Overview of mathematical knowledge prior to differential calculus in first-year university students

Abstract

The present study analyzes the level of prior mathematical knowledge among first-year Computer Systems Engineering students to understand how this knowledge influences their transition into the differential calculus course. Through a diagnostic test administered to 58 students, heterogeneous performance was identified, characterized by basic strengths in arithmetic and geometry, but with significant weaknesses in algebra and, more critically, in trigonometry. These results reveal conceptual gaps that constrain the development of the variational and functional reasoning required for calculus. Grounded in learning theories such as Ausubel, Piaget, and Vygotsky, the analysis shows that the absence of robust prior structures hinders the acquisition of new mathematical concepts. The study underscores the need to reinforce specific content before the course and to implement institutional diagnostic and leveling strategies to strengthen student retention and performance in engineering programs.