Sequencing arithmetic, area, and algebraic instruction for teaching the distributive principle

The current study examined the effect of different instructional sequences for teaching the distributive principle for multi-digit multiplication. Third graders experienced one of four sequences: Algebra-Arithmetic, Algebra-Area, Arithmetic-Algebra, and Area-Algebra. All sequences produced improvements in solving practiced 2D × 2D problems. Critically, the Area-Algebra and Arithmetic-Algebra sequences had the largest learning effects, with the former better for participants with some prior knowledge of 2D × 2D multiplication and the latter better for participants with no prior knowledge. All sequences also produced improvements on unpracticed transfer problems, with the Area-Algebra sequence producing the largest learning effects. Finally, improvements were most associated with prior knowledge of single-digit addition and subtraction – but not multiplication – facts. The implications of these results are discussed and future directions outlined.