Background knowledge required for differential calculus. A case study at the National Technical University of Costa Rica: Competencias previas en estudiantes de cálculo diferencial. Análisis de un caso de estudio en la Universidad Técnica Nacional de Costa Rica - Garita Araya, Tonny Andrey (2025)
This article shows that, despite variations in standardized mathematics tests at the end of high school, student performance over the years remains low. It also presents data on student performance in the Calculus course at public universities in Costa Rica. The study focuses on examining the relationship between the official curriculum of the Ministry of Public Education and the mathematical competencies that students acquire to enter higher education, with emphasis on preparation for differential calculus. To this end, we present the results of a diagnostic test that evaluated students' performance in: determining the image of a function, analyzing graphs, solving equations and application problems. These topics, addressed in high school, are fundamental for the understanding of key concepts of differential calculus, such as the interpretation of the derivative and its applications. The research was carried out with a sample of 23 students and revealed significant difficulties in the understanding of basic concepts, such as the calculation of the slope of a line from two points, as well as in the execution of elementary algebraic procedures to solve equations. Based on these results, we compare the proposal for the secondary school mathematics program with the performance of the students, identifying possible barriers that affect the learning of differential calculus.