ABSTRACT
In the previous chapter, we showed that children who use counting-on— understanding that 5 + 3 can be solving by counting up three times from five— have made a substantial conceptual advance. These children can use increasingly sophisticated arithmetic reasoning. For example, they should be decomposing and recomposing numbers. This chapter reviews research on three topics whose shared core is the increasingly sophisticated composition of number: arithmetic combinations ("facts"), place value, and multidigit addition and subtraction.
