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…

Discussed are students' understandings of the relationship between fraction and decimal interpretations of rational numbers, where both interpretations are represented symbolically. The methodology employed in this study, interviews, results, and a discussion of the implications of the results are presented. (CW)

Discussed are the background and implementation of a method of teaching fractions to primary children referred to as "The Visual Concept of Fractions." The advantages and criticisms of the use of this method are stressed. (CW)

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)

Approximately half of a group of 12-year-old students were taught fraction and ratio topics by a concrete process-oriented method. The others were taught in the regular way. The concrete, process-oriented approach resulted in significantly improved achievement in, and attitude toward, fractions and ratios. (Author/DC)

Considered is a conceptual analog of buggy algorithms and rule-based mathematical development. The investigations consider whether children's efforts to make conceptual sense of new mathematics instruction in terms of their available knowledge may sometimes lead them to make systematic errors. In particular, the possibility is explored that…

Examines the development of students' understandings about fractions during six weeks of instruction. Reports that all students possessed informal knowledge disconnected from their knowledge of fraction symbols and procedures and that knowledge of rote procedures often interfered with students' attempts to build on their informal knowledge.…

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)

The ability of students to sort cards based on surface features and deep patterns is investigated. The effect of the presence of variables and what makes a pattern difficult or easy for students to recognize are discussed. Study revealed that students are unsuccessful at making connections between expressions, sentences, and sequences which share…

This report describes an investigation in England of some of the problems children experience with fractions. In particular, the restricted view that some children have of fractions is investigated. The methodology involved a large number of interviews with secondary school children (aged 12-14). The results of these interviews led to the design…

This booklet is a catalog of error patterns found in basic arithmetic and algebra courses. It is intended to be used as a resource by instructors and tutors teaching these concepts. The material is divided into major concept headings with subheadings. The error patterns are named and given a brief general description followed by a specific example…

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…

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)