Learning Basic Arithmetic: A Comparison Between Rote and Procedural Learning Based on an Artificial Sequence

It is commonly accepted that repeatedly using mental procedures results in a transition to memory retrieval, but the determinant of this process is still unclear. In a 3-week experiment, we compared two different learning situations involving basic additions, one based on counting and the other based on arithmetic fact memorization. Two groups of participants learned to verify additions such as "G + 2 = Q?" built on an artificial sequence (e.g., "XGRQD horizontal ellipsis "). The first group learned the sequence beforehand and could therefore count to solve the problems, whereas the second group was not aware of the sequence and had to learn the equations by rote. With practice, solution times of both groups reached a plateau, indicating a certain level of automatization. However, a more fine-grained comparison indicated that participants relied on fundamentally different learning mechanisms. In the counting condition, most participants showed a persistent linear effect of the numerical operand on solution times, suggesting that fluency was reached through an acceleration of counting procedures. However, some participants began memorizing the problems involving the largest addends: Their solution times were very similar to those of participants in the rote learning group, suggesting that they resulted from a memory retrieval process. These findings show that repeated mental procedures do not systematically lead to memory retrieval but that fluency can also be reached through the acceleration of these procedures. Moreover, these results challenge associationist models, which cannot currently predict that the process of memorization begins with problems involving the largest addends.