Suggests that using the iconic and computing features of a spreadsheet enhances the transition from natural language sentences to pictorial and numerical representations of algebraic word problems. Presents work performed in a lab setting with preservice and inservice teachers enrolled in contemporary general mathematics and problem-solving…

In a cooperative research program, classroom teachers and university researchers developed and implemented a contextualized performance-based assessment in mathematics. The assessments were intended to model what students may do in the course of daily activity and designed to assess problem solving, and conceptual and procedural understanding.…

Our research is concerned with teacher's knowledge, and especially with teacher's processes of learning, in the classroom, from observing and interacting with students' work. In the first part of the paper, we outline the theoretical framework of our study and distinguish it from some other perspectives. We argue for the importance of…

The purpose of the study was to present a precise interpretation of the Poincare-Hadamard conception of mathematical problem solving, to provide a transition from theory into practice by making tactical suggestions on how to generate productive problem-solving thought, and to translate these specific suggestions into tentative objectives and…

Two mathematical brainteasers, with solutions depending on involved trial-and-error processes, are shown to have ingenious solutions. (MP)

Polya claims that true problem solving is accompanied by the cognitive activities of mobilization, organization, isolation and combination, and by the evaluations of relevancy, proximity, and quality. Evaluations occur as a result of monitoring cognitive activities. According to Polya, these particular cognitive activities are a necessary part of…

If equivalent operations are performed on the left term and right term of an equation, a new equation results. This principle allows one to produce equations with a variable isolated on one side and its value(s) on the other. It also underlies problem-solving in situations where equations are not explicitly used, but the problem calls for…

Solutions are given to the problem of determining the number of regions obtained by connecting points on the circumference of a circle; implications are drawn for teaching problem solving to students. (DT)

Modular arithmetic is used to show that there is at least one Friday the 13th in every year. A case-by-case proof is outlined and a proof of the general case is given. (DT)

Discussion is focused on standard teaching procedures that contain the elements of modern mathematics. Of the various methods which have been tested, it is concluded that the solving of problems remains the most effective basic activity. A sample collection of problems is presented to indicate relationships and the principles they illustrate. (RP)

Presents content and approaches for teaching geometry at the K-6 level. By use of the discovery technique, the author demonstrates how various topics can be taught beginning in three-dimensionalspace with the study of solid shapes. The sequence begins with the sorting of solid shapes, is followed by the ordering of solids by size and leads to the…