THE GEOMETRY THROUGH THE BODY: DOING, ACTING, THINKING

The visual disability assumes, in the processes of teaching and learning, a particular connotation for the specificity that over the years the vision in the overall structure of knowledge has had. The whole western tradition on the knowledge stood on a "oculocentric" vision of knowledge. The view has always been considered the “sense for excellence". An educational activity, therefore, that emphasizes and promotes strategies of inclusion / integration of students with visual impairment is significant and essential to the whole class group. We present here an experimentation with primary school children: in a closed bag, there are objects of everyday life: every time a child extracts an object and has to describe what he is touching. The teacher begins to distinguish between polyhedra and solids of revolution. For all solids, children and teacher find relationships and focus their attention on the polyhedra. This activity provides an opportunity to understand the differences between different polyhedra; children compare objects that have similar shapes but different sizes: for example, children can discover that parallelepipeds have edges of different lengths while in the cube the edges have the same length. Both have the same number of vertices, edges and faces, but the shapes of the faces are different. 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 experiments with the action too late; it is necessary, indeed, that the manipulative and concrete experience comes before the others.

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. 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)