Didactics of Infinitesimal Calculus (first part)

The main objective of the course is to introduce the theoretical and applicative aspects of the Didactics of Infinitesimal Calculus, with particular attention to the context of secondary school. In the first part of the course the student will revisit the main topics of study of infinitesimal calculus (limits, derivatives, integrals) deepening the historical roots and the motivations behind their development, and will obtain a critical vision of contents and techniques, and their role in modern Mathematical Analysis.
In the second part of the course will be presented an adaptation to the case of infinitesimal calculus of some results of national and international research in mathematics teaching, with reference to the national indications and reference frameworks for the evaluation of skills, to the criteria underlying the design and implementation of mathematical teaching activities for secondary school, to the tools for the analysis of difficulties and teaching strategies oriented to the enhancement of excellence or inclusion in mathematics. Students will develop skills in didactic design and analysis of the criticalities of learning processes in the case of infinitesimal calculus.

Students must be able to present in an exhaustive way their knowledge related to the first and second part of the course and to design teaching activities and evaluation/assessment tests for secondary school students, based on the results and theoretical frameworks of the research in mathematics teaching presented in the course and on the national indications, in relation to the case of infinitesimal calculus. They must also have developed analytical skills, in particular to be able to critically analyze mathematics textbooks and other teaching resources related to the teaching of infinitesimal calculus. At the same time they will have to acquire communication skills, arguing their choices and exposing their knowledge with a good balance between precision in language and discussion of concrete examples.