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)

Three methods for using four-function, counting calculators for developing understanding of the meaning of square roots and operations on whole and rational numbers are described. (MP)

Describes the kinds of computational abilities achieved by a class of 4th grade students who were part of a research program for teaching rational numbers. In this program, students build on intuitive understandings of percents and proportions for the development of overall understanding of the number system and are encouraged to invent their own…

The representation of equivalent fractions is traditionally illustrated by diagrams showing division of units into parts. A second approach using linear graphs is suggested. (SD)

The development of a quantitative concept of rational numbers was explored in interviews with 16 fourth and fifth graders in two cities. High performers used a flexible and spontaneous application of concepts of rational number order and fraction equivalence, and a reference point, while low achievers tended not to. (MNS)

The mechanisms, images, and language needed for the development of rational-number ideas are briefly discussed. Such ideas are sophisticated and different from natural-numbers ideas. (MNS)

Devises a new curriculum to introduce rational numbers by using developmental theory as a guide. Experiment concluded that students in the treatment group showed a deeper understanding of rational numbers than those in the control group, showed less reliance on whole-number strategies when solving novel problems, and made more frequent references…

The author describes a model for operations on the set of rationals. Thi s model, used by students in a laboratory situation, is based on an easily constructed number balance. (SD)

By varying task conditions and constraints on subjects, this study attempted to extend and refine a developmental theory of partitioning as a foundational process undergirding children's construction of a rational number. Subjects were 31 preponderantly higher-grade pupils enrolled at an elementary school in Nova Scotia, Canada. Two tasks were…

A two-year study was conducted with fourth-grade children in the context of extensive teaching experiments concerned with the learning of rational number concepts. Representational difficulties in using the number line model were investigated. While instruction in the second year attempted to resolve observed learning difficulties, the results of…

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…

This is part one of a two-part SMSG mathematics text for sixth-grade students. Chapter topics include: Exponents; Multiplication of Rational Numbers; Side and Angle Relationships of Triangles; Introducing the Integers; and Coordinates. (MK)

This book is part 2 of a 2-part manual for teachers using SMSG text materials for grade 4. The purpose for each of 5 chapters is stated and mathematical background for the teacher is presented. Detailed lesson plans are then provided, including sequences of statements and questions, activities, and exercise sets with answers. Needed materials and…

Interpretation of rational numbers as fractions, ratios, percentages, and quotients of integers are discussed. Then coding conventions are noted, and equivalence classes are described. Finally, density and order are discussed. (MNS)

Over the past five years, Pesek (Simoneaux), Gray and Golding have been actively involved in the Louisiana Systemic Initiative Program (LaSIP) and the Louisiana Collaborative for Excellence in the Preparation of Teachers (LACEPT) grants through Southeastern Louisiana University. Through these grants teachers from the region are inserviced on…