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)

A technique for doing long division without the usual estimation difficulty is presented. It uses multiples of 2 combined with a recording technique. (MNS)

The article identifies five incorrect beliefs about mathematics often held by students who have difficulty with mathematics. They include: the relative size of numbers is more important than the relationships between quantities; computation problems must be solved by using a step-by-step algorithm; mathematics problems have only one correct…

Computational algorithms from American textbooks copyrighted prior to 1900 are presented--some that convey the concept, some just for special cases, and some just for fun. Algorithms for each operation with whole numbers are presented and analyzed. (MNS)

Shows that the rules of thumb for propagating significant figures through arithmetic calculations frequently yield misleading results. Also describes two procedures for performing this propagation more reliably than the rules of thumb. However, both require considerably more calculational effort than do the rules. (JN)

Provides several algorithms that use extended precision methods to compute large factorials exactly. The programs are written in BASIC and PASCAL. The approach used for computing N considers how large N is, how the built-in limitation on exact integer representation can be bypassed, and how long it takes to compute N. (JN)

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

A procedure is described that enables students to perform operations on fractions with a calculator, expressing the answer as a fraction. Patterns using paper-and-pencil procedures for each operation with fractions are presented. A microcomputer software program illustrates how the answer can be found using integer values of the numerators and…

Shortcuts to use when performing operations with the calculator are given. Algorithms discussed include reciprocals, powers, parentheses, infinite series, and synthetic division. (MP)

A strategy to make the transition from manipulative materials to a written algorithm for division is outlined in dialogue form. (MNS)

The multiplication and division algorithms that are taught in German schools are presented. It is suggested that these algorithms may be better than standard algorithms in terms of development of useful concepts and processes. (MK)

Possible ways of mechanization for counting using a binary system are discussed. Shows a binary representation of the numbers and geometric models having eight triples of lamps. Provides three problem sets. (YP)

A collection of games and puzzles that teachers can use to replace or supplement the usual textbook subtraction examples involving large numbers is given. Most of the nine activities are self-checking. (MNS)

Several subtraction algorithms are analyzed to see if they involve borrowing. The main focus is on an analysis of a procedure called the residue method. The operational arithmetic which underlies the symbolic manipulations is examined and conditions where the method does and does not use borrowing are highlighted. (MP)

Solutions to difficult equations are illustrated with numerical techniques that can be used easily on calculators. Flowcharts and programs for computers and calculators are included. (MP)