A genetic decomposition for continuity of function of a real variable
DOI:
https://doi.org/10.5007/1981-1322.2026.e99881Keywords:
Continuity Of A Function, Genetic Decomposition, APOS TheoryAbstract
The study described in this work, which presents part of the results of a doctoral research, aimed to conjecture about which mental structures and mechanisms need to be constructed by an individual, in order to enable them to understand the concept of continuity of a function . To this end, it was guided by the assumptions of the APOS theory (ARNOON et al., 2014), the authors' knowledge about the mathematical object itself, and the students' understanding of continuity for the formulation of a Genetic Decomposition (DG) for the aforementioned concept. In this sense, the importance of different mathematical objects, such as the concepts of function, limit and domain, among other elements, being included in a DG for the Continuity of a Function object, was highlighted. It is reiterated that the Genetic Decomposition presented can guide both assessment tools and instructional materials that enable the learning process within the scope of Calculus.
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