Abstract

MARTINEZ-MIRAVAL, Mihály André  and  GARCIA-RODRIGUEZ, Martha Leticia. Covariational Reasoning and its Role in the Study of the Defined Integral from Problem Solving. Rev. Fac. Cienc. Tecnol. [online]. 2023, n.54, pp.154-171.  Epub Feb 09, 2024. ISSN 0121-3814.  https://doi.org/10.17227/ted.num54-16602.

This study aims to analyze if there are descriptors associated with covariational reasoning in the processes of problems-solving related to definite integrals. In research about this subject, the presence of covariational reasoning is implicitly or explicitly identified, which suggests the need to know about the relationship between this type of reasoning and the resolution processes that involve the concept of definite integral. In this study, the theoretical construct of covariational reasoning was adopted, and a documentary research was carried out through a systematic review of research papers that addressed the study of the definite integral published during the last 8 years, according to four assessment indexes in Mathematics Education. As a result of the systematic review, four works were identified that address this concept through approximation or accumulation processes; in which is reported that the students made reference to: changes in the value of one quantity as occurring simultaneously with changes in the value of another; two variables continuously changing; and, a new element that result from the coordination of the values of two quantities that vary together, . all descriptors of different levels of covariational reasoning. It is concluded that student's reason covariationally during the resolution of problems related to the definite integral and it seems that the characteristics of their reasoning are related to success in the resolution process, an aspect that requires further investigation.

Keywords : definite integral; covariational reasoning; problem-solving; technologies.

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