Answers and examples are given to sixteen questions related to traditional ways of performing the operations of arithmetic. (MP)

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)

Two difficulties that students have in computing with fractions are idenfitied. Then a procedure is described, stressing the identity element, that resolves these difficulties and increases students' understanding and retention. (MNS)

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)

Student performance on division exercises in the recent National Assessment of Educational Progress (NAEP) is reviewed. Pupil performance on selected exercises is reported and followed by some suggestions for improvement in the teaching of this skill. (MP) Aspect of National Assessment (NAEP) dealt with in this document: Results (Utilization).

Discusses the use of manipulative materials to model operations and algorithms. Indicates that they clarify the several interpretations of each operation, establish a basis for correct mathematical language, and show why algorithms work. (JN)

Allowing students to examine different ways of performing an operation is suggested as a means of increasing their understanding. (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)

Three short essays provide teaching suggestions for lessons on base two, order of operations, and ratios used to motivate a number of mathematical ideas. (MK)

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)

This response to Usiskin's editorial comment on calculator use in the May 1983 issue considers why arithmetic is taught. The belief that mathematics improves thinking and the humanist position that it is part of our cultural heritage are noted. The role of mathematics in the curriculum should be reconsidered. (MNS)

Some techniques for developing the ability to multiply and divide by powers of ten with ease and understanding are presented. (Author/MK)

A study to determine if "random" or "careless" errors in multiplication made by individual students take on discernible patterns is described. Implications for teaching are discussed. (MK)

Outlines various subtraction methods, such as the decomposition method, equal-addends method, and low-stress algorithm. Describes a subtraction method by addition of complements. Discusses the advantages and disadvantages of the method. (YP)