Positional value and the writing of natural numbers in primary school through the synergy of artefacts

This contribution proposes a didactic path for Primary School aimed at conceptualizing the positional value in writing natural numbers, the concept of base, and polynomial representation, through the integrated use of manipulative and digital artefacts. The proposal is based on a research project conducted within the theoretical framework of the Theory of Semiotic Mediation (Bartolini Bussi & Mariotti, 2008) and aims to describe the design process and analyze key moments of the didactic intervention. The Italian National Guidelines highlight the importance of writing, reading, and counting natural numbers in problem-solving, but the traditional approach tends to favor mechanical counting. According to Baccaglini-Frank, Di Martino, and Maracci (2020), it is fundamental to promote a number sense to encourage mental management. The experiment was based on two didactic cycles: one with manipulative artefacts (straws and elastic bands) and one with the digital artefact "ValorePosizionale" (PositionalValue). The analysis of the results highlights the effectiveness of the synergy between the two artefacts in promoting the construction of the meaning of natural numbers.