The relation between mathematical and computational aspects of recursion are discussed and some examples analyzed. Definition, proof, and construction are considered, as well as their counterparts in computer languages (illustrated with Logo procedures). (MNS)

Describes two methods to resolve common difficulties in solving problems. The first is used when the solver becomes stuck with a problem and no idea seems to come to mind. The second is suitable when the solver is trapped in a loop and goes in circles around the problem. (JN)

A framework is presented for integrating use of a microcomputer into a statistics unit. Descriptions of some programs suitable for the Apple microcomputer and ideas for lessons are included. (MNS)

The LOGO Turtles, originally developed at the Massachusetts Institute of Technology Artificial Intelligence Laboratory for teaching concepts in elementary geometry to primary-age children, can also be used in teaching higher-level mathematics. In the exercises described here, the turtle was programed to traverse curved surfaces. Both geometric and…

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)

Explores the parallel axes representation (PAR) of linear functions. Illustrates the influences of slope and intercept values on the representation. Appended are five exercises for making the PAR programs using BASIC language. (YP)

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)

Computer graphing makes it easier for students and teachers to create and manipulate graphs. Scale issues are nearly unavoidable in the computer context. In interviews and protocol analysis with six students from grade 8, and 12 students from grades 11 and 12, it became apparent that some aspects of scale are clearly understood very early while…

Presented are some current facts about symbol manipulators and their relation to high school mathematics. The development of computer algebra systems is discussed. Five areas of computer algebra needing investigation (skill proficiency, understanding, curriculum content, student homework, and equity) are identified. (MVL)

A computer program, making use of interactive computer graphics, has been developed to help students become fluent in the mathematical procedures needed to understand concepts of addition of waves. Background theory, use of the program, and technical and educational features of the program (written in Fortran) are discussed. (Author/JN)

Discusses dimensionality in Euclidean geometry. Presents methods to produce fractals using LOGO. Uses the idea of self-similarity. Included are program listings and suggested extension activities. (MVL)

Explores the concept of extraneous roots in radical equations using an alternative to traditional algebraic methods. Using calculator- or computer-based graphs, accounts for extraneous roots by examining the four possible cases of systems of equations that can produce the solution to the radical equation. (MDH)

Examines the historical development of logarithm tables. Suggests that students should write computer programs to calculate logarithms. (PK)

Uses a LOGO program and probability to solve systems of equations. Provides a physical model and a LOGO model. Lists programs and explains the methodology used. (MVL)

This manual provides a resource for mathematics teachers who wish to take advantage of the extensive library of computer software materials available to expand and strengthen classroom instruction. Classroom management procedures, software duplication guidelines, copying procedures of diskettes for MS DOS and Apple II computers, and methods for…