The author suggests that slope be introduced as a topic independent of graphs, and that it be presented in a way that makes some sense of using a fraction to represent it. Many examples are included. (MNS)

Decimal expansions of fractions are considered. Theorems and corollaries for some properties and for prime and composite denominators are presented. It is suggested that students write computer programs to deliver decimal expansions. (MNS)

This paper provides some guidance as to what to listen for to help students make sense of expressions in ways that connect to their ideas and honestly address the mathematics of rational numbers. It offers a reasonable initial answer to the question, "Where do students' ideas about fractions and ratios come from, and how can we work productively…

Fractions and division are two topics that receive considerable attention in elementary school mathematics, particularly in grade three and beyond. Despite this attention, fraction and division concepts and skills prove difficult for many middle school students to learn and for teachers to teach. This paper reports on part of a larger study…

The purpose of this study was to document and trace how students' understanding of situations that involve finding a fractional part of a fraction developed during a course of instruction in which students explored and represented various kinds of situations using each of the five representational systems. A class of 5th grade students (n=22)…

The study of fractions is fundamental in mathematics, yet it is among the most difficult topics for school students. This digest discusses the issues that students face in studying fractions and offers a curriculum consisting of four modules for teaching about fractions. Information about the Rational Number Project, additional resources, and…

This textbook is designed for common schools, normal schools, high schools, academies, and other schools. Among the topics covered are: arithmetical language, fundamental operations, prime numbers, fractions, practical measurements, percentages, ratios, and mensuration. A section providing miscellaneous problems is also included. Appendices…

Examples are presented in which students are able to answer test items requiring manipulation of numbers for such topics as reducing fractions, but lack understanding of the operation. In addition to paper-and-pencil test, interviews are recommended for evaluating a student's understanding. (JP)

A teacher's notes of ideas on how to teach decimals and what everyday examples to use. For part 1 of this article, see volume 2, number 3, pages 23-24. (MM)

Rules are specified for a card game used to help fifth and sixth graders learn equivalent fractions and the renaming of whole numbers as fractions. (DT)

Ninety-six fifth graders, stratified by achievement, were randomly assigned to training as individuals or pairs in one of three variety-of-training conditions for multiplication with fractions. Variation in training tasks facilitated transfer for students trained as individuals but inhibited transfer when trained as pairs. Training individuals in…

The author compared the relative efficiency of three methods of presenting and teaching fractions to slow learners in secondary school: formal-traditional method, cuisenaire (unimodel) material, and specially prepared multi-model materials; multi-model materials were found to be the most effective method. (Author/AN)