Seeking symmetry in distributive property: Children developing structure sense in arithmetic

Andrea Maffia (1) , Maria Alessandra Mariotti

1 UNIMORE - Università degli Studi di Modena e Reggio Emilia = University of Modena and Reggio Emilia

Structure sense can be mobilized by pupils to compare and to transform arithmetical expressions, however sometimes it can lead to mathematical inconsistency that pupils might be not aware of. This paper provides evidence of this type of phenomenon. Through the analysis of an interview with a third grader, it is shown that the development of structure sense can result in transformations as a×b+a×c→(a+a)×(b+c). It is concluded that a development of structure sense requires a dialectical control between the syntactic and semantic interpretations of symbolic sentences.

Keywords: Structure sense; distributive property; arithmetic; syntactical transformations

Domains: Mathematics [math]; Humanities and Social Sciences

Andrea Maffia, Maria Alessandra Mariotti. Seeking symmetry in distributive property: Children developing structure sense in arithmetic. CERME 10, Feb 2017, Dublin, Ireland. ⟨hal-01873466⟩