ABSTRACT
For several centuries, being able to find “one’s sums and differences” has been considered one mark of a schooled person. Although today we may have expanded our expectations about what constitutes literacy, we still expect all children to efficiently carry out operations on whole numbers. Yet, in spite of these expectations about the skills of addition and subtraction, there has been little consensus about how such skills develop. Lack of consensus does not mean there has been little research. Recent reviews (Carpenter, Blume, Hiebert, Anick, & Pimm, 1981; Carpenter & Moser, in press; Riley, Greeno, & Heller, in press) have identified an extensive body of research on addition and subtraction. Some of these studies have been quite influential. For example, Thorndike’s instructional suggestions in his Psychology of Arithmetic (1922) became the model of how to teach arithmetic for decades, 1 and Brownell’s (1947) research on subtraction demonstrated the superiority of the “decompositions” subtraction algorithm over the “equal additions” algorithm when taught with rational explanation. This made the “fair trading” procedure central to contemporary instruction in subtraction. But, to a large extent, the many studies on addition and subtraction represent an eclectic morass. This copious literature has lacked an implicit body of intertwined theoretical and methodological beliefs that permit selection, evaluation, and criticism. However, today we believe a change is imminent. The research and theoretical positions set forth in this volume should be viewed as foreshadowing the emergence of a firm research consensus in this area.
