Mathematics and children's mind: the role of geometry in the European tradition from Pestalozzi to Laisant

The great cultural and political project of a gradual extension of primary education to every child during the 19th century was accompanied by an effort to rethink mathematics for children. The challenge was to overcome the European tradition of utilitarian training aimed at numeracy. The attention paid to very young children (Pestalozzi, Fröbel) and to children with disabilities (Séguin, Montessori) led to a stronger focus on naïf geometrical concepts as preparatory to reading and writing and further education. Many ideas played a role in this evolution: the confidence in the precocity of mathematical intelligence and the suitability of mathematical concepts (number and form, as Pestalozzi put it) to the enhancement of the child's mind; the revival of the philosophical-mathematical component of classical paideia (liberal education) as a counterbalance to religious influence in education. An interesting change in the mode of presentation of mathematics to children at the beginning of primary school was presented by Laisant in his book Initiation mathématique (1906), combining the essential arithmetical rules with geometry. These contributions can be linked to the evolution of 19th century ideas regarding an intuitive geometry for the middle school. They are a source of inspiration in present practice regarding mathematical education in primary school because they throw light on the place of geometrical thinking in children's first approach to mathematics.