Impacto de la Modelización Matemática asistida por IA en el desarrollo del pensamiento Variacional: Un estudio longitudinal en la Educación Superior para el Cálculo Diferencial e Integral

Johnny Mauricio Lima-Narvaez; Aracely Dayanara Toapanta Ortiz; Carlos Eduardo Pule Andrade; Michael Estuardo Ponce Rosero; Esteban David Lima Narváez; Tamara Soledad Pucha Vargas

doi:10.70625/rlce/548

Authors

Johnny Mauricio Lima-Narvaez Universidad Técnica del Norte Author https://orcid.org/0000-0001-7248-2211
Aracely Dayanara Toapanta Ortiz Unidad Educativa Municipal Quitumbe Author https://orcid.org/0009-0002-1314-2035
Carlos Eduardo Pule Andrade Academia Pule Author https://orcid.org/0009-0008-8157-2639
Michael Estuardo Ponce Rosero Unidad Educativa Municipal Sebastián de Benalcázar Author https://orcid.org/0009-0000-9607-9881
Esteban David Lima Narváez Ministerio de Educación, Deporte y Cultura Author https://orcid.org/0009-0009-4391-886X
Tamara Soledad Pucha Vargas Universidad Central del Ecuador Author https://orcid.org/0009-0000-3392-2800

DOI:

https://doi.org/10.70625/rlce/548

Keywords:

Inteligencia Artificial, Pensamiento Variacional, Modelización Matemática

Abstract

Los retos cognitivos que representa aprender cálculo en ingeniería son abordados por la tecnología contemporánea. Este estudio investiga la manera en que el pensamiento variacional puede ser estimulado utilizando modelización matemática respaldada por inteligencia artificial. En una investigación longitudinal, el propósito principal fue determinar la relación entre estas variables en alumnos de la facultad FICA de la Universidad Técnica del Norte. La metodología utilizada fue de carácter cuantitativo y correlacional, con una muestra compuesta por 75 estudiantes. Se empleó el instrumento IMIP-C, que cuenta con una validación mediante un Alfa de Cronbach de 0,934. Las cifras descriptivas mostraron un alto nivel de percepción de covariación (90,7%), mientras que el modelado con IA se posicionó sobre todo en un nivel medio (54,7%). La prueba de Pearson reveló una correlación positiva moderada-fuerte (p < 0,01; r = 0,664) entre el dominio técnico-instrumental de la IA y las mejores competencias para razonar simbólicamente y analizar cambios. Se concluye que la inteligencia artificial es un compañero cognitivo que reduce la carga computacional, posibilitando que el alumno se concentre en entender conceptualmente la integral y la derivada; por lo tanto, es indispensable su integración curricular de manera reflexiva.

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