ABSTRACT
This chapter focuses on the concepts of counting and number that form the foundation of additive reasoning for the youngest students. Learning to count a set of objects involves developing understanding of three principles: knowing the sequence of the number words, one-to-one correspondence, and cardinality. Children develop more flexible strategies for using counting to solve problems as they come to understand several interrelated concepts: hierarchical inclusion, conservation, and perceptual and conceptual subitizing. Once children develop the understanding that a number can represent the result of a count without needing to actually do the counting, an important milestone is achieved; they are able to develop more sophisticated and efficient problem solving strategies, such as counting on, using part–whole relationships, and counting by groups. Engaging young children in solving meaningful problems around determining and comparing quantities helps to build a foundation for developing a conception of number that moves beyond treating quantities as collections of ones, a hallmark of additive reasoning.
