The book synergizes research on number across two disciplines--mathematics education and psychology. The underlying problem the book addresses is how the brain constructs number. The opening chapter frames the problem in terms of children's activity, including mental and physical actions. Subsequent chapters are organized into sections that…

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…

Reviewed is research indicating problems in teaching and learning fractions and possible ways to improve instruction and learning. (RH)

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)

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

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)

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.…

Documented are major categories of errors that appear as children learn decimal fractions. Then the conceptual sources of these errors are established. Different curriculum sequences influence the probability that these classes of errors will appear. They can be used as diagnostic tools to detect children's understanding of mathematics topics.…

This aptitude-treatment interaction study explored the relationship between cognitive restructuring ability and treatments varying in the amounts of teacher guidance on tasks with fractions. An interaction was found between cognitive restructuring ability and levels of teacher guidance for items having continuous perceptual distracters. (MNS)

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)

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…

Reports on a study designed to investigate aspects of young children's knowledge of fractions and partitions of quantities. Findings suggest that although children did not have a deep understanding of the concept of one half, a significant number demonstrated a powerful systematic procedure leading to the creation of accurate equal fractional…

This paper presents results from a study of 19 teacher education students' knowledge of mathematics and discusses an analytic framework for examing and appraising teachers' and prospective teachers' subject matter knowledge. Participants in the study were 10 elementary education majors and 9 mathematics majors or minors who were preparing to teach…