ABSTRACT
This chapter discusses arithmetic—from one perspective. That is, other chapters, including those on conceptual subitizing (see quantities in parts and wholes quickly) and number composition (arithmetic as partitioning numbers), also deal with arithmetic. This chapter focuses on counting-based arithmetic. In high-quality education, all these perspectives combine to provide children with powerful, efficient, fluent arithmetical thinking. Although the perspective of this chapter, arithmetic problem solving via counting, is familiar to most educators, there is much we can learn from research and the wisdom of expert practice to do it better. As with all topical chapters, this one introduces the mathematics of this approach. Next, the various types of problems children should be able to solve, and the counting strategies children learn to solve them are described. The section on experience and education completes the third, instructional, part of the learning trajectory. As with all topical chapters, these ideas are woven into a learning trajectory summarized in a table. As always, this learning trajectory is explicitly connected to the Learning and Teaching with Learning Trajectories, or [LT]2 web tool, a valuable addition to this edition.
