This research pursued a fine-grained analysis of the acquisition of a procedural skill. In two experiments (n = 29 and n = 27), adults practiced 12 alphabet arithmetic problems (e.g., C + 3 = C D E F) in two sessions with 20 practice blocks in each. If learning reflected speed up of a counting algorithm, response time (RT) speed up should be proportional to the number of counting steps (+1, +2, or +3). Instead, we found about 50% of RT gains occurred in the first six blocks of practice during which speed up was parallel for +1, +2, and +3 problems. In both experiments, RT initially was a linear function of addend size, reflecting a letter counting strategy. Mean RT for +3 problems was eventually equal to +2 problems, which suggests that speed up reflected a gradual shift to associative fact retrieval. Trial by trial strategy self-reports in Experiment 2 revealed that the proportion of trials reported as memory retrieval as opposed to counting predicted 96% of the variance in RT as a function of addend size and practice block. As such, the results provided no evidence for speed up of a counting algorithm and indicated that skill acquisition for this task entailed speed up of task-general processes independent of addend size and rapid transition from counting to fact retrieval.