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…

This is the second unit of a 15-unit School Mathematics Study Group (SMSG) mathematics text for high school students. Topics presented in the first chapter (Informal Algorithms and Flow Charts) include: changing a flat tire; algorithms, flow charts, and computers; assignment and variables; input and output; using a variable as a counter; decisions…

The first part of this four-part dissertation reviews conceptual and operational approaches to human communication systems. A new conceptual model for studying communication, General Algorithm for Studying Structuring in Complex Systems (GASSICS), is developed in the second part, and an operational method for applying GASSICS is presented in part…

A case is given against teaching division of fractional numbers. Types of problems usually solved by division are solved by methods involving only multiplication. (JP)

The purpose of this study was to ascertain whether children in grade 3 who differ in cognitive processing capacity add and subtract differently. The researchers drew upon information from three sources: individual results from a battery of 14 tests, an objective-referenced achievement test measuring a variety of arithmetic skills related to…

To make training cost-effective for its small systems customers, Digital Equipment Corporation provides self-paced training packages for several years that can be used by its customers on-site. To control the quality of this training, Digital is now incorporating computer managed instruction (CMI) into some of these packages. This CMI component…

The 15 papers and summaries of presentations in this collection provide technical information and guidance offered by representatives from federal agencies and private industry. Topics discussed include physical security, risk assessment, software security, computer network security, and applications and implementation of the Data Encryption…

Refinements of work with calculator algorithms previously conducted by the author are reported. Work with "chaining" and the doing/undoing property in addition and subtraction was tested with 24 third-grade students. Results indicated the need for further instruction with both ideas. Students were able to manipulate the calculator keyboard, but…

As the use of online literature searching systems increases, the need for reducing the amount of nonrelevant material encountered by the users becomes more apparent. One method for achieving greater selectivity in document retrieval is by using relevance (or utility) estimates from past users to estimate document values for future users. However,…

A visual problem-solving technique applicable to several different classes of mechanics time-dependent problems is discussed. The computer is used to solve the equations of motion of various mechanical systems by one of several standard methods, and the solutions are displayed in time increments. A specific example is provided to illustrate this…

Ninety students in an introductory chemistry class were divided into three groups to test the power of algorithms to increase logical thinking abilities. The experimental group received approximately 10 hours of laboratory instruction based on the use of procedural algorithms. Experiment and control groups were tested for logical thinking…

Abstracts of 28 research reports are provided. The reports were prepared by investigators for presentation at the 54th annual meeting of the National Council of Teachers of Mathematics. A broad range of topics related to mathematics education are covered. Three reports concern the effects of differing presentations of mathematics, four are related…

The absence of suitable external criteria is a recurrent problem for test, battery, and inventory developers in selecting items or tests for inclusion in final operational instruments. This report presents a computing algorithm developed for use when no adequate external selection criterion is available. The algorithm uses a multiple linear…

The concept of an algorithm derives from the physical sciences, but it has often been misunderstood and misapplied in the social sciences and in education. The theoretical and practical significance of algorithms stems from their applicability to problems of learning, instruction, and instructional design, and they may potentially provide the…

The purpose of this study was to compare the repeated subtraction method of long division of a partitioning distributive method, both taught by recording manipulation of popsicle sticks. Two instructional units were prepared. Twelve fourth grade classes were used, with six being taught one approach and six using the other. Tests consisting of…