How set theory, combinatorics, probability, and the study of algorithms can be used in solving two problems is described in detail. Three computer programs are listed. (MNS)

A procedure is described that enables students to perform operations on fractions with a calculator, expressing the answer as a fraction. Patterns using paper-and-pencil procedures for each operation with fractions are presented. A microcomputer software program illustrates how the answer can be found using integer values of the numerators and…

Four methods of filling a square using programing with Logo are presented, with comments on children's solutions. Analysis of the mathematical or programing concepts underlying a few simple algorithms is the focus. (MNS)

Described is a simple algorithm that can be used for the input, arithmetic manipulation, and output of large integers in their exact representations. Three BASIC programs are included that apply this method to the problem of multiplication of large integers, computation of factorials, and the generation of palindromic integers. (MNS)

This paper outlines the development of an activity that uses the computer's unique capabilities to provide students with a meaningful and highly motivating experience with the graphing of equations. The basic design of the game calls for the computer to display a coordinate grid on which it graphs any equations that are typed in by the student.…

Ways to combine the strengths of teacher and computer are suggested. Multiplication concepts and an algorithm for multiplication are taught in the same lessons. The computer is used as an electronic chalkboard to teach at a semiconcrete level. The computer program is included. (MNS)

Programing a microcomputer to solve problems in whole-number arithmetic, rather than using the built-in operations of the computer, is described. Not only useful, it also enhances important mathematical concepts and is adaptable to a range of student abilities. (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)

Describes the use of simulation to introduce the bootstrapping technique of creating confidence intervals for the mean, median, and variance. These bootstrap confidence intervals are compared to the traditional confidence intervals for the purpose of analyzing accuracy of the technique. A Minitab program to produce confidence intervals is…

Suggestions are given for having students write or modify computer programs for listing prime positive integers and continued fractions, to help them discover mathematical concepts. Sample programs are included. (MNS)

Presents an algorithm to estimate pi by approximating a unit circle with a sequence of inscribed regular polygons. Demonstrates the application of the algorithm with a hand-held calculator and an Apple computer. Provides a program to calculate pi in Pascal programing language. (12 references) (MDH)

Studies the simple dynamical system of the pendulum and the chaotic behavior that occurs when the pendulum is both damped and driven. Provides an algorithm and BASIC program for the numerical solution to the differential equations encountered in the discussion. (MDH)

Presents a series of solution methods to the Eight Queens Problem of placing eight queens on a chess board so that no one queen can capture another. Solution methods progress from empirical approaches to the use of computer algorithms. Geometric transformations are used to find other solutions. (MDH)