From Euclid as Textbook to the Giovanni Gentile Reform (1867–1923): Problems, Methods and Debates in Mathematics Teaching in Italy

Giuseppe Peano and his School: Axiomatics, Symbolism and Rigor

“…Other philosophical explanations have also been suggested: Peano's utilitarian approach to logic [Grattan-Guinness 2000] and symbolic notation [Bellucci, Moktefi et al 2018]; the lack of a shared and explicit epistemological framework for relevant logical and methodological issues such as functions [Luciano 2017], [Cantù 2021], logical identities [Cantù 2007], definitions by abstraction [Mancosu 2018], and questions of purity [Arana & Mancosu 2012]; a subdivision of labour that led to Giovanni Vailati in Italy [Arrighi, Cantù et al 2009] and Louis Couturat in France [Luciano & Roero 2005] becoming the chief philosophical spokesmen of the group; the belief that Peano's presentation of arithmetical axioms had less interesting philosophical implications with respect to logicism and structuralism than that of Dedekind [Ferreirós 2005]; the interest of Peano's collaborators in pedagogical and political issues [Giacardi 2006], [Luciano 2012].…”

“…It was neither a negation of the importance of experimental methods in the early stages of mathematical education [Luciano 2020] nor a simplistic negation of mathematical intuition which was banished from the proofs of a theory but remained decisive in the choice of axioms [Rizza 2009]. It was instead a didactical objective developed through exchanges with school teachers and their associations, the publication of new textbooks, and participation in educational Governmental Committees [Giacardi 2006].…”

History of Mathematics Teaching and Learning

“…There is a tremendous amount of literature on these reforms (e.g. Giacardi 2006Giacardi , 2009ain Russia: Karp 2009.…”

“…This influence may be at times construed as beneficial or harmful. Kilpatrick (2012b) looks into the role of mathematicians in the New Math movement, which remains a striking (albeit not the only) example of mathematicians' taking an active part in curriculum reform (another example is to be found in Italy in the first quarter of the 20th century; see Giacardi 2006). Nor should it be forgotten that the major international reforms in mathematics education in the early 20th century were connected with mathematicians, most notably Felix Klein.…”