Analyzed were the relationships between and among mathematical ability, verbal ability, mathematical achievement, general scholastic intelligence, number of years of high school training in mathematics, plans to specialize in mathematics education in college, sex, and the student's performance in solving mathematical problems by the discovery…

This report represents a survey of some of the school mathematics contests which are conducted in the United States. The report is based on information obtained from fifty-nine national, state, regional, and local level contests. National contests are described separately. Brief accounts of certain school mathematics contests, the extent of such…

The teacher's guide for Unit 10 of this SMSG series covers the chapter on problem solving and the chapter on solution sets of mathematical sentences. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed, behavioral objectives…

The purpose of this study was to discover what strategies children use to solve verbal arithmetic problems and which strategies are most successful, and to determine relationships between success in problem solving and strategy and a group of selected student characteristics. Four hundred fifty-five fourth grade students took a test consisting of…

In order to provide high school students with general problem-solving skills, two LOGO computer-assisted instruction units were developed--one on the methods and strategies for solution and a second on the relation between formal and informal representations of problems. In both cases specific problem contexts were used to give definition and…

The problem investigated was the analysis of a complex figure by identifying simpler figures embedded in it. The primary goal was to determine the level of sophistication of analysis employed by children in the primary grades; a secondary goal was to determine if students could be led to expand their analyses. Drawings and problems were prepared…

This study analyzed students' ability to estimate length, area, and answers to numerical computations and to solve problems by trial and error. Randomly assigned to one of three groups, 196 students enrolled in eleventh grade college preparatory classes were given two of three different test batteries. Scores from these tests along with the PSAT…

The calculator is used to solve certain formidable equations, which arise naturally and which may be difficult or impossible to solve by standard methods, by a method of successive approximations. (MP)

The author outlines a possible approach to the discovery of Euler's Theorem that results from a search for a classification of polyhedra. (MN)

The probability of selecting two matching socks is discussed. (MNS)

Competitions at one high school are described: they try to attract as many participants as possible, not just excellent students. In one type, creativity is stressed; another is a tournament; a third involves problem solving activities. Examples are included. (MNS)

Circuits are described, with discussion on how to help students find the algorithms to solve a variety of problems involving circuits. (MNS)

Appreciating the power and beauty of mathematical thought should be an integral component of a student's mathematical education. The meaning of aesthetics in the realm of mathematical reasoning, the relationship of aesthetics to problem solving, the results of two studies, and recommendations for developing aesthetics are included. (MNS)

A possible method of derivation of prescriptions for solving problems, found in Babylonian cuneiform texts, is presented. It is a kind of "geometric algebra" based mainly on one figure and the manipulation of or within various areas and segments. (MNS)