Two mental algorithms, one for addition and one for subtraction, are described. It is felt such algorithms should be taught explicitly. The usual process taught for paper and pencil is seen to inhibit mental arithmetic, and a need to include mental algorithms in the regular mathematics curriculum is promoted. (MP)

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)

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)

The use of the calculator is suggested in teaching algorithms for the four basic operations, in place of any difficult standard algorithm. (MP)

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)

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)

Two worksheets are given, outlining algorithms to help students determine the day of the week an event will occur and to find the date for Easter. The activity provides computational practice. A computer program for determining Easter is also included. (MNS)

Typical instruction of the division algorithm fails to justify why one brings down a number during the process. The construction and use of an aid is described which can be used to help explain the process of division to students. The aid emphasizes place-value aspects. (MP)

An approach is suggested to the use of sets of practice exercises that is more like the actual use of computation by adults and may be more effective in attaining accuracy and speed. (MP)

Three alternative methods of finding averages of two numbers are presented. (MP)

The use of developmental algorithms to develop skills is described. Children make the transition from using concrete materials to using a standard algorithm. (MNS)