Starting from the concept of one-to-one correspondence, an introduction to the different types of infinities is presented. The usual problems concerning the infiniteness of the rational numbers, the real numbers, and the unit interval are given. Several other theorems follow. (LS)

A distinction is made between an algorithm and the justification for the algorithm. Examples of both are given for the operations with whole numbers. (DT)

Illustrations of the misuse of the associative property in elementary school texts are given; the question is raised as to the appropriateness of stressing the commutative and associative properties at the elementary level. (DT)

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)

Described are patterns in Pascal's triangle which are obtained when the entries are reduced modulo a prime number. (MM)

Problems involving infinity and paradoxes are included in a discussion of how students can be exposed to the human element of mathematics. (DT)