One mathematician's view of real problems is given. Described (with some humor) are magic retail numbers, the highway bypass, the elliptical table, and the senior-class schedule. (MNS)

An experimental program in New York City to improve the rate of success in first-year algebra is described. Students, teachers, techniques used, and Regents Examination results in the double-period class are described. (MNS)

A drill-and-practice game called "Digits Delight"; the story of Parabella (and Hyp and Elli); and a method for finding inverse functions, using Rubik's cube and algebra, are included. (MNS)

Two problem-solving skills, guess-and-test and simplification, are introduced and reinforced through a variety of motivating problem situations. Solutions of sample problems and extensive directions for the teacher encourage the use of Polya's four-step model of problem solving. (MNS)

Two graphics programs for students in grades six-12 are given. "Circle Through 3 Points" and "Star Polygons." Students gain familiarity with the xy-plane, the radii and centers of circles, and ellipses, while more advanced students learn about parametric equations and using random numbers to produce random shapes. (MNS)

One schools' experiences with mathematics contests are described, with American Pi, the Great Calculator Contest, and the Forest View Math Olympics in problem solving each detailed. (MNS)

Pessimism is voiced that some solutions to the shortage of qualified mathematics teachers will be effective nationally. The author fears that differential pay will only redistribute the supply of available teachers, while retrained teachers will be attracted by nonteaching salaries and, moreover, may not communicate an appreciation of mathematics.…

Three approaches for teaching students to solve inequalities involving absolute values, quadratic expressions, and rational expressions are illustrated. Then one technique that can be used with all of these problems is presented. (MNS)

The author uses Stella the Spider as the main character in a number of three-dimensional geometry problems. Eight of these problems are discussed, with solutions. (MNS)

In this section, suggestions are given for working with radian measures, proving logarithmic properties, the law of cosines as seen by Pythagoras, and an alternative proof of a theorem. (MNS)

The estimation strategies of "using compatible numbers,""averaging," and "rounding" are used. The first two worksheets review easy arithmetic facts and ask students to identify compatible numbers. Worksheet Three introduces averaging and provides practice with rounding, while the fourth worksheet contains problems for group practice. (MNS)

Explores a particular method of searching for roots that lends itself well to discovery learning through writing a computer program. The teacher-student interaction is given, and two computer program listings are included. (MNS)

Use of the computer to simulate or imitate probability problems that are difficult to analyze in any other way is discussed. How the Monte Carlo method works is clarified, with sample problems and programs. (MNS)

In one school, algorithmic development has been infused in the mathematics curriculum. An example of what occurs in mathematics classes since the teachers began using the computer is given, with two students' conjectures included as well as the algebraic justification. (MNS)

The mathematical content involved in self-teaching enrichment models for students in grades 8-12, the pedagogy employed in a summer institute for such students, and the results obtained are presented. (MNS)