Approaching the distributive law with young pupils, PNA, vol. 3, n.2, 73-85

This paper contributes to the research strand concerning early algebra and focuses on the distributive law. It reports on a study involving pupils aged 8 to 10, engaging in the solution of problem situations, purposefully designed and presented through concrete objects, drawings, oral or written descriptions. The study focuses on ways in which perception leads to different mental images that influence the choice of either the (a+b)c or the (a)c)+(b)c) representation. Our hypothesis is that understanding these dynamics is a fundamental step for the construction of a meaningful approach to properties based on suitable activities, organised so as to favour an explicit statement of proposed solutions and a collective comparison of arithmetic expressions that codify solution processes.