The paper details a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts to force limit discussion into the language of individual real numbers and equality. The system of near-numbers…

Divisibility tests for digits other than 7 are well known and rely on the base 10 representation of numbers. For example, a natural number is divisible by 4 if the last 2 digits are divisible by 4 because 4 divides 10[sup k] for all k equal to or greater than 2. Divisibility tests for 7, while not nearly as well known, do exist and are also…

In this article, the author believes that a visual image of the number system is helpful to everyone, especially children, in understanding what is, after all, an abstract idea. The simplest model is the number line, a row of equally spaced numbers, starting at zero. This illustrates the continuous progression of the natural numbers, moving to the…

The modular exponentiation, y[equivalent to]x[superscript k](mod n) with x,y,k,n integers and n [greater than] 1; is the most fundamental operation in RSA and ElGamal public-key cryptographic systems. Thus the efficiency of RSA and ElGamal depends entirely on the efficiency of the modular exponentiation. The same situation arises also in elliptic…

This programed mathematics textbook is for student use in vocational education courses. It was developed as part of a programed series covering 21 mathematical competencies which were identified by university researchers through task analysis of several occupational clusters. The development of a sequential content structure was also based on…

This is the first volume of a series produced by the State Education Department of the University of the State of New York. Mathematics objectives and sample items included were originally developed by four local school districts and are not intended to be official or comprehensive, but an aid to teachers in constructing curricula and making…

The first of three volumes of a mathematics training course for Navy personnel, this document covers a wide range of basic mathematics. The text begins with number systems, signed numbers, fractions, decimals, and percentages and continues into algebra with exponents, polynomials, and linear equations. Early chapters were designed to give insight…

Discusses the history of different methods of representing numbers and how these representations facilitated counting and computing devices such as the abacus. (MDH)

Modular arithmetic is used to find the frequency of Friday 13th's in any year. (MM)

After briefly presenting possible origins for the use of the decimal system for counting and the duodecimal (base twelve) system for many measures, a notational scheme using six positive'' digits and six negative'' digits is presented. Examples and algorithms using this set of digits for operations with whole numbers, fractions, and in…

Developed by a committee of the National Council of Teachers of Mathematics, this publication is designed to help teachers provide interesting and worthwhile learning opportunities for slow learners in grades five through eight. It employs a variety of teaching strategies, many not commonly known or practiced, which are particularly helpful with…

Arithmetic reading can be made lighter if teacher explains vocabulary, selects simple text, and aids in improving reading skills. (DS)

Discusses the traditional number systems and the origin of the number names used by several African peoples living south of the Sahara. Also included are limitations in African mathematical development, and possible topics for research. (RP)

Evaluates the National Numeracy Strategy (NNS) as a successful framework for promoting confidence and competence with numbers and measures, an understanding of the number system, a repertoire of computational skills, and the ability to solve number problems in a variety of school contexts. Suggests taking steps to change children's mathematical…