In a 9-month training experiment, 64 first graders with a risk factor were randomly assigned to computer-assisted structured discovery of the add-1 rule (e.g., the sum of 7 + 1 is the number after "seven" when we count), unstructured discovery learning of this regularity, or an active-control group. Planned contrasts revealed that the add-1 conditions were more effective than regular instruction/practice in promoting the learning of the add-1 rule. Contrary to the conclusions of Alfieri, Brooks, Aldrich, and Tenenbaum (2011) and Kirschner, Sweller, and Clark (2006), participants in the structured add-1 condition did not outperform those in the unstructured add-1 group on practiced and unpracticed n + 1 and 1 + n items at the posttests. The control participants did not exhibit evidence of learning a general near-doubles reasoning strategy (if 4 + 4 is 8 and 4 + 5 = 4 + 4 + 1, then the sum of 4 + 5 must be 9). The add-1, but not the active-control, participants achieved success, including transfer, because the former had mastered the developmental prerequisites for add-1 rule and the latter had not mastered the prerequisites for the near-doubles strategy. (Contains 4 tables, 6 figures, and 4 notes.)