The mathematics associated with division is discussed, working from a theorem for the real division algorithm. Real-world, geometric, and algebraic approaches are discussed, as are related topics. (MNS)

The forum is focused on thinking about and with algorithms as a way of unifying all one's mathematical endeavors. The lead article by Maurer presents examples and discussion of this point. Responses, often disagreeing with his views, are by Douglas, Korte, Hilton, Renz, Smorynski, Hammersley, and Halmos. (MNS)

The Euclidean algorithm for finding the greatest common divisor is presented. (MNS)

Mathematical models that are used to solve facility location problems are presented. All involve minimizing some distance function. (MNS)

Algorithms to determine the optimal locations of emergency service centers in a given city are presented, with theorems and proofs. (MNS)

Suggests and illustrates ways in which systematic consideration of selected unary operations can be facilitated by using electronic calculators. Emphasis is placed upon unary operations suitable for exploration and investigation at the pre-algebra level, using calculation algorithms as a basis for generating examples and non-examples to develop…

A program for drawing a line segment is developed. (MNS)

An efficient division algorithm is developed, using a computer program, to convert any positive fraction to its decimal representation. The computer program listing is included. (MNS)

A method is presented for determining cube roots on a calculator with square root facility that has a rapid rate of convergence. (MP)

Variations on a card trick are noted, with a formula for generalizing them. Another trick which can be proved with algebraic principles is then presented. (MNS)

Studied the interpretation of mathematics in terms of algorithmic or coherent views of 1,287 teachers from 12 countries using responses to items from the Third International Mathematics and Science Study (TIMSS). Teachers from four high-achieving Asian countries were more likely to see mathematics as algorithmic than were teachers from four…

A "neat and general" divisibility algorithm for prime numbers is presented. Five illustrative examples are included. (MNS)

Presented are the mathematical explanation of the algorithm for representing rational numbers in base two, paper-and-pencil methods for producing the representation, some patterns in these representations, and pseudocode for computer programs to explore these patterns. (MNS)

Common mathematical errors of pupils as identified by the Concepts in Secondary Mathematics and Science Project are identified and traced to the use of methods invented by students rather than formally taught methods. (MP)

Describes teaching strategies that help students improve problem solving skills. Lists three factors good problem solvers were found to possess. Gives step by step instructions for solving problems. (MVL)