The National Center for Leadership in Intensive Intervention (NCLII), a consortium funded by the Office of Special Education Programs (OSEP), prepares special education leaders to become experts in research on intensive intervention for students with disabilities who have persistent and severe academic (e.g., reading and math) and behavioral…

This paper argues that the introduction of the scientific method in the very rich environments of the natural sciences or human sciences may disguise the process and create difficulties for students because of the multiplicity of variables involved, whereas the variables present in a mathematical context can be readily manipulated and their…

Fourteen steps are suggested: perceive problem, decode written symbols, formulate general meaning, translate the general message into the mathematical message, determine question(s), gather data, analyze relationships, decide on processes, estimate answers, encode data into mathematical sentences, perform operations, answer questions, and check…

An exhibit at the San Francisco Exploratorium is used to discuss problem solving and illustrate optimization. The solution is discussed in detail. (MNS)

The problem "Given three planar points, find a point such that the sum of the distances from that point to the three points is a minimum" is discussed from several points of view. A solution that uses only calculus and geometry is examined in detail. (MNS)

Finding a fractional number equal to an infinite decimal is solved by two usual methods. Then a third method is discussed that allows students to avoid having to confront the idea of an attained infinity of symbols. (MNS)

The article offers suggestions for helping gifted elementary students learn to use independent thinking skills to challenge their own thinking as well as to solve mathematical problems. (DB)

A situation is presented that is intended to lead to open-ended mathematical discussions that allow students to conjecture, discover, and prove mathematical statements. (MP)

Discusses some theorems and properties of figures produced when circles are tangent to one another. (GA)

Demonstrated is how the concept of equivalence classes modulo n can provide a basis for solving a wide range of problems. Five problems are presented and described to illustrate the power and usefulness of modular arithmetic in problem solving. (MNS)

By translating inequalities into equations (e.g., x greater than 0 can be written x- absolute value of x = 0) and forming equations for unions and intersections of solution sets, students can develop equations for polygons. The method can be generalized to yield equations in three dimensions. (SD)

Mathematical models that are used to solve facility location problems are presented. All involve minimizing some distance function. (MNS)

Algorithms to determine the optimal locations of emergency service centers in a given city are presented, with theorems and proofs. (MNS)

Evaluates 25 software packages (consisting of more than 40 individual programs), all aimed at one or another facet of mathematics learning. Title, source, current price, and detailed review (indicating the educational quality of the package) are included for each entry. (JN)

The author arranges 26 current states of mathematical knowledge (in relation to solving a problem) in an informal taxonomy and comments on them. (MNS)