Towards a “resonance” comprehension of the polynomial representation of numbers

In this paper we present some of the main aspects of the cognitive model of “resonance”, as a tool to describe, plan and manage teaching and learning processes in mathematics. According to the Vygotskian tradition, in this model mathematics education is seen as the gradual development and refinement, by means of cultural mediation and social interaction, of natural strategies that are known to be at the root of mathematics. In this paper, we aim to show how resonance dynamics can be triggered through the intentional use of suitable artefacts. In particular, we describe the first steps of a possible early approach to the polynomial representations of numbers in a first grade class.