Back-of-the-envelope problems call for approximate calculations of quantities that can be related to information in a person's knowledge but are not solved precisely. These problems provide an opportunity for the study of processes and the role of general knowledge in ill-defined problem solving. Subjects with advanced and intermediate knowledge…

Students in adult basic education/general educational development classes need skills in analyzing and solving programs, extending beyond those learned through word problems in the mathematics curriculum. The following strategies can help students broaden their problem-solving skills: (1) act it out, (2) construct a table, (3) draw a picture, (4)…

A study examined in detail the initial encoding of worked-out examples of mechanics problems by "good" and "poor" students, and their subsequent reliance on examples during problem solving. The subjects, three males and five females, were selected from responses to a university campus advertisement. Six of them were working…

This review examines 12 programs designed for use in classrooms to develop "general thinking skills" used in learning and problem-solving situations inside and outside classrooms. Analysis of program features focuses on the extent to which each program shows promise in helping students transfer the skills they develop through completing…

Among ways suggested for teaching problem solving strategies are to select problem situations appropriate to the learner and to encourage learning from errors. A problem solving process which can be used with young children includes the components of formulation; interpretation; generation; decision making; implementation; evaluation; and…

Presents suggestions for helping students broaden their learning skills: tell students you plan to help them learn to learn, hold class discussions where students share learning strategies, give students practice using unfamiliar learning strategies, pick a complex learning exercise and present it in steps, and vary your approach over the course…

Discusses how networking provides an effective means of learning about one's environment and of gaining help and support in improving it. The process of networking is examined through case studies. The difference between networking and organizing is also discussed. (CT)

This chapter examines research on the cognitive processes involved in mathematical problem solving. The introduction includes definitions of key terms and a summary of four cognitive processes used in mathematical problem solving: (1) translating; (2) integrating; (3) planning; and (4) executing. Examples are then provided and exemplary research…

Presents an interesting problem intended to introduce students to an application of algebra and to help them make the transition from arithmetic to algebra. Uses different problem representations including making successive approximations, interpreting graphs, and solving equations. Discusses pedagogical issues involved. Contains 11 references.…

Presents results of preliminary trials that suggest that the program devised helped UK Year 12 (A-level) learners develop useful concepts of current and voltage, acquire a more integrated understanding of circuit behavior, and overcome their tendencies towards localized and sequential reasoning. Provides learners with a valuable aid for problem…

Developed a heuristic strategy (SOLVED) to explain the processes involved in understanding and solving mathematical word problems (problem translation, problem interpretation, solution planning, solution execution, and solution monitoring) among upper elementary students. Results indicated that SOLVED was more effective in aiding both short-term…

This study explored 5- to 17-year-olds' use, self report, and awareness of verbal problem-solving strategies and strategy effectiveness. Findings indicated that children's verbal strategies moved from overt, to partially covert, to fully covert forms with age. Self-reports of strategy use were accurate yet incomplete. Strategy awareness was low…

Describes a research program that provides insight into the nature of phylogenetic problems and problem-solving methods and how these might be applied to teaching evolution. Contains a new description of the nature of phylogenetic problems and factors contributing to their difficulty. (AIM)

Traditional conceptions of problem solving in education are critiqued, and a new framework is proposed to conceptualize open- ended problem solving in ill-structured domains. How innovative curriculum design is informed by this conceptualization is described, and research findings from studies in grades 4 through 12 are presented. (SLD)

Introduces a special triangle for which many different problems can be posed on the basis of one unusual property. Presents three problems and considers different approaches for the first problem. Explores other mathematical problems using the "What if not?" strategy that can be used as classroom activities. (KHR)