Reviews research using diagrams, number sentences, and algorithms to help students learn to add and subtract; poses questions on the relationship of instruction to children's knowledge construction; and proposes a research agenda in this area. (86 references) (MKR)

This material is designed to examine the research on how children acquire basic addition and subtraction concepts and skills. Two major lines of theories of the development of basic number concepts, called logical concept and quantification skill approaches, are identified. Major recurring issues in the development of early number concepts are…

Provided is an examination of the methodology used to study the problems of learning addition and subtraction skills used by developmental researchers. The report has sections on categories of theory and their methodologies, which review: (1) Behaviorist, Neo-Behaviorist and Piagetian Theories; (2) the Behaviorist and Piagetian Paradigms; (3)…

This report opens by asking how operations in general, and addition and subtraction in particular, are characterized for elementary school students, and examines the "standard" instruction of these topics through secondary schooling. Some common errors and/or "sloppiness" in the typical textbook presentations are noted, and…

Suggests that children enter school with a great deal of informal intuitive knowledge of mathematics that can serve as the basis for developing much of the formal mathematics of the primary school curriculum. Describes a research-based model of children's thinking that teachers can use to interpret, transform, and reframe their informal or…