A big body of research has been devoted to the complications faced by undergraduate students with basic calculus and the means of overcoming them. This situation imposes the urge to try educational approaches that are different from the traditional ones used in most curriculums worldwide. In this paper, we deal with a non-traditional method in teaching basic calculus for undergraduate students. In particular, this study explores the efficiency of a numerical methodology for dealing with infinity and infinitesimals introduced by Yaroslav Sergeyev in the early 2000’s. The Grossone methodology proposed by Sergeyev is a non-classical one yet it doesn’t contradict the classical mathematics. Instead, it provides a simple and easy computational way for dealing with infinite quantities. It is noted that this methodology has been widely used in mathematics and applied sciences. Moreover, it has proved to be fruitful for educational purposes according to the results of several studies done recently. The experimentation involves grade 11 and 12 students in Lebanon in addition to a small group of grade 12 students from an arbitrary secondary public school in Lebanon (ages 17–19). The aim of this study is to check students’ intuitive reactions with the Grossone methodology and compare it to their performance after being subject to a teaching unit highlighting this methodology. It is noted that this study follows the guidelines of a study done recently in Italy for the purpose of comparing the results of addressing Grossone methodology among different educational systems.