Sixth grade students' explanations and justifications of distributivity

Kerstin Larsson (1)

1 Stockholm University

Equal groups and rectangular arrays are examples of multiplicative situations that have different qualities related to students' understanding of the distributive and the commutative properties. These properties are, inter alia, important for flexible mental calculations. In order to design effective instruction we need to investigate how students construct understanding of these properties. In this study sixth grade students were invited to reason with a peer about calculation strategies for multiplication with the goal of explaining and justifying distributivity. Their discussions demonstrate that the representation of multiplication as equal groups helps them to explain and justify distributivity. At the same time this representation hinders their efficient use of commutativity.

Mots clés: Multiplicative reasoning; distributivity; commutativity; equal groups

Domaines: Education; Histoire et perspectives sur les mathématiques [math.HO]

Kerstin Larsson. Sixth grade students' explanations and justifications of distributivity. CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education, Charles University in Prague, Faculty of Education; ERME, Feb 2015, Prague, Czech Republic. pp.295-301. ⟨hal-01281847⟩