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)

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

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 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)

Five reports from a 2-year study are presented. Frequencies and descriptions of systematic errors in the four algorithms in arithmetic were studied in upper-middle income, regular, and special education classrooms involving 744 children. Children were screened for adequate knowledge of basic facts and for receiving prior instruction on the…

Described are two methods of calculating developed by the Dutch WISKOBAS Project: addition and subtraction with a loop abacus and multiplication using a grid model. (MP)

Instructional sequences are presented for teaching two-digit multiplication and division with one- and two-digit divisors using a base-oriented approach. (MN)

Discusses mathematics education research on multiplication and division which implies that instruction should emphasize development of a sound conceptual basis for multiplication and division rather than memorization of tables and rules. Presents action research ideas. (10 references) (MKR)

Programing a microcomputer to solve problems in whole-number arithmetic, rather than using the built-in operations of the computer, is described. Not only useful, it also enhances important mathematical concepts and is adaptable to a range of student abilities. (MNS)

Students from six fourth-grade classes were paired and randomly assigned to computer or worksheet treatments on multiplication and division. Those using computer-based drill-and-practice programs made greater gains on some tests of basic facts, but had no higher retention of algorithms. (MNS)

A 14-year-old Brazilian boy in the fourth grade was given 170 problems orally, each asking for the sum of 2 2-digit numbers. Responses indicated he had invented his own algorithm for addition, similar to the school one, based largely on his experiences with money. (Contains 13 references.) (JAF)

The concept of multiplication is described and illustrated using several different representational systems. A conceptual approach to teaching mathematics is compared with the procedural approach commonly found in the school curriculum. Four different methods of representing the multiplication process with numbers larger than ten are presented:…