By using ill-structured problems and examining problem- solving processes, this study was conducted to explore the nature of solving complex, multistep problems, focusing on how prior knowledge, problem-solving process utilization, and analogical problem solving are related to success. Twenty-four college students qualified to participate by…

The cognitive difficulties encountered by 40 high school and 13 college students beginning to learn the proof technique of mathematical induction were investigated. Students provided data in the form of proof-writing and proof-analysis tasks followed by interviews to clarify their written responses. Both groups of students had significant…

This book is designed to present mathematical problems and tasks that focus on the National Council of Teachers of Mathematics (NCTM) curriculum and evaluation standards in the context of aerospace activities. It aims at actively engaging students in NCTM's four process standards: (1) problem solving; (2) mathematical reasoning; (3) communicating…

This paper describes an intervention in two Algebra II classes in which the graphing calculator was incorporated into the curriculum as often as possible. The targeted population consisted of high school students in a growing middle to upper class community located in a suburb of a large city. The problem of a lack of understanding of the…

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…