This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…

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)

Three different models with continuous materials, discontinuous materials, and number lines were used to study the operation concept in six investigations on multiplication with fractions with pupils aged 11-12 in a Penang International School. All approaches could be understood by pupils, but they preferred the area and fractional models. (MNS)

Concepts of fractions from an adult perspective as well as from a child's perspective are examined. Types of students' schemes for some terms related to fractions are reported. (YP)

Analyzes two transcripts of children's mathematical behavior to observe the nature of recursive levels and interrelationships among them. Describes several levels of the recursions. (YP)

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…

This exploratory study describes fourth-grade students' opinions and knowledge about fractions. A coherent and elaborate fraction knowledge base results when students establish connections between their conceptual knowledge and procedural knowledge of fractions. One possible juncture between concepts and procedures might involve establishing…

Investigated was the use of cognitive conflict to probe the misconceptions held by preservice elementary teachers that in a division problem the quotient must be less than the dividend. Explains how preservice teachers' reliance on information about the domain of whole numbers and their instrumental understanding support their misconceptions.…

A study on the impact of misconceptions on preservice elementary teachers' processes in solving problems involving multiplication and division of decimals is described. Included are the purpose of the study, a description of the subjects, instruments, and interviews, the findings, and discussion. (KR)

This book contains revised versions of the major papers presented at the Research Agenda Project Conference on Number Concepts in the Middle Grades. It is organized into three major sections, along with an introductory chapter and two brief summaries. Part I includes chapters that deal primarily with analyses of subject matter. The four chapters…

Reported are the effects of a conceptually oriented unit on decimal fractions. The relationships between short-term changes in solving processes and the stability of these processes over time, performance of students, and entry achievement level and the long-term effects of conceptually based instruction are discussed. (KR)

The Education Technology Center (ETC) Fractions Group works to investigate well-documented difficulties that children have in understanding fractions. A central assumption underlying this group's inquiry is that students' difficulties in manipulating fractions arise from their lack of understanding about the nature of fractions. In order to learn…

Described are the conceptions held by United States and Israeli students about multiplication and division that may impede their work with decimals. Included are the introduction, method, division and multiplication task results, and the implications for education and textbook development. (KR)

The processes and strategies used by Finnish second graders in solving verbal multiplication and division tasks were investigated, and the relationship of these processes and strategies to Piagetian abilities, memory capacity skills, and rational number concepts was charted. Three categories of strategies were classified: operations based on…

This paper describes the BUD project which surveyed childrens' conceptions of division, and of fractions and decimals. The lack of connection between counting skills and conceptual understanding is discussed. The expectations for new algorithms and the basic idea in planning the BUD project are summarized. Some previous studies on counting, the…