The principle of the permanence of the rules of calculation is contrasted with the concretization permanence principle. Both apply to situations where some arithmetical operation known to children for numbers of a certain kind is to be extended to include further numbers. (MNS)

This is unit three of a fifteen-unit secondary mathematics textbook. This unit contains two chapters. The first chapter discusses integers and the second chapter discusses rational numbers. Operations with both types of numbers as well as the structure of the systems are discussed. (MK)

The major portion of the article establishes the basis for the stated rule - to divide by a fraction, turn it upside down and multiply. With this background, three justifications for the rule are given. Several possible errors in students' use of the rule are noted. (LS)

The first of four quins intended to develop computational skills with non-negative rational numbers through applications to business and industry, this guidebook on minimum course content is designed for the student who has acquired basic computational skills with non-negative rational numbers. Overall course goals are specified, a course outline…

Noitcarf numbers provide a simulation activity that allows teachers or education students to gain an understanding of the feelings of students who are taught mathematics by a "rules" method. They are actually an abstract presentation of operations with fractions. (MK)

Describes examples of rational representation as a guide for translating terminology and information encountered in manuals for computers. Discusses four limitations of the representation. (YP)

The third of four quins intended to develop computational skills with non-negative rational numbers through applications to business and industry, this guidebook on minimum course content is designed for the student who has acquired basic computational skills with non-negative rational numbers. Topics include measurement and geometrical…

Measurement experiences can promote and illustrate number work in an intuitively satisfying way. Some current practices that are counterproductive for developing number sense and some alternative strategies that are more constructive are included in discussions of the approximate nature of measurement, realistic measurement, and work with rational…

The second of four quins intended to develop computational skills with non-negative rational numbers through applications to business and industry, this guidebook on minimum course content is designed for the student who has acquired basic computational skills with non-negative rational numbers. Overall course goals are specified, a course outline…

The fourth of four quins intended to develop computational skills with non-negative rational numbers through applications to business and industry, this guidebook on minimum course content is designed for the student who has acquired basic computational skills with non-negative rational numbers. Topics include ratio, proportion, and percentage…

A mathematical game that reinforces basic multiplication facts, strengthens concepts of factors and multiples, and also provides arithmetic drill is described. Four variations of the game are also provided. (JT)

Analyzed students' reasoning with fractions. Found that skilled students applied strategies specifically tailored to restricted classes of fractions and produced reliable solutions with a minimum of computation effort. Results suggest that competent reasoning depends on a knowledge base that includes numerically specific and invented strategies,…

Seven questions concerning the role of computation and the role of electronic calculators in arithmetic were posed to a sample of teachers, mathematicians, and laymen. Responses are given in percentage form and typical comments are included. (LS)

A straight forward process for working in fractions on any calculator is presented. The method involves converting a decimal back into a fraction in its lowest terms. (MN)

Three different methods of teaching fraction computation were compared using community college student scores on measures of fraction computation, fraction understanding, and attitude towards mathematics. One method used conventional algorithms; the second, a control for the effect of using a calculator, used conventional algorithms and…