Notes that problem solving may become the focus of school mathematics to an extent never before experienced. It is felt much more systematic research is needed. Studies which focus on perception and cognitive processing ability are viewed to have potential for producing important results of wide applicability. (MP)

Lessons given to a group of mathematically talented eleventh and twelfth graders enrolled in a problem-solving course that provided practice in applying the heuristic strategy of working backward are detailed. Special attention was given to the process of formulating generalizations that represent large problem classes. (MP)

Social-matching problems were verbally presented to children either with or without concrete models. In each condition, information was provided which was sufficient, superfluous, or irrelevant. Problems containing only irrelevant information were the most difficult, although models enhanced the performance of younger children but depressed the…

This guide focuses on the role of problem solving in developing mathematical concepts of young children, selected problem situations or tasks for engaging children in problem solving, and criteria designed to provide a guide to teachers and parents of young children in formulating appropriate problem-solving situations. (MP)

The beauty of discovering some simple yet elegant proof either to something new or to an already established fact is discussed. A combinatorial problem that deals with covering a checkerboard with dominoes is presented as a starting point for individual investigation of similar problems. (MP)

Many science curriculum development projects have the goal of increasing students' ability to employ scientific or formal reasoning strategies. Argues that longitudinal data of students who acquired formal reasoning strategies as a consequence of specific instruction are needed to provide evidence that these skills will help in other academic…

Defines the concept of problem and notes that primary-grade teachers need to help nurture problem-solving skills. Discusses six practical ways instructors can promote such skills and views the ability and willingness of teachers to transform typical activities into problem-solving opportunities as essential. (MP)

Incorporating problem solving as an integral part of mathematics programs in the classroom is discussed. The teacher's focus is seen as stretching pupil thinking. (MP)

Some important issues related to teaching problem solving in the elementary grades are addressed, with particular emphasis on the intermediate grades. Presents one point of view and some specific questions often raised by teachers who wish to incorporate problem solving into the mathematics program. (MP)

Alternative techniques are suggested to some of the conventional approaches to teaching problem solving. Three general, conventional approaches are noted, and the nature and use of visual thinking is detailed as the fourth alternative. Examples of lessons with fifth graders using the fourth approach are provided to promote this method. (MP)

A computer software package designed to lead students through exploration using ancient sailing ships is reviewed, focusing on features, educational value, design quality, written materials, and ease of use. The price was seen to be too high for most individual teachers or parents. (MP)

Evaluation is one method of determining accountability in human service programs. A generic evaluation approach contains several steps: (1) stating a purpose for evaluating the program; (2) identifying evaluation questions; (3) identifying the nature of evaluation information; (4) collecting evaluation information; (5) analyzing evaluation…

A hungry worm is looking for something to eat according to very specific rules, and the path he takes is a graph. The problem is detailed in Applesoft BASIC using low resolution graphics for worms that turn 90 degrees and high resolution for worms that can turn 45 degrees. (MP)

Organizational barriers to creativity are examined. It is noted that resistance to change is a major impediment to creative problem solving in most organizations. Understanding the barriers to change that exist is viewed to help people exercise and develop their creativity more fully and effectively. (MP)

Ideas are presented regarding: (1) unique learning activities for students who have difficulty with operations with signed numbers; (2) a mathematical inspection of a unique card trick that can be expressed as an equation; and (3) sketching of graphs of composite trigonometric functions. (MP)