This chapter focuses on the interaction of two first graders as they attempt to make sense of a particular instructional context for learning negative numbers. The context is one where they move an elevator to a building's floors above and below ground in order to model integer addition and subtraction problems. In particular, the focus of the…

We define and describe how subitizing activity develops and relates to early quantifiers in mathematics. Subitizing is the direct perceptual apprehension and identification of the numerosity of a small group of items. Although subitizing is too often a neglected quantifier in educational practice, it has been extensively studied as a critical…

How children play around with new numerical concepts can provide important information about the structure and patterns they notice in number systems. In this chapter, we report on data from 243 second graders who were asked to fill in missing numbers on a number path (encouraging them to play around with numbers less than zero) and to solve…