This volume, a part of the Elements of Mathematics Program (EM), provides the student with an experience in developing a mathematical model for a "real-life" situation. After discussing the process of mathematization by reference to geometry, and presenting a flow-chart diagram describing the relationship of mathematical models to real…

The purpose of this doctoral thesis was to collect, analyze, and evaluate research of written problems in elementary school mathematics conducted between 1925 and 1965, and to determine generalizations resulting from the studies fulfilling certain criteria. The analytical-documentary method of research was employed in the study. A total of 239…

The purpose of this study was to investigate the effects of the addition of geometry and geometric illustrations as a supplement to the teaching of factoring second-degree polynomials. Sixty eighth-grade students with certain prerequisite skills were randomly assigned to six treatment groups. Each group was taught factoring of quadratic…

This is one of a series of reports on the National Longitudinal Study of Mathematical Abilities (NLSMA). It is the report of a dissertation that sought to identify characteristics correlated with problem solving. The type of problem used was classified as "insightful," meaning nonroutine and challenging but not of a trick or puzzle type.…

This extension of Harris' classification system permits classification of the interval-scale properties of any 2 x 2 (two person, two choice) game. The system is compared to taxonomies developed by various previous researchers. It is shown to permit compact description of any 2 x 2 game as an octet of numbers. It also permits rapid classification…

A problem solving card program was constructed on the basis of Gagne's hierarchical sequence model to teach Unit II of the Physical Science Study Committee (PSSC) course in physics. The program was used to diagnose areas of difficulty in problem solving. Remediation on 52 identified mathematical abilities involved in the problem solving tasks was…

When a simple game was presented as a challenge to a primary-school girl, she solved the problem, and went on to generalize her solution. (SD)

Performance on several word problems used in the National Assessment of Educational Progress is discussed. Errors are analyzed for different age groups, and the overall findings are compared with results of related research. Implications for instruction are derived. (SD) Aspect of National Assessment (NAEP) dealt with in this document: Results…

Potential uses for computers include: programing the solutions to problems; simulating situations in order to test hypotheses; gaming, as a study of probability and statistics; and practicing, testing, and tutoring. (MP)

Some problems and classroom problem-solving settings presented in a mathematics methods course for elementary teachers are described and some results of student's involvement in the program are illustrated. (MN)

An example of a mathematical modeling problem involving student enrollment and attrition is given along with a discussion of methods and conclusions. (MN)

An example is given of a mathematical modeling problem involving the number of people that get on and off an elevator and the expected number of stops it makes. (MN)

The author outlines where we've been and where we ought to be going with computer-enhanced mathematics especially with respect to student motivation and problem solving. (MN)

An analysis of sixth-grade students' problem solving found the process to be a series of behaviors for each of which an explanation can be elicited. Advocates that teachers use questioning and discussion techniques rather than a "right-wrong" approach to the evaluation of verbal arithmetic problems. (CP)

Described is the development of a simulation, or model of an existing congested pedestrian crossing situation by elementary school students in order to conduct trials of their solutions. (MN)