A problem-solving approach is developed for secondary or college students to estimate the number of piano tuners in a large city. The answer and method are analyzed for appropriateness. Four similar problems are suggested. (DC)

The theorems and proofs presented are designed to enhance student understanding of the theory of infinity as developed by Cantor and others. Three transfinite numbers are defined to express the cardinality of infinite algebraic sets, infinite sets of geometric points and infinite sets of functions. (DC)

The four-color theorem stating that any map in a plane can be colored using no more than four colors represents a problem suitable for the liberal arts student. Presented is an algorithm for coloring familiar maps through the temporary removal of states bordering three or fewer states. (MDH)

A dialog shows how student-teacher interaction on problems can help students learn. Fifty sample problems are provided as starting points for class discussions from grade three through college. Six purposes such problems can serve are identified. A method of classroom presentation, the mathematical scavenger hunt, is discussed. (MP)

Shows that the ratio of the area of the quadrilateral formed by joining the kth points to the area of the original quadrilateral is constant whether it is convex or concave quadrilateral. Presents many geoboard or dot paper diagrams and geometrical expresssions. (YP)

Notes that the derivative of the area of a circle yields the circumference and the derivative of the volume of a sphere yields the surface area. Explores where these or other such relationships are generalizable. (PK)

Argues that the college preparatory curriculum should include more than three years of mathematics. Presents data indicating that 86 percent of students with less than three years of college preparatory mathematics take remedial mathematics and relatively few students are ready to take calculus when they enter the university. (PK)

The following ideas are presented: (1) an approach to exploring some of the patterns of prime numbers as a junior high activity; and (2) an informal introduction to continuity functions that uses pictures to represent simple physical situations, with suggestions for follow-up exercises. (MP)

The use of exponentiation as a starting point for an open-ended exploration of real number ideas is presented. (MP)

Discusses the use of the mathematics classroom for discovering the relationship among computers, mathematics, and real-world problems. Provides three probability problems and compares the results of three methods, actual trial, computer simulation, and mathematical solution. (YP)

Discusses an activity which models the building of a tunnel by ants using the definitions of derivative and indefinite integral from calculus. Includes a discussion of reasonableness and interpretation of the problem. (MKR)

Reviews for three software packages are given. These include "Equation Math," consisting of three programs for exploring graphs of the equations; "Recycling Logic," instructing students in the basics of reasoning; and "Turboplot-3D," intended for university-level mathematics, physics, engineering, and computer courses. (PK)

Presents three traditional problems from discrete mathematics with alternative solutions and discussion of those solutions. (PK)

Describes a remedial college course in intermediate algebra designed to improve student success rate. Suggests that the course was easy and inexpensive to implement and required a minimum of reorganization. (PK)