Errors, misconceptions, and obstacles in the understanding of function limits: an epistemological and didactic analysis of university students
DOI:
https://doi.org/10.71112/bznkyt39Keywords:
Limit concept, mathematical errors, epistemological obstacles, calculus education, undergraduate mathematics, conceptual understandingAbstract
The learning of the concept of limit of a function remains one of the most challenging topics in undergraduate calculus education, due to the persistence of errors, conceptual difficulties, and epistemological obstacles. This study aims to analyze students’ conceptions and errors related to the understanding of limits from an epistemological and didactical perspective, in order to construct an explanatory taxonomy of mathematical error.
A qualitative interpretative approach was adopted, based on the analysis of written productions, semi-structured interviews, and observation of problem-solving processes. Data analysis was conducted through open, axial, and selective coding, allowing the identification of emerging categories and their articulation with the theoretical framework.
The findings reveal three levels of error: procedural, conceptual, and epistemological. Within the epistemological level, three main obstacles were identified: the algebraic obstacle, the infinitesimal obstacle, and the unitary-pragmatic obstacle, the latter characterized by the reduction of mathematical knowledge to procedural tools aimed at task completion. It is concluded that errors are not isolated failures but manifestations of knowledge structures shaped by the interaction of cognitive, epistemological, and didactical factors.
This study contributes to mathematics education research by proposing a taxonomy of errors that provides an integrated understanding of students’ difficulties in learning limits and offers insights for the design of instructional strategies in higher education.
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