Intuitive and formal models of whole number multiplication: Relations and emerging structures

Multiplication can be presented to students through different models, each one with its pros and cons. In this contribution we focus on the repeated sum and the array model to investigate the relations between the two models and those between them and multiplication properties. Formal counterparts are presented. Taking both a mathematical and cognitive perspective, we highlight that even at a mathematical structure level the models are different. Relating to literature, we connect differences in the mathematical structure with possible educational difficulties. We conclude that experiencing relations between models is a source of learning about the operation and its structure.