## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 1073-1076 |

Number of pages | 4 |

Journal | Proceedings of International Conference of the Learning Sciences, ICLS |

Volume | 2 |

Issue number | 2018-June |

State | Published - Jan 1 2018 |

Event | 13th International Conference of the Learning Sciences, ICLS 2018: Rethinking Learning in the Digital Age: Making the Learning Sciences Count - London, United Kingdom Duration: Jun 23 2018 → Jun 27 2018 |

## Keywords

- Distributive principle
- Mathematics education
- Multi-digit multiplication