Uses the notion of focusing phenomena to explain how a teacher's actions were connected to her students' interpretations of a linear equation. Conducts interviews and analyzes a high-school classroom that emphasized dependency relationships in real-world situations. Describes how the teacher directed attention away from functional relationships…

Presents a typical cost-allocation problem with possible solutions, including geometric and combinatoric ones. Provides students with a real-life application of the mathematics that they know. (KHR)

Presents activities designed to introduce a mathematical idea having several applications for determining the optimal location for a radio station's transmitter and the best locations for a fire station. Includes student worksheets and solutions. (KHR)

Describes a group project that involves geometry and falls into an area of mathematics known as operations research, which is crucial to making decisions in business and industry. Includes problem statements and project assessment guidelines and illustrates solutions. (KHR)

Explores why it is impossible to make a square from six tangram pieces and, in the process, develops insight into the nature of learning mathematics as well as strategies for teaching. (YDS)

Describes a beginning algebra course that places stronger emphasis on learning to solve problems and introduces topics using real world applications. Students learn estimating, graphing, and algebraic algorithms for the purpose of solving problems. Indicates that applications motivate students by appearing to be a more relevant topic as well as…

Describes some mathematical investigations of the necktie which includes applications of geometry, statistics, data analysis, sampling, probability, symmetry, proportion, problem solving, and business. (MKR)

Two scheduling problems, one involving setting up an examination schedule and the other describing traffic light problems, are modeled as colorings of graphs consisting of a set of vertices and edges. The chromatic number, the least number of colors necessary for coloring a graph, is employed in the solutions. (MDH)

Discusses ways to simulate a probability problem of interest to middle school students in which students calculate the average number of packets of trading cards purchased to obtain a complete set of cards. Simulations utilize a spinner, a table of random numbers, and a computer. Includes the BASIC program utilized in the simulation. (MDH)

Utilizes the problem of determining the number of different ice cream cones and cups that can be made from a choice of 31 flavors to investigate the concepts of combinations and permutations. Provides a set of six related problems with their answers. (MDH)

Presents a public-key cryptosystem application to introduce students to several topics in discrete mathematics. A computer algorithms using recursive methods is presented to solve a problem in which one person wants to send a coded message to a second person while keeping the message secret from a third person. (MDH)

Clapping music for two performers provides the basis for a series of mathematical problems in combinatorics and group theory. A discussion provides insight about how to avoid overlooking global extrema in constrained max-min problems when solving systems of algebraic equations. (JJK)

The simple physics behind the mechanism of the toy are explained. Experimental and mathematical steps are given that help in understanding the motion of the doll-pair. The geometry of the setup is described. (KR)

Students with language and learning disabilities may have difficulty solving mathematics word problems. Use of a sequential checklist, identifying clues and keywords, and illustrating a problem can all help the student identify and implement the correct computational process. (DB)

States that problem-solving skills receive inadequate attention in many mathematics classrooms, and that preservice teacher-education programs can address the lack of instruction in problem solving. Provides rationale for teaching problem solving in the middle grades as an alternative to textbook exercises and worksheets and as a means of…