Review and restructuring of the teaching of calculus in engineering: content analysis, evaluation strategies and contextualization in the academic programs of the School of Mines
DOI:
https://doi.org/10.26507/paper.4422Keywords:
Content analysis, differential calculus, integral calculus, pedagogical strategies, evaluation strategies.Abstract
The teaching of differential and integral calculus is an essential component in the education of engineering students, as it provides key tools for the analysis and resolution of complex technical problems. However, in contexts such as the Faculty of Mines at the National University of Colombia, persistent difficulties have been identified that affect the learning process of these courses.
As a starting point, the findings from a previous study were revisited, in which an exhaustive diagnosis of the teaching of calculus at the Faculty of Mines was conducted. This diagnosis included surveys of students, interviews with professors, and a comparative review of calculus curricula at Colombian and foreign universities, as well as within the same institution. The results revealed critical factors impacting the learning process, such as the lack of solid mathematical foundations, the presence of topics that are addressed but never revisited, excessive class sizes, limited personalized interaction with teachers, and an evaluative approach focused solely on outcomes. These elements have contributed to a superficial and fragmented understanding of mathematical concepts.
In response to these issues, a pilot proposal for an innovative integral calculus course was designed, centered on meaningful and contextualized learning. This proposal includes an active methodology, with reorganized content, multiple representations, and formative assessments instead of traditional exams. It envisions the use of face-to-face classes, collaborative activities, tutoring, digital platforms, and engineering projects to encourage student participation and the practical application of knowledge.
The project is structured in three phases: course design, implementation with a voluntary group of students, and comprehensive evaluation through both qualitative and quantitative techniques. Although the implementation phase has not yet been carried out, it is expected that this intervention will contribute to strengthening the teaching of calculus in engineering, improving academic performance, and fostering the development of long-lasting and applicable knowledge in the professional context.
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