The Proposals of the School of Peano on the Rational Teaching of Geometry

Between 1890 and 1940, the School of Peano formulated many proposals for the renewal of the teaching of mathematics, showing a sensitivity regarding the pedagogical tasks and the syllabuses. In this context we intend to analyze the reflections of some members of this team about the introduction of the results of their research activity on the foundations of geometry into education, illustrate the ways used to train teachers in this field, and examine the debates that the ‘rational teaching’ of geometry ignited. An examination of the textbooks by G. Ingrami and A. Pensa will make explicit the epistemological assumptions, elaborated by Pieri Peano and Padoa, on the possibility of presenting maths in classroom as an hypothetical-deductive abstract system and the use of the logical symbolism.