Proportionality can be considered among the most important mathematical notions in the middle school math curriculum (grades 5 to 8). It is the capstone of elementary arithmetic, number, and measurement concepts, and at the same time one of the most elementary understandings one needs for more advanced mathematics. Understanding proportionality is…

This paper examines the use of analogies in statistics instruction. Much has been written about the difficulty social work students have with statistics. To address this concern, Glisson and Fischer (1987) called for the use of analogies. Understanding of analogical problem solving has surged in the last few decades with the integration of…

Since Polya, Wertheimer, and Hadamard's descriptions of qualitative reasoning strategies used by scientists and mathematicians, very little data have been collected on whether these strategies are actually used by experts. This study used video-taped thinking-aloud interviews to examine the problem solving strategies of professors and advanced…

A teacher offers six suggestions for giving students opportunities to exercise their commonsense thinking skills. This allows the teacher to ask rather than tell, listen rather than talk, and allows the children to provide for themselves. (MT)

The author reviews the role of logic problems in teaching thinking strategies to LD students. Devising one's own written logic problems is advocated to present less wordy tasks. (CL)

Differences between arguing "ad hominem" and "ad rem" are explored in two case studies of fifth-grade gifted boys, demonstrating the need for gifted children to be helped to approach problems by considering issues rather than personalities. (Author/DB)

One of the best tools for sharpening students' problem solving skills can be found in the mystery story, which calls for logical thinking, paying attention to detail, and distinguishing between facts and assumptions. Activities that can help to develop problem solving skills are described along with several references to mystery magazines and…

Three mathematical problems are discussed to point out the need to use problems with more than one solution, but at least one readily available solution. As well as encouraging logical thinking, problems should involve pattern recognition and the generation of guesses to be tested. (MNS)

Three studies investigated the effects of concrete versus abstract wording and negative versus positive premises on the difficulty subjects had in solving several kinds of reasoning tasks. Subjects for all three studies were college undergraduates who received booklets containing either hypothetical, disjunctive, or linear syllogisms. Each booklet…

The purpose of this paper is to demonstrate methods for developing cognitive processes in adult students. It discusses concept formation and concept attainment, problem solving (which involves concept formation and concept attainment), Bruner's three stages of learning (enactive, iconic, and symbolic modes), and visual thinking. A curriculum for…

Suggests activities that can assist in learning how to develop hypotheses. (HOD)

A program designed to teach cognitive strategies through logical problem-solving and developed for elementary learning disabled students is presented. For each problem set, the instructional procedure involves a discovery activity, discussion, conclusion, follow-up activities, and integration. Five samples of the program's problem sets (e.g.,…

Suitable for secondary school students, the workbook provides flowcharting activities to help students understand the logical steps used in problem solving. Before applying the flowcharting procedures to mathematical problems, students are first introduced to familiar non-mathematical problems such as sharpening a pencil or eating peanuts. Section…

One third-year clinical clerkship in pediatrics has included Sherlock Holmes mysteries in its introductory curriculum, providing students with a model clinical problem-solving process and a list of issues on which they will need information. The nonclinical cases provide an effective and entertaining vehicle for learning clinical reasoning. (MSE)

This article details an approach to teaching one step in a mathematics word-problem-solving strategy, that of organizing the facts. A lesson plan is offered which involves directed instruction and supervised practice in five strategies for organizing facts. (DB)