The author argues that the idea of canonical elements provides a coherent relationship between equivalence relations, the basis of modern approaches to too many mathematical topics, and the traditional aspect of computation. Examples of equivalent relations, canonical elements, and their calculations are given. (MK)

The historical development of the integers, the rationals, the reals, and the complex numbers is traced. (MK)

Discusses mastery goals and developmental levels of students aged 3-7 for learning numbers in informal situations. (KHR)

In most languages encountered by linguists, the numerals, considered as a paradigmatic set, constitute a morpho-syntactic problem of only moderate complexity. The Indo-Aryan language family of North India, however, presents a curious contrast. The relatively regular numeral system of Sanskrit, as it has developed historically into the modern…

The topics discussed are, "Helping Students Understand the Distributive Property,""Converting from Base 10: Nonintegral Bases?,""Rapid Mental Squaring of Mixed Numbers," and "Some Nonstandard Binary Operations and their Properties." (JT)

Worksheets for the lower grades involve locating numbers on the number line; the activities for the upper levels focus on the estimation of sums and products. (DT)

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)

Negative numbers extend our number line and greatly simplify our calculations, but sometimes students struggle with the concepts. These fun activities will help kids to make sense of the "other half" of our number system.

The teacher's guide for the third unit of this SMSG series covers the two chapters on number theory and on the integers. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed, behavioral objectives are stated, and a time…

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)