In this study, a researcher-teacher examined seventh-graders' experiences with a problem-centered curriculum and pedagogy. Analyses of interviews, surveys, teaching journal entries, and audio recordings focused on differences between lower- and higher-socioeconomic status (SES) students' reactions to learning mathematics through problem solving.…

Games and puzzles in which a checkerboard can be used to develop mathematical concepts are described. (SD)

Investigations which employ a search for a number pattern as an approach to solving a geometry problem are discussed. Four problems are presented, with suggestions for testing simple cases, discussion questions, organizing information, and conclusions to be drawn. (MNS)

Outlines the use of computer programs in modeling and simulation to provide a link between science and mathematics education. (GS)

The author observes that checking the closure property is redundant for most number systems and therefore hard for students to understand. He defines several systems which are not closed, develops two concepts related to closure, and provides many related examples. (SD)

The mathematics of the game "Instant Insanity" is described in terms of graph theory, a part of combinational mathematics. (SD)

High-performance computers coupled with highly efficient numerical schemes and user-friendly software packages have helped instructors to teach numerical solutions and analysis of various nonlinear models more efficiently in the classroom. One of the main objectives of a model is to provide insight about the system of interest. Analytical…

This project addressed the question: What knowledge and processes enable individuals to construct and modify representations of novel, nonroutine problems? The theoretical goal was to extend the information-processing theory of problem solving to include processes that have been characterized as restructuring of problems and productive thinking by…

A practicum intervention was designed and implemented over an 8-month period for the purpose of enhancing the mathematics-related cognitive and social interaction skills of primary school students in five kindergarten one pre-first, and seven first grade classrooms. Students interacted in group discussions and activities involving interest…

The Rule Space Model, a cognitive error diagnostic methodology, is discussed, and the philosophy behind it is related to the question of what really determines item response curves. The Rule Space approach integrates Item Response Theory and the algebraic theory of databases. An application of Graph Theory is introduced as a way to acquire a list…

Most teachers of mathematics would agree that a student's major difficulty when studying mathematics is the mastery of "vocabulary." A taxonomy could provide an outline of the various types of vocabulary and could suggest their relative interrelationships. One proposed taxonomy has five levels that seem to recur. The levels seem to have…

Arguments for and against the use of computers in mathematics classes have centered on whether students benefit from or are merely hindered by practicing computational skills. This paper claims that the true essence of mathematics lies not in computation, basically a mechanical operation, but in problem-solving. Since no amount of computational…

On a triangular grid of equilateral triangles an analytical procedure is presented for solving puzzles that require one to measure out a specified amount of liquid from containers of various volumes. (JP)

The nature of measurement, the standard measurement concepts are discussed in terms of children's preconceptions and activities for building measurement concepts through primary school instruction. A broad range of activities including counting, computation, calibration, and relating measure to size is presented. The metric system is briefly…