An easily made device can be used for drill and practice on computational skills. The procedure, which involves use of the overhead projector, is described in detail. Teachers using it can vary content and the speed with which students should respond. (SD)

The mathematics of the game "Instant Insanity" is described in terms of graph theory, a part of combinational mathematics. (SD)

The author proposes a method of diagnosis through activities rather than traditional testing. In this approach the teacher assigns activities in which the student is known to have an interest and which require the skill to be tested. (SD)

The author describes an introduction to, and development of, the complex number field. (SD)

Three games played with regular bridge decks of cards are described. By playing the games students gain practice in use of basic operations on integers and in the development of strategies. (SD)

The inequality involving the arithmetic and geometric means is a powerful tool in dealing with applications of mathematics. It is very important in geometric programming. The article discusses this inequality and demonstrates two real world applications accessible to secondary teachers and students. (Author/KM)

Common strategies for teaching proofs are discussed. Prerequisite behaviors, components of a learning hierarchy, are expressed in behavioral terms. The six categories are knowledge about logic, knowledge about the components of a deductive system, knowledge about proof strategies, knowledge of proof formats, proof completion, and generalization.…

An algebra class asked: What is the smallest positive integer that is divisible by each integer less than or equal to ten? Students discovered factorials and a solution. Verifying the solution produced a series of numbers. Successive differences between entries, triangular arrays, and successive quotients finally led to Pascal's triangle. (KM)

This article extends number bases to negative integers, then to positive rationals and finally to negative rationals. Methods and rules for operations in positive and negative rational bases greater than one or less than negative one are summarized in tables. Sample problems are explained and illustrated. (KM)

Using a set of worksheets, students will discover and apply Euler's formula regarding connected planar graphs and play and analyze the game of Sprouts. One sheet leads to the discovery of Euler's formula; another concerns traversability of a graph; another gives an example and a game involving these ideas. (Author/KM)

This article shows how two discoverable theorems from elementary calculus can be presented to students in a manner that assists them in making the generalizations themselves. The theorems are the mean value theorems for derivatives and for integrals. A conjecture is suggested by pictures and then refined. (Author/KM)