Competenze in didattica della matematica. Quarta parte: metodologie ed epistemologie del presente. Skills in teaching Mathematics” Fourth part: Methodologies and Epistemologies of the Present.

In Annex A to the DPCM of 4 August 2023 it is stated that «the qualified teachers must demonstrate mas-tery 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 con-nections existing among the knowledge areas to which the competition class refers or toward other dis-ciplines». In a series of four notes, we intend to ad-dress the points mentioned above. In this fourth note, we will discuss the epistemologies and mathematical teaching methodologies of the present times. Regard-ing the epistemology of present times, we will show the great changes that occurred recently. As regards the teaching methodology, we will talk about the min-isterial initiatives of the last 50 years up to the recently published STEM guidelines and we will give examples of teaching approaches consistent with these lines.