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The present study explores the effect of two instructional methods for children with different levels of mathematical skills. One of these methods uses a conventional approach to learning multiplication and emphasizes the memorization of all arithmetic facts, whereas the other method is based on psychological principles and combines: a) the memorization of a small subset of problems aided by color cues and a portable time-table, with b) the use of single-step rules. One hundred and sixty second-grade children (aged 7-8) received instruction in one of these approaches – either the conventional method or the memory and rules method (M&R) – over the course of 6 months as part of their normal school education. Moderation analysis revealed that children with poor mathematical skills in the conventional group scored significantly better than their counterparts in the M&R group, whereas a significant advantage was observed in the M&R group for those children with strong mathematical skills.