We tested human performance on the Euclidean Traveling Salesman Problem using problems with 6-50 cities. Results confirmed our earlier findings that: (a) the time of solving a problem is proportional to the number of cities, and (b) the solution error grows very slowly with the number of cities. We formulated a new version of a pyramid model. The…

This paper outlines the increasing prospects for improving the problem solving component of future mathematics programs. Of particular interest is the development of a viable growth schema for general problem solving strategies and skills. The plan presented here provides for five levels of problem solving sophistication. The main body of the…

Outlines the academic responsibilities connected with the nation's transition to the metric system and indicates how these responsibilities relate to the general task of problem solving. (GS)

Two methods of solving problems are discussed: the step method and the translation method. The results of training students to use these methods are compared. (SD)

A series of problems concerning a geoboard with "holes" is suggested. (SD)

Two experiments on the translation of verbal expressions into mathematical expressions are described. The author concludes that the usual way of training students to solve arithmetic word problems is inadequate. (SD)

Elucidated is the relationship among three threads of mathematical investigations: Kirkman's schoolgirl problems, finite geometries, and Euler's n-square officer problems. (JP)

This material was prepared to help students understand the algebraic process involved in solving mixture problems. The paper copy is designed to be used with a 25-minute audiotape. Students are given a problem which is solved step by step; then they are to answer questions about each step. (MNS)

This study involved the development and experimental tryout of 22 lessons designed to teach 23 primary grade children a set of specific procedures, focusing on the drawing of meaningful diagrams, for analyzing and solving arithmetic story problems. Major dependent variables studied were gain on (1) a 20-item test on stories of the eight types…

Sex-related differences in mathematical problem solving performances and intellectual abilities were investigated. A battery of 19 "reference" tests for intellectual abilities and a mathematical problem solving test were administered to 82 fourth-grade females and 97 fourth-grade males. Sex-related differences were found for only two of the…

This pamphlet is designed to give help in developing problem solving by examples of techniques at grade levels one through six. A number of illustrations are presented of problems that are typical of the types appropriate at each grade level. For each problem, a suggestion of a solution appears with alternative methods suggested in several cases.…

Three preliminary studies and one exploratory main study investigated the effect of calculator use on elementary, middle, and secondary school students' solution methods on routine mathematical problems. Items were identified for which a longer and a shorter solution method existed. Half of the sample worked these using a calculator and half used…

TEN WORD-PROBLEMS ARE PRESENTED IN EACH OF THE FOLLOWING AREAS--MULTIPLICATION, DIVISION, FRACTIONS, AND DECIMAL FRACTIONS. SPECIALLY PREPARED TO MOTIVATE CULTURALLY DEPRIVED STUDENTS IN MATHEMATICS, THE PROBLEMS CONTAIN REFERENCES TO OBJECTS FAMILIAR TO THESE STUDENTS.