THE GEOMETRY THROUGH THE BODY: DOING, ACTING, THINKING

The geometry has been for more than two millennia one of the most important fields of knowledge of mathematics, identifying with it for a long time. In education, the relationship between the geometry and the physical world has always been considered one of the main elements for the acquisition of specific skills and competences. In the teaching-learning processes the thinking and the interconnection between doing, acting, thinking is therefore crucial.Teaching through the body may prove effective for teaching mathematics which, very often, is hard to be learned because of difficulties that the child encounters in assimilating mathematical symbolism and, after, applying it to real life and the abstract context of academic problems.The difficulty that the child encounters in the acquisition of a mathematical concept, is often due to the reason that he experiences with the action too late; it is necessary, indeed, that the manipulative and concrete experience comes before the others.Piaget stated that "the intelligence is a system of operations [...], the operation is nothing more than action: a real action, but internalized, that becomes reversible. In order that the child comes to combine operations, whether numerical operations or space operations, it is necessary that he has manipulated, it is necessary that he has acted, made experience not only on pictures but on real materials, on physical objects" [1].The child, therefore, learns by doing, and the body, in all its forms, becomes a useful tool for learning.We present here an experimentation with primary school children, in order to teach a few fundamentals of elementary Euclidean geometry; for example, properties of triangles: when we can compose triangles with side lengths ( the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side).