The operation of rounding is shown to lead into an investigation of an abstract mathematical system. Properties of the system are discussed and graphs of the rounding function are drawn. Some questions for discussion are given. (MP)

A theorem on divisibility in decimal and non-decimal numeration systems is developed; its use in a series of discovery-centered lessons is suggested. (DT)

Reports on the development of a course in modern mathematics for elementary school teachers. The subject matter for the course is concentrated on whole numbers, integers, and rational numbers. Ideas of logic and set theory are brought into the discussion incidently as needed for developing the number systems. Part 1 of the course is a brief essay…

An approach close to the original Greek geometric point of view regarding the question and proof of the irrationality of the square root of two is given. (MN)

Tests for divisibility in bases 2 through 10 are presented. Two strategies used by a group of fourth-year students are described. (MNS)

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…

Representation of integers in various bases is explored, with a proof. (MNS)

The archaeology of mathematics is discussed by tracing a portion of the research of Otto Neugebauer and Abraham Sacks. Patterns found on an ancient cuneiform tablet are explored. (MK)

Born in 1707, Leonhard Euler was the son of a Protestant minister from the vicinity of Basel, Switzerland. With the aim of pursuing a career in theology, Euler entered the University of Basel at the age of thirteen, where he was tutored in mathematics by Johann Bernoulli (of the famous Bernoulli family of mathematicians). He developed an interest…

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…

This booklet has been written for elementary school teachers as an introductory survey of the real number system. The topics which are developed include the number line, infinite decimals, density, rational numbers, repeating decimals, irrational numbers, approximation, and operations on the real numbers. (RS)

In a thesis written for the Doctor of Arts in Mathematics, the connection between Euclid's algorithm and continued fractions is developed and extended to n dimensions. Applications to computer sciences are noted. (SD)