Suggests using episodes from the history of mathematics as source material for mathematical investigations, particularly for use in teaching problem solving. Representative examples are included. (JN)

Methods of determining probabilities of various outcomes of the game Yahtzee are described. (SD)

A technique is illustrated for solving relative motion problems using a maneuvering board and vector algebra. The technique can be used to visually illustrate properties of vector algebra in a non-theoretical context. (MP)

Five calculator activities are described that are designed to explore ordered operations. Suggestions are given on mathematical objectives, strategies for solving, and possible extensions or follow-up activities. (MP)

Problems are discussed in which addition facts are presented using words instead of numbers. The letters are then replaced by numbers that will make the addition problems correct. (MP)

Definitions of estimating and approximating are given and areas where these skills are used (such as practical situations, problem solving, and measurement) are discussed. Nine activities which range from second to twelfth-grade level are suggested. (MK)

Brainstorming is suggested as one approach to problem solving. Generating possibilities stimulates creative and independent thinking and can facilitate problem solving in many situations. (MP)

A sample of novel verbal problems which can be solved by using systems of linear equations with free variables is presented. The procedure of Gaussian elimination is used to solve the system. (KR)

This article examines the Pythagorean Theorem from a geometric point of view by suggesting some natural extensions of the theorem. The use of a more general theorem to prove a difficult one is suggested, where possible. The article includes figures and proofs. (Author/MA)

The vast majority of people are most familiar with arithmetic in base ten. This article presents a follow-up on a problem with several divisibility tests valid in base ten which are related to Freitag's general test and which follow directly from it. Base 13 is also explored. (Author/MA)

Develops a division algorithm in terms of familiar manipulations of concrete objects and presents it with a series of questions for diagnosis of students' understanding of the algorithm in terms of the concrete model utilized. Also offers general guidelines for using concrete illustrations to explain algorithms and other mathematical principles.…

termined that students who completed writing assignments on mathematics problems were better problem solvers than students in control groups, supporting the contention that expository writing is an effective, practical, and innovative tool for problem solving. (Sample problems and writing assignments are included.) (DH)

Examines principles which can be applied to determine how hints can be used effectively in problem-solving. Conscious and unconscious hints, timing of hints, expected functions, and teaching are discussed. Conscious hints are explained in detail with suggestions and references. Charts are included for types, timing, and expected functions. (DH)

Describes three studies in which students (N=515; N=60; N=135) were asked to indicate appropriate operations and numbers used in solving open mathematical sentences. Analysis of data and interviews suggest two error patterns: "finding a solution" and "inverse operation." Indicates that "finding a solution" strategy…

An example is discussed in which a drill exercise, initially involving whole number addition, can be used to develop concepts in equations of many variables. (MP)