Enseñanza del Cálculo Integral en Contextos Reales con mediación Tecnológica: Revisión Crítica y Sistematización de una Experiencia Formativa
Resumen
El cálculo integral suele enseñarse como repertorio de técnicas, aunque su potencia epistemológica reside en representar acumulaciones, cambios netos y relaciones entre tasas y cantidades totales. El objetivo de este artículo es analizar críticamente estrategias para enseñar cálculo integral en contextos reales con mediación tecnológica, reconocer los vacíos de investigación y sistematizar una experiencia formativa del semillero CEEMA, asociado a CITEM-UA. Se realizó una revisión documental integrativa y trazable de un corpus cerrado en agosto de 2026. La auditoría identificó 173 unidades documentales: 161 registros de publicaciones y 12 páginas de resultados de búsqueda. Después de normalizar 14 duplicaciones, se reconocieron 147 publicaciones únicas; 51 tenían descripción detallada y una editorial metodológica genérica fue excluida. El corpus final quedó constituido por 50 publicaciones: 23 atribuidas a Scopus, 12 a Redalyc, 9 a Google Académico y 6 a SciELO. La síntesis muestra cinco núcleos: educación matemática realista y modelación; resolución de problemas; visualización y simulación; evaluación y formación docente; e inteligencia artificial y otras tecnologías. Solo dos publicaciones estudian de manera directa el diseño o la intervención en cálculo, lo que impide generalizar la eficacia de una herramienta. La experiencia analizada articuló definición formal, GeoGebra, técnicas simbólicas y un montaje eléctrico, pero el registro visual permite documentar actividades, no demostrar aprendizaje. Se propone una ruta de seis fases: fenómeno; datos, variables, unidades y supuestos; acumulación discreta; formalización integral; exploración tecnológica; e interpretación, validación y comunicación. La conclusión central es que la tecnología adquiere valor cuando hace examinable la relación entre integrando, diferencial, límites, unidades y fenómeno; sin esta articulación puede automatizar procedimientos y conservar errores conceptuales.
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Derechos de autor 2026 Ernesto Araujo Chavarro, Yonathan Andrés Bermeo Orozco, Manuel Alejandro Cleves Ortega, Cristian Eduardo Hernández Pillimue, Antonio Gutiérrez Morales
Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
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