The reasons for teaching programming in school are indeed manifold. Programming can for example be utilized as a vehicle for understanding and learning particular mathematical subject matter, or as a tool for solving mathematical problems. In this paper, however, we propose to utilize programming as a vehicle for developing mathematical…

Typical difficulties involved in solving combinatorial problems are examined and seven common pitfalls are discussed. (MP)

A rationale is provided for the notion that mathematical games can be a valuable resource for the stimulation and support of student collaboration and cooperative classroom mathematical discussion. Included are examples of tangram games, people games, and board strategy games. (JJK)

Student research projects are open-ended questions or sets of questions intended to give undergraduate students experience doing introductory mathematical research. Proposed is an investigation of a Faro shuffle that is performed by cutting the deck exactly in half and then perfectly interleaving the cards of the two halves. (Author/JJK)

Presented is the solution to the problem of calculating the probability of winning or losing a game played by moving a counter from the center of a hexagonal grid according to the number shown after the toss of a die. The exercise is an example of an interesting mathematical investigation. (MDH)

Fifth graders performed better than third graders on discovering the function rule relating two number pairs. Task difficulty and mode of presentation (graphic or symbolic) varied by function. The children seemed ready to relinquish a hypothesis in the face of disconfirming evidence. (MNS)

Presents three hands-on, discovery geometry lessons based on the use of special pieces called Polydrons by a fifth-grade class to build and investigate special properties of polyhedra and to stimulate students to think geometrically. Includes reproducible student worksheets. (MKR)

These worksheets suggest activities through which secondary school students may be introduced to the ideas of simulation. All can be played as games to give students a feel for the situation modeled; most use coins or dice and a few use random digits. Directions are detailed for each of the 17 worksheets, with variations suggested for many. (MMS)

Three examples are given in which students create their own Logo software to explore the topics of number patterns and operations, fractions, and decimal parts in measurement. (MNS)

This review features new examples of using the computer relative to college-level mathematics to enhance pedagogy, solve problems, and model real-life situations. Included is a LOGO program that can be used to create and to stimulate subsequent investigations of spirolaterals, those figures generated by repeatedly drawing basic loops. (JJK)

Discusses the use of computer visualization to motivate and support mathematical dialogues. Describes the "Scientific Visualization Software Suite," a set of public domain visualization tools from the National Center for Supercomputing Applications. (Author/MDH)

Presents activities that use visual-geometric models to help students develop their understanding of exponents and division of powers with the same base. Presents opportunities for students to discover patterns for themselves and communicate these findings to others. (MDH)

Presents activities that utilize representations of the side, front, and top views of three-dimensional configurations of blocks to develop spatial-visualization skills and aspects of the concept of function. Provides worksheets of these open-ended investigations. (MDH)

This collection of documents promotes simulation as an attractive topic in mathematics instruction that provides game-like activities likely to interest pupils, by illustrating the important ideas of probability and showing how mathematical models can be used in practical problems clearly relevant to everyday life. While computer programs written…

Described is an alternative first year algebra program developed to bridge the gap between the NCTM's Curriculum and Evaluation Standards and institutional demands of schools. Increased attention is given to graphing as a context for algebra, calculator use, solving "memorable problems," and incorporating geometry concepts, while…