The School as “Laboratory”. Giovanni Vailati and the Project to Reform Mathematics Teaching in Italy

At the beginning of the twentieth century, although the high level of both Italian mathematical research and the scientific preparation offered by Italian universities was internationally recognised, the secondary schools were in a bad state. In order to address this situation, in 1905 the Minister for Education, Leonardo Bianchi, nominated a Royal Commission charged with drawing up a reform of secondary schools that would respond to the new requirements of Italian society and take into account the reform movements in other parts of Europe. The project for reform was presented in February 1908, but was deemed too radical and was never enacted. The mathematics programme and the methodological instructions related to it were drafted by Giovanni Vailati, a mathematician who belonged to the school of Giuseppe Peano and whose cultural interests were wide ranging. In my paper, I concentrate on the following points: Vailati’s intellectual training; his criticisms of the secondary schools of the time; the pedagogical and methodological assumptions upon which he based his reform project; his concrete proposals for renovating mathematics teaching; the criticisms of his proposals; and the results actually achieved.