New Approaches to Basic Calculus: An Experimentation via Numerical Computation

The introduction of the first elements of calculus both in the first university year and in the last class of high schools, presents many problems both in Italy and abroad. Emblematic are the (numerous) cases in which students decide to change their course of study or give it up completely cause the difficulties with the first exam of mathematics, which usually deals with basic calculus. This work concerns an educational experimentation involving (with differentiated methods) about 170 students, part at the IPS "F. Besta" in Treviso (IT) with main focus on two 5th classes where the students' age is about 19 years old, and part at the Liceo Classico Scientifico "XXV Aprile" in Pontedera, prov. of Pisa (IT). The experimental project aims to explore the teaching potential offered by non-classical approaches to calculus jointly with the so-called "unimaginable numbers". In particular, we employed the computational method recently proposed by Y.D. Sergeyev and widely used both in mathematics, in applied sciences and, recently, also for educational purposes. In the paper will be illustrated tools, investigation methodologies, collected data (before and after the teaching unit), and the results of various class tests.