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…

Describes the constructs of referents, relationships, and modes and illustrates how these constructs may be reflected in students' written responses to a decimal task that requests an explanation. Examines sets of responses from two classrooms using the proposed framework to illustrate the type of information that teachers may acquire through the…

This paper describes the Rational Number Project (RNP), teaching experiments concerned with the teaching and learning of fractions among 4th and 5th grade students. Interviews with 4th grade students who used the RNP curriculum and with students who used a traditional curriculum were conducted by RNP staff as well as classroom teachers. This paper…

This yearbook contains articles that give insight into students' thinking about factions, ratios, and proportions. Suggestions are offered on how to develop the concepts and skills associated with these topics. The book is divided into elementary, middle school, and professional development sections. Chapters include: (1) "The Development of…

Described are children's strategies in thinking about fraction order and equivalence. The data are based on two teaching experiments with fourth and fifth-grade children. Some sample activities for teaching order and equivalence are included. (RH)

Describes a process which allows students to explore repeating decimals without being inhibited by the limitations of the calculator display. In addition, the process can take some of the mystery from the decimal forms of rational numbers. (JN)

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)

Student exploration at a secondary school level of fraction relationships using special graphs is described. (MP)

This volume presents a partial description of the lessons in the preliminary version of the PLATO fractions curriculum. Each lesson has three parts: review, new material, and a student-selected option. Students receive immediate feedback from the computer as they progress through each lesson. Five groups of lessons are described: meaning of…