No Performance Benefit of Random Over Table-ordered Multiplication Training in Children: Does Memory Interference Between Facts Constrain Arithmetic Learning?

Abstract Interference between multiplication facts is often mentioned as a key source of children’s difficulty in learning and retaining multiplication tables. Shared operands and results (e.g., 6 × 4 = 24 and 8 × 3 = 24; 7 × 8 = 56 and 9 × 6 = 54) are indeed thought to create overlap between facts, leading to blurred representations in memory. One proposed way to reduce such interference is to practice facts in a mixed order across tables (e.g., 6 × 7 = 42; 3 × 8 = 24; 4 × 9 = 36) rather than table by table (e.g., 6 × 7 = 42; 6 × 8 = 48; 6 × 3 = 18). This approach was tested in the present study, in which sixth graders practiced multiplication facts from x 3 to x 9 tables either by table (N = 81) or in a mixed order (N = 62). Their performance on a multiplication fluency task was compared to that of a control group engaged in regular classroom activities (N = 71). Children in the mixed-order condition showed less improvement from pre- to post-test than those in the table-by-table condition and did not progress more than the control group. These findings show that randomly practicing multiplications facts may not be a productive pedagogical method for relearning. They more broadly suggest that the role of interference in multiplication learning may not be as central as commonly thought.