Proposes a four-category classification of semantic structures of one-step word problems involving multiplication and division: forming the n-th multiple of measures, combinatorial multiplication, composition of operators, and multiplication by formula. This classification is compatible with semantic structures of addition and subtraction word…

The effects of several variables on the ability of students to solve open sentences involving multiplication and division were examined. The variables considered were sex, grade level, position of the unknown in the sentence, and operation. (SD)

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

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

The author urges that subtraction be introduced by "taking away" rather than by equal addition; multiplication be first demonstrated in sets; division be understood as sharing; and unit fractions be denoted at first by using the written word for denominator. (MN)

Determined effects of two task types on 12- and 13-year-olds' understanding of applications of multiplying and dividing positive numbers. Results indicate the persuasive nature of certain misconceptions and specific effects of context attributable to such aspects as relative familiarity. Implications of these and other results are discussed.…

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

Discussed are the concepts of intuition, the general properties of an intuitive knowledge, and the classification of intuitions as problem solving of affirmative. An example of intuition using multiplication and division is described in some detail. (MNS)

Ways to use popsicle sticks as concrete models of multiplication and division of fractions are given. (MK)

Preskills and strategy training were shown to be effective in helping four eight- to nine-year-old learning disabled children acquire basic multiplication and division skills. (Author)

This article focuses on the aspect of mental arithmetic that uses thinking strategies that are effective with large numbers as well as basic facts. Two activities are suggested for lack of the four operations. (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 teacher discusses his attempt to analyze his pupil's difficulties with arithmetic by looking at the component parts of each operation. (MP)

Demonstrates the number theory property that the number of divisors of an integer n times the number of positive integers k, less than or equal to and relatively prime to n, equals the sum of the divisors of n using theory developed about multiplicative functions, the units of a convolution ring, and the Mobius Function. (MDH)

This six month study investigated the similarities and differences between 137 fourth graders' understanding of and reasoning about multiplication, division, and proportion tasks. All students were administered a pretest mid-year and a posttest at the end of year. A sample of 18 students was interviewed individually on tasks involving reasoning…