Detailed is a strategy for teaching the transformation of word problems into equations, equation systems, or inequalities. Classroom experiments using the method are described and are favorable. The underlying philosophy of the method is that the transformation will be accomplished by means of comprehension at first, but in the second stage the…

Human information processing is analyzed in terms of eight fundamental concepts: procedures, operations on procedures, frames, planning language or meta-language, heuristics, knowledge in other forms, critics, and pointers. Examples of this processing are given. (MK)

The research reported in this paper was designed to analyze the incidence of use of higher-order rules by students solving geometric construction problems. A carefully selected set of construction problems was subjected to rigorous a priori analysis by mathematics educators to determine what basic and second-order rules might be used by able high…

This study compared two techniques of teaching verbal problem solving. The consensus method is a commonly used decision-making strategy, while the expository (control) method is the most familiar teaching strategy for verbal problems. Two sets of sixth-grade students under two teachers were divided into treatment groups. Both sets of subjects were…

Investigated was the problem-solving ability of secondary school students as it related to their verbalization. Experimental treatment followed the students' demonstration of awareness of some mathematical concept. The four experimental groups included students who: (1) did not verbalize, (2) verbalized correctly, (3) verbalized incorrectly and…

The series is a collection of translations from the Soviet literature of the past 25 years on research in the psychology of mathematical instruction and the related methods of teaching mathematics. The aim of the series is to acquaint educators and teachers with directions, ideas, and accomplishments in the psychology of mathematical instruction…

The nature of insight is discussed as it relates to mathematical models. Intuition and the intuitively obvious are argued to have no necessary connection with models. (MP)

A small-group tutorial technique is described that develops creative thinking in students having difficulties in problem solving. (MP)

Chapter two of the book, "Problem Solving with Calculators,"is presented. Topics covered include parts of a problem, steps in problem solving, guessing, and methods of calculation. (MP)

Recommendations for teaching problem solving stem from a discussion of the differences in the functioning of the left and right hemispheres of a person's brain. (JT)

This article examines the Pythagorean Theorem from a geometric point of view by suggesting some natural extensions of the theorem. The use of a more general theorem to prove a difficult one is suggested, where possible. The article includes figures and proofs. (Author/MA)

The vast majority of people are most familiar with arithmetic in base ten. This article presents a follow-up on a problem with several divisibility tests valid in base ten which are related to Freitag's general test and which follow directly from it. Base 13 is also explored. (Author/MA)

Described are random, systematic, and guided trial-and-error strategies for problem-solving with a computer. (JH)

The paper-and-pencil game "Tri" is described. The authors argue that students gain logical skills by playing the game, and that the game lends itself to the introduction of diverse mathematical ideas. (SD)

Suggests a way of helping students apply their reading skills to solve math word problems. Claims comprehension monitoring is a set of skills that can be applied to both reading and math problem solving to help students integrate their reading skills with their computational skills. (MS)