If the prospective students of probability lack a background in mathematical proofs, hands-on classroom activities may work well to help them to learn to analyze problems correctly. For example, students may physically roll a die twice to count and compare the frequency of the sequences. Tools such as graphing calculators or Microsoft Excel®…

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)

Offers heuristic arguments showing that a simple closed curve of specified length that encloses a maximum area must be a circle. Develops the problem by demonstrating that such an n-gon must be convex, that such a convex n-gon must be regular, and that such a simple closed curve must be a circle. (MDH)

The article discusses the classic problem: "Given an equilateral triangle and a point P inside the triangle, what is the sum of the distances from P to the three sides?" The problem is used to illustrate the generative nature of problem-posing using the heuristic "What happens if...?" (PK)

Presents three problems that help students develop a repertoire of heuristics and persistence in problem solving: the water-jug problem; the missionaries-and-cannibals problem; and the census-taker problem. Discusses methods to encourage students to persist. (MDH)

Presents an activity in which students develop their own theorem involving the relationship between the triangles determined by the squares constructed on the sides of any triangle. Provides a set of four reproducible worksheets, directions on their use, worksheet answers, and suggestions for follow-up activities. (MDH)

Presents two activities that utilize problem solving to promote concept development. The first uses a treasure hunt to teach locus of points. The second uses a tug-of-war model to teach mixture problems involving ratios. (MDH)

Discusses research involving instruction to help students develop their mental managerial processes or metacognition, the role of a framework for problem-solving activities, the teacher as model or moderator, problem solving involving groups or pairs, and weaving writing into problem solving. (Contains 18 references.) (MKR)

Provided is a teacher's guide for a problem-solving activity that establishes a link between number patterns and geometry by focusing on the development of recurrence relations established when generating central polygonal numbers. Reproducible worksheets and a 3.0 BASIC program for the activity are given. (MDH)

During a six-week methods course for preservice elementary school teachers, student pairs were asked to solve a problem and record their experiences in a dairy. Presented are the dairy entries of two students as they worked on determining the number of squares that can be formed on a five-peg geoboard. (MDH)

Described is an alternative first year algebra program developed to bridge the gap between the NCTM's Curriculum and Evaluation Standards and institutional demands of schools. Increased attention is given to graphing as a context for algebra, calculator use, solving "memorable problems," and incorporating geometry concepts, while…