By working through well-designed tasks, students can expand their thinking about mathematical ideas and their approaches to solving mathematical problems. They can come to see the value of looking at tasks from different perspectives and of using different representations. This article discusses four tasks that encourage high school students and…

Five graded sets of examples of alphametrics are provided. The puzzles are suggested for use in developing the traits of considering all possibilities and systematic working. (MP)

This document is designed to assist teachers in helping students in further development of problem-solving skills. It consists of: a statement of purpose; an introduction (noting the place of problem-solving in junior high school mathematics curricula); a definition of problem-solving; a four-stage general framework for solving problems (which…

This document is designed to assist teachers in helping students in further development of problem-solving skills. It consists of: a statement of purpose; an introduction (noting the place of problem-solving in junior high school mathematics curricula); a definition of problem-solving; a four-stage general framework for solving problems (which…

Involving students in generating and solving their own problems is proposed. A method for generating problems by using a number puzzle is presented. Ideas for using the "what if not" technique are also given. (MNS)

Presented are eight student worksheets of block problems. Included are diagrams of the squares and hollow squares involved and a separate answer sheet for the problems. (CW)

The author describes simple techniques for providing individualized help within a group teaching situation. (SD)

This study was designed to compare the relative effectiveness of word problem instruction based on Polya's approach to problem solving with Dahmus' word by word translation approach. When ninth-grade students were randomly assigned to one of these approaches, no differences in mean number of problems solved were observed. (SD)

The use of trial-and-error strategies to solve problems is endorsed. Types of problems with which trial and error is effective are discussed, with examples of how it is used, and teaching considerations are briefly considered. A computer program for one problem is included. (MNS)

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)

The mathematical content involved in self-teaching enrichment models for students in grades 8-12, the pedagogy employed in a summer institute for such students, and the results obtained are presented. (MNS)

A collection of brief articles on mathematics and teaching mathematics. (FL)

Provided are the activity sheets for students and the teaching guide for this middle school geometry activity. Materials, prerequisites, objectives, and procedures are listed. Extension activities are suggested. An answer key is included. (CW)

Argues that there is a sense of surprise and wonder that can result from looking back at problem solutions and there is a potential for then creating unexpected, even memorable, alternative solutions. Example problems with routine solutions and alternative approaches uncovered while "looking back" at the solution are given. (PK)