Questions about teaching rational numbers are discussed, dealing with when to teach the meaning of fractions and of decimals, when and how to teach computation with fractions and with decimals, and other issues. (MNS)

The purpose of this study was to assess the ability of students in grades 6 and 7 to order rational numbers in both decimal and fraction form, including the identification of their thinking strategies. Implications for instruction are included. (MNS)

The approaches taken by two elementary school teachers in using computers as tools to stimulate and guide mathematical thinking are described. One had students design a BASIC program for counting; the other used demonstration programs to develop ideas about fractions and decimals. (MNS)

Activities are given to assist students in seeing a rationale for the difficult algorithms we teach for fractions. Both interpretations of fractions and operations with fractions are discussed. (MNS)

Discusses area models that can be used in grades three through nine, showing how the model generalizes from discrete situations involving the arithmetic of whole numbers to continuous situations involving decimals, fractions, percents, probability, algebra, and more advanced mathematics. (14 references) (MDH)

It is suggested that elementary school students find rational numbers troublesome because some teachers have an inadequate understanding of rational number concepts and poor facility with rational numbers skills. How to help them overcome difficulties, develop concepts, and know what topics to emphasize are discussed. (MNS)

Twenty-nine students in grades four, six, and eight were asked to find solutions to fraction equivalence problems and to verify their solutions using discrete material. Discontinuities were observed between strategies students used for producing solutions and supporting knowledge grounded in physical reality. (Author/MNS)

The behavior of one child as she constructed knowledge about fractions over a nine-month period is presented. The intent is to explain behavioral patterns for which certain mental processes, called schemes, seem responsible. (MNS)

Use of low-stress algorithms to reduce the cognitive load on students is advocated. The low-stress algorithm for addition developed by Hutchings is detailed first. Then a variation on the usual algorithm is proposed: adding from left to right, writing the partial sum for each stage. Next, a "quick addition" method for adding fractions proposed by…

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…

What makes a fraction meaningful and a definition of the quantitative notion of fractions are discussed. Then observations from teaching experiments are presented. (MNS)

Division of fractions and division of decimals, both troublesome, are discussed in relation to helping students learn well and retain what they have learned. A strong conceptual base, mastery of related concepts and skills, and meaningful development are stressed. (MNS)

This brief report focuses on the cognitive level of decimal problems in 16 textbooks. Activities at the application level are included, but seldom are higher-order intellectual behaviors found in the books. (MNS)

The ideas and techniques involved in learning about fractions were investigated with students in grades 1-12, in the first 3 years of colleges, in community college mathematics courses, and in graduate school. Also included were some high school mathematics teachers, some mathematicians, and some retired persons. Part I provides the rationale and…

Fourth-grade students' understanding of the order and equivalence of rational numbers was investigated in 132 interviews during an 18-week teaching experiment. Six children were instructed individually and as a group at two sites, with instruction relying heavily on manipulative aids. Strategies used to compare fractions were identified. (MNS)