Recent research has provided a reasonably coherent picture of how children learn to add and subtract. There is clear evidence that children do not learn simply by mastering a procedure and storing in memory. Instead, learning is structured in meaningful ways, connected to previous knowledge, and adapted to new contexts. This view of learning has important implications for the way arithmetic should be taught in the first or second year of school. This paper discusses: (1) the "part whole" concept (which refers to the idea that a number can be interpreted as a whole and two parts; (2) strategies children invent to add and subtract; (3) addition strategies (direct modeling, counting strategies, and number fact strategies); (4) activities to develop direct modeling, counting, and number fact addition strategies; (5) subtraction strategies (direct modeling strategies, counting strategies, and derived number facts); (6) activities to develop modeling, counting, and number fact subtraction strategies; (7) incorrect inventions and errors; and (8) drill and practice. (JN)