Students in grades 1, 3, 4, 5, 6, and college were timed as they produced the answers to simple addition problems or verified a given problem as true or false. First graders clearly relied on a counting process for their performance, as advanced by the Groen and Parkman "min" (for minimum addend) model. Third grade appears to be a transitional age with respect to addition processing; from fourth grade on, however, performance in both tasks yields evidence of a memory retrieval process as the major vehicle of mental addition. The results are discussed in terms of the Ashcraft and Battaglia (1978) "network-retrieval" model, a model which asserts that simple arithmetic facts are stored in a network representation, and are accessed in a spreading activation-like fashion. (Author)