Arguments for and against the use of computers in mathematics classes have centered on whether students benefit from or are merely hindered by practicing computational skills. This paper claims that the true essence of mathematics lies not in computation, basically a mechanical operation, but in problem-solving. Since no amount of computational…

Proposes a criterion for selecting a sequence of objectives from a learning hierarchy and describes a sequence generating algorithm which is designed to generate a minimal memory load sequence from a learning tree. Its effectiveness in generating low memory load sequences from hierarchies that are not trees is also discussed. (RP)

Describes ECAL (extended computer-assisted learning) which was designed to incorporate artificial intelligence ideas to extend traditional CAL tools. Intelligent tutoring systems are discussed; authoring tasks in CAL and intelligent computer-assisted instruction (ICAI) are described; and the general architecture of the system is explained. (8…

A detailed analysis and computer-based solution to a puzzle addressing the arrangement of dominoes on a grid is presented. The problem is one used in a college-level data structures or algorithms course. The solution uses backtracking to generate all possible answers. Details of the use of backtracking and techniques for mapping abstract problems…

Presents a public-key cryptosystem application to introduce students to several topics in discrete mathematics. A computer algorithms using recursive methods is presented to solve a problem in which one person wants to send a coded message to a second person while keeping the message secret from a third person. (MDH)

The design of a re-usable instructional algorithm for computer based instruction (CBI) is described. The prototype is implemented on IBM PC compatibles running the Windows(TM) graphical environment, using the prototyping tool ToolBook(TM). The algorithm is designed to reduce development and life cycle costs for CBI by providing an authoring…

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.…

Error analysis performed on data sets revealed that seventh grade students used a variety of rules of operation for solving the signed-number arithmetic problems. The data sets were obtained from an experimental study in which students were randomly assigned to study either of two lessons written on a computer based education system. The two…

The total system capability, including all the special purpose and general purpose hardware comprising the Airborne Electro-Optical Sensor Simulation (AEOSS) System, is described. The functional relationship between hardware portions is described together with interface to the software portion of the computer image generation. Supporting rationale…

Frame-oriented computer-assisted instruction (CAI) systems dominate the field, but these mechanized programed texts utilize the computational power of the computer to a minimal degree and are difficult to modify. Newer, generative CAI systems which are supplied with a knowledge of subject matter can generate their own problems and solutions, can…

LOGO is a programming language developed at Bolt, Beranek and Newman, Inc., specifically for use in teaching. It provides the student with a set of numerical and symbolic primitives as elements for gradually building extended, complex program structures. The building of these structures is facilitated by a procedure-oriented programming heuristic…

The aim of this article is to identify the natural relationships that exist between using computer programming in BASIC, and some particular mathematical concepts. Specific examples are given for use by the mathematics teacher who has the necessary facilities available. (MN)

The development of computer-assisted and computer-managed instruction for handicapped students involves a number of instructional design issues requiring research. Discussed are algorithmic and heuristic procedures, individual rate of learning, feedback, and instructional task hierarchies.(Author/DB)

A serious drawback in introducing sound into computer programs for teaching foreign language speech has been the lack of an algorithm to turn off the cassette recorder immediately to keep screen text and audio in synchronization. This article describes a program which solves that problem. (SED)

Examples are provided which demonstrate the use of the computer as an instructional aid for the algebra curriculum. While the basic content of an algebra course would remain intact, computer technology can enhance and expand methods of algebra instruction. (JN)