Thought experiments in the multiplication of natural numbers:

theoretical reflections by means of an alternative methodology

Abstract

This article is part of the theoretical research entitled "Semiotics and Thought Experiments in teaching and learning in Mathematics". It aims to present a theoretical reflection, by means of Thought Experiments, about the operation of Multiplication with natural numbers. Thought Experiments are conceptualized as ways that the subject has to represent its own thinking, which is placed as an object of consideration in the development of a concept, activity and/or problem in Mathematics, through a well-defined theoretical context, which is called representation system, fulfilling the role of showing the consistency of the concept itself (or even its modification) and verify the possibility of applying such concept in different contexts. These categories of experiments, in the context of Mathematics Education, can be considered as an alternative methodology for teaching mathematics. The application of this methodology is important in teaching and respectively in learning mathematics because it provides the development of an environment of investigation and reflection, working in different semantic universes in the understanding of the activity and/or the proposed problem, generating debates and contradictions.