| Summary: | Based on the Genetic Epistemology of Piaget, according to which the main problem is the construction of thoughts by individuals, this researchpaper examines the cognitive instruments that facilitate the progress of mathematical thinking before arriving at the organization of the concepts. The aim of this research paper is to take Piaget’s theory as the main support for investigating which mental processes are activated and how they give form to concepts when an individual is faced with solving a problem relating to mathematics. This reflection, which is part of the investigative project “Genetic Epistemogy and mathematics”, is the result of the revision and analysis of several arguments put forward in the thesis “Cognitive mechanisms common to the history and the psychogenesis of geometry”. It is found that the Intra-Inter-Trans mechanism is of great help in understanding how the mind of individuals behaves, and that its study is valid and has useful consequences for epistemology and the pedagogy of mathematics.
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