Competenze in didattica della matematica. Terza parte: metodologie ed epistemologie del passato. Skills in teaching Mathematics” Third part: Methodologies and Epistemologies of the Past

In Annex A to the DPCM of 4 August 2023 it is stated that the qualified teachers must demonstrate mastery in relation to the basic nuclei of disciplinary knowledge, to contemporary epistemologies and methodologies, to epistemologies and methodologies used in the past and to the main interdisciplinary connections existing among the knowledge areas to which the competition class refers or toward other disciplines. In a series of four notes, we intend to address the points mentioned above. In this third note, we will discuss the epistemologies and mathematical teaching methodologies of the past. As regards the epistemology of the past, we will emphasize the three natures of mathematics: pure mathematics, applied mathematics and mathematics as a language to describe natural phenomena. As regards the teaching methodology, we limit ourselves to commenting on the mathematics programs developed by the Ministry of Education from the Unification of Italy until 1985.