Understanding the concept of the Limit of a Real Function

in different academic stages of higher education

Abstract

In this qualitative study with an interpretive approach, the understanding of the concept of the limit of a real-variable function was analyzed in five students from the Faculty of Physical and Mathematical Sciences at the Benemérita Universidad Autónoma de Puebla, who were at different stages of their undergraduate and graduate programs in mathematical sciences. The design and analysis of the activities carried out by the participants are framed within the APOS theory and the Theory of Semiotic Representations. The purpose was to explore how the understanding of the limit of a function change throughout the students' mathematical education from the perspective of APOS theory. The analysis also considered different semiotic registers and identified difficulties that might persist among students during their mathematical training. The methodology of this research was based on the APOS theory cycle, which consists of three components: theoretical analysis, the design and application of questionnaires, and the analysis and verification of data. The analysis of the results indicates that the doctoral student has constructed the Object of the limit of a real-variable function, performing all the requested semiotic transformations in the given registers using formal and precise language. Meanwhile, the master's and undergraduate students showed evidence of a Process conception of the limit of a function under construction and had difficulties performing some treatments in the algebraic register.