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)

Suggests that algorithms, both traditional and student-invented, are proper objects of study not only as tools for computation, but also for understanding the nature of the operations of arithmetic. (Author/NB)

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)

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

Traditional methods of teaching addition include algorithms that involve right-to-left procedures. This article describes efficient procedures for left-to-right addition and subtraction involving computation and computational estimation that reflect children's natural behaviors observed during activities with unifix cubes. (MDH)

Debates the place of standard methods, the calculator, and mental mathematics in elementary education. Proposes a framework for computation that emphasizes a sequence for introducing computational procedures. (ASK)

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)

Indicates that there has been a lot of work done and that a great deal needs to be done in the future to explore the world of children's early number. Discusses the counting, the use of algorithm, practical mathematics, the use of manipulatives, individual differences and pedagogical concerns, and classroom applications. Contains 18 references.…

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

Examines 250 sixth-grade students' understanding of arithmetic average by assessing their understanding of the computational algorithm. Results indicate that the majority of the students knew the "add-them-all-up-and-divide" averaging algorithm, but only half of the students were able to correctly apply the algorithm to solve a…

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…

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

Fourteen third graders were given numerical computation and division-with-remainder (DWR) problems both before and after they were taught the division algorithm in classrooms. Their solutions were examined. The results show that students' initial acquisition of the division algorithm did improve their performance in numerical division computations…

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