The method described here converts a given problem in a base other than ten to a related problem in base ten, solves the related problem in base ten, and converts the answer back to the original base. Limitations are discussed. (MP)

Four methods of filling a square using programing with Logo are presented, with comments on children's solutions. Analysis of the mathematical or programing concepts underlying a few simple algorithms is the focus. (MNS)

Fifty Brazilian children aged seven-13 were individually given addition and subtraction exercises. Counting was the preferred procedure, with use of school-taught algorithms limited. Some children decomposed numbers into tens and units and then worked at both levels. They rarely referred to previous results when doing related exercises. (MNS)

Second-grade students were randomly assigned to either an instructional unit within which addition and subtraction of two digit numbers were treated as a single integrated process of regrouping or one which developed the addition and subtractive algorithms sequentially. Periodic assessments favored the sequential approach, but differences were not…

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

This report illustrates a simple, short, yet relatively little known partial check on addition that elementary school pupils can be lead to discover, and later taught to understand. The process can also be used for subtraction and is viewed as more useful than the traditional check of casting out nines. (MP)

The author feels teaching division of fractions is worthwhile because it will help students understand other algorithms. (MK)

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 multiplication algorithm based on a perfect square is described. (SD)