probability and statistics, trigonometry, equations, and sequence and limits. For the most part these…

Various methods for solving the problem of finding when the hour and minute hand of a watch have the same direction are explored. The relationship of these problems to the educational environment and the maturity of the student are discussed. (CW)

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)

Discussed is the benefit of the inclusion of historical material in a student's text. Several geometry problems are used as examples. A suggested list of problem sources is provided in the appendix. (YP)

Illustrates some learning encounters for facilitating first graders' understanding of geometry. Describes some of children's approaches using Cuisenaire rods and teacher's intervening. Presents six problems involving various combinations of Cuisenaire rods and cubes. (YP)

Five sets of activities for students are included in this document. Each is designed for use in secondary school mathematics instruction. Topics include: (1) "5-Con Triangles"; (2) "Striking Sequences"; (3) "Invariants"; (4) "On the Ball," (a geometry lesson); and (5) "Coloring Maps." These topics focus on geometric and statistical concepts. Each…

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…

This book contains about 200 problems. It is suggested that it be used by students, teachers or anyone interested in exploring mathematics. In addition to a general discussion on problem solving, there are problems concerned with number theory, algebra, geometry, and combinatorics. (PK)

The purpose of this study was to examine the relationships between classroom instructional practices and computation and geometry achievement. Relationships between mathematics achievement and classroom characteristics were also explored. The sample of 1,032 students and their teachers (n=147) was selected from the 1992 Trial State Mathematics…

Designed to serve as a supplement for high school level mathematics, this publication contains activities which aim to enhance mathematical knowledge and skills and to assist students in understanding aerospace technology and its achievements. This volume updates an earlier supplement that was published in 1972. Problems are grouped into chapters…

This document is designed to assist teachers by providing practical examples of real world applications of high school mathematics. Fifteen problems are presented that individuals in industry and business solve using mathematics. Each problem provides the contributor's name, suggested skills required to solve the problem, background information…