Analysis of definitions of limit provided by University students
DOI:
https://doi.org/10.15359/ru.35-2.18Keywords:
limit concept, calculus, mathematical content, didactics of mathematical analysis, university students, advanced mathematical thinkingAbstract
This paper serves two objectives: analyze the definitions provided by college students for the concept of limit at a point in a function as well as design and validate a category system to carry it out. The definitions of limit were provided by 38 university students in the Biology and Engineering in Industrial Chemistry program, enrolled in a Differential and Integral Calculus course during the first semester of 2018, at Universidad Nacional, Costa Rica. A priori categories were used and complemented with other categories of an inductive nature, which emerged during the analysis of the responses. These categories were validated through a reliability analysis. Approximately half of the students’ answers showed the limit category as an object and over three-quarters showed the limit category as a process. In addition, approximately half of their answers showed the categories terms of relative position and general lack of coordination of the processes. The category system created allowed for the analysis of information units in an organized, simple, and replicable way. Finally, students showed a dual conception of limit either as an object, fixed and static notion, or as a process, processual and dynamic notion. Furthermore, the content analysis described in the methodology may allow future researchers to create a similar category system or use this one for research in other contexts.
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