Early calculating methods and devices are discussed. These include finger products, the abacus, ancient multiplication algorithms, Napier's bones, and monograms. (MP)

Discusses an algorithm from Vedic mathematics that has similarities to FOIL and the standard algorithm for multiplication. (Author/NB)

The author advocates the classroom consideration of new algorithms as a means of leading students to make original hypotheses. He discusses a multiplication algorithm based on the differences between squares. (SD)

Computational algorithms appearing in early American arithmetic text are discussed. (SD)

A rationale is given for the Russian-peasant algorithm for multiplication indicating why it works as well as how it works. (DT)

In this first of two articles, computational algorithms for multiplication and division which encourage use of one operation at a time are proposed. (DT)

The Russian-peasant algorithm for multiplication is described and then extended to developing an algorithm for renaming base ten numbers in other number bases. (DT)

A computer program in BASIC is presented, with the underlying algorithm explained, for multiplying any two multi-digit numbers and obtaining an exact answer. (MP)

The role of division of whole numbers in problem solving and the implications for teaching division computation are examined. Deleting the teaching of division facts, and obtaining solutions by using multiplication facts, is advocated. (DT)

The focus is upon the introduction of multiplication within the framework of an algorithm program. Analysis of some observations of student solutions to multiplication problems is included. (MN)