A Reuleaux triangle is an example of a curve of constant width; the distance between parallel tangents is the same no matter which direction is used. A consideration of a particular set of Reuleaux triangles is offered which leads to a good example of problem-solving in geometry. (JN)

Presents an activity for students in grades 7-10 (with ready-to-copy worksheets and overhead projector transparency masters) designed to develop the problem-solving skills of making and reading an organized list and searching for a pattern, and to provide practice in using the general heuristics of the problem-solving process. (JN)

The focus is on how line graphs can be used to approximate solutions to rate problems and to suggest equations that offer exact algebraic solutions to the problem. Four problems requiring progressively greater graphing sophistication are presented plus four exercises. (MNS)

Compares the ability of students in Michigan (N=302) and Scotland (N=221) to do simple calculation exercises and relational/practical problems involving number and operation. Although this is not a controlled statistical study (data collected included birth date and sex), sample sizes are sufficient to make the reported results meaningful. (JN)

This book offers games and mathematics activities using a hands-on approach for middle school students and features games, puzzles, experiments, and projects. Contents include: (1) "Boxed In!"; (2) "Oddball"; (3) "Pig"; (4) "Madagascar Solitaire"; (5) "Fantastic Four"; (6) "Eratosthenes' Sieve"; (7) "Hopping Hundred"; (8) "Tic-Tac-Toe Times"; (9)…

We explore the nature and consequences of teachers' problem solving through an example of a teacher's mathematical problem solving as it was occasioned by a student's mathematics. This illustration demonstrates the value of an interpretive framework that points to the mathematics of the classroom as a collective. Arising from this exploration is…

This article points out that many students, even of college age, lack familiarity with and confidence about probability problems. Several examples are given, including a "fair game" situation which would probably cause many readers some initial concern. (LS)

An anecdote shows why children studying mathematics should be given freedom to explore, generalize, classify, and originate proofs. (RS)

Provides a brief, condensed biography of the eighteenth-century mathematician, Leonard Euler, focusing on some of his contributions to mathematics. Also presents several problems and suggests how Euler might have solved them. (JN)

A procedure using calculators is described to test Ulam's conjecture that all positive integers converge to 1, if subject to certain iterated transformations. (MNS)

A new version of a standard old problem is presented. Ways of solving, extending, and continuing the problem that make it applicable to many grade levels are discussed. (MK)

The history of formal mathematical proofs is sketched out, starting with the Greeks. Included in this document is a chronological guide to mathematics and the world, highlighting major events in the world and important mathematicians in corresponding times. (MP)

A group of unsolved geometry problems is presented. Several problems that were unsolved for a length of time and then solved are also discussed. (MK)

The conditions necessary for a circumscribable quadrilateral also to be inscribable are discussed. Three propositions are presented and proved. (MK)