The death of Paulo Freire in May 1997 was a momentous event for educators everywhere, especially adult educators, and a sad one for those who knew and loved him. The author has been thinking and writing about Freire's work for many years, exploring his contribution to a radical politics of adult education. While Freire's work features strongly in…

Elementary number theory is a standard topic in the mathematical preparation of preservice elementary teachers. To understand elementary number theory, a student must be comfortable with the representation of natural numbers as the product of primes. This paper discusses methods for accomplishing this goal in a mathematics course. It also…

This textbook presents the divisions of arithmetic in their natural order. The fundamental operations upon integers, common fractions, decimals, denominate numbers, and numbers expressed by letters, are followed by their applications to business and to various employments. The pupil is taught to develop observation and thought power, rather than…

This textbook seeks to (1) present to the young mind, unacquainted with the methods of exact reasoning, the elementary principles of arithmetic in their simplest form and combination; and (2) explain and illustrate the various applications of arithmetic in the transactions of business, and thus make known its great practical utility.

Demonstrated are binary operations on whole numbers which are commutative but not associative, or associative but not cummutative. Also presented are sets of numbers within which the Unique Factorization Theorem does not hold true. (JP)

This article explains the generation of Kaprekar's constant in terms that upper elementary pupils can understand. The procedure is explained and the result proven. This is an example of a new, interesting problem for students that gives them drill in subtraction at the same time. (LS)

Research supported in part by a grant from the U.S. Public Health Service. (DD)

A 30-minute lesson on exponents was taught to 249 fourth graders assigned randomly to groups of 1, 2, 5, or 23. Students in the smaller groups had better attainment of ten objectives than did those in the group of 23. Individual instruction was better than instruction in groups of five. (MS)