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)

Describes a lesson on long division using chip trading which follows that algorithm for long division. (MKR)

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)

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)

Suggests that issues surrounding the teaching of algorithms focus not on whether to teach them but rather on balancing and connecting the development of algorithmic thinking. Presents an approach to help students develop their algorithmic thinking. Contains 18 references. (ASK)

Presents research on students' use and understanding of algorithms in Poland. Concludes that there are detrimental side effects that stem from the teaching and learning of standard written algorithms. (ASK)

Reviews the historical development of subtraction algorithms used in the United States. Discusses different algorithms used and developed throughout history that had a major impact on the way subtraction is taught today. (Contains 22 references.) (ASK)

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)

Presents several alternatives to customary algorithms for whole number arithmetic. Includes a brief history of each algorithm and discusses why each might be useful for particular kinds of children. (KHR)

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.…

Illustrates how upper elementary grade students can develop an understanding of the invert-and-multiply algorithm. (CCM)

Compares methods of subtraction used by children and teachers. Suggests ways to encourage children to invent their own subtraction algorithms. (CCM)

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…