This paper deals with the problems of rigorous research within the dynamic organizational context. Definitions and axioms establish the natures of a social problem, a social intervention program, continuous program monitoring, a method of describing alternative treatments, treatment effect testing, and programmatic change. These definitions and…

This volume contains four articles by A. A. Krutetskii. The first article is a report of a study of individual differences in ability to solve algebra problems. The second article reports on a two-year study of a young girl who showed exceptional mathematical giftedness. Article three presents a summary of the author's theoretical position on the…

This teacher guide is part of the materials prepared for an individualized program for ninth-grade algebra and basic mathematics students. Materials written for the program are to be used with audiovisual lessons recorded on tape cassettes. For an evaluation of the program, see ED 086 545. In this guide, the teacher is provided with objectives for…

This literature review focuses on determining the psychological variables related to problem solving and presents arguments for self-correcting manipulatives as a media for teaching problem solving. Ten traits are considered: attitude, debilitating anxiety, self-concept, orderliness, set, confidence, impulsive/reflective thinking, concentration…

A quasi-systematic strategy of devising rule sets for problem solving is applied to ruler and compass geometrical constructions. "Lower order" rules consisting of basic skills and "higher order" rules which govern the selection and combination of lower order rules are identified by an analysis of problem types; three types of…

The purpose of this investigation was to determine the relationship between the acquisition of conservation skills and achievement in mathematics. The conservation skills measured were numbered, mass, area and volume. Mathematics achievement was measured by the Computation, Concepts, Problem-Solving and Total Mathematics scores on the Metropolitan…

This booklet contains some 80 problems in mathematics suitable for computer solution. The problems range from very simple to complex. Problems have been included from most mathematic disciplines, including number theory, analytical geometry, probability and statistics, trigonometry, equations, and sequence and limits. For the most part these…

This last paper in a set of four reviews research on a wide variety of computer applications in the mathematics classroom. It covers computer-based instruction, especially drill-and-practice and tutorial modes; computer-managed instruction; and computer-augmented problem-solving. Analytical comments on the findings and status of the research are…

This paper focuses on the relationship of verbal factors to mathematics achievement and reviews research from 1930 to the present. The effects of verbalization in the mathematics learning process are considered; mathematics functioning as a unique language in its own right is analyzed. Research on the readability of mathematics materials and…

The game of roulette is analyzed. (SD)

Six different methods were used by students to solve the problem of finding the area of a given trapezoid. A seventh method used by textbooks is also discussed. (MP)

Topics covered include alternate methods for finding LCM and GCF, imaginative word problems, and a primes-breakdown method of factoring quadratics. (MP)

The objective were to explore some of the ways in which the calculator can be used and to determine the effects. Areas covered are: computation, mathematics readiness, problem solving, and discovery learning. (MP)

This problem solving strategy is illustrated by examples from the fields of algebra, trigonometry, geometry, and calculus. (MP)

Several examples of student-written programs "teaching" a computer to guess systematically in finding a number between 0 and 10,000 are illustrated. These lend support to the contention that rather than being a "natural" application, using a binary search is a learned technique. (MN)