Enseñanza de precálculo en un aula invertida y formación de profesores: Análisis de resultados de una experiencia local

• Autores: Eliana Pepa Risma, Julio Banegas
• Localización: Revista de Educación Matemática (RevEM), ISSN-e 1852-2890, ISSN 0326-8780, Vol. 41, Nº. 1, 2026, págs. 15-35
• Idioma: español
• DOI: 10.33044/revem.52594
• Títulos paralelos:
  • Teaching Precalculus using flipped-classroom and pre-service teacher training: analysis of the results of a local experience
• Enlaces
  • Texto completo
• Resumen
  • español

    Se describen los resultados de una experiencia didáctica que utiliza la estrategia de aula invertida en un curso de precálculo para alumnos de Profesorado en Matemática de una universidad pública nacional. Como actividades previas a la parte presencial de cada clase invertida, los estudiantes debían ver videos explicativos en línea y completar un ejercicio sencillo de aplicación, explicando individualmente sus resultados en un breve video que debían enviar al profesor para su evaluación. Utilizando un diseño de investigación del tipo ex post facto los avances de aprendizaje estudiantil se evaluaron mediante la aplicación de la prueba Precalculus Concept Assessment al inicio y al final del curso, obteniendo una ganancia normalizada g = 0,48. La instrucción no fue efectiva en comportamiento de la tasa de cambio de funciones de una variable, ni en aplicaciones y modelado de situaciones cotidianas o de otras disciplinas. Los estudiantes que completaron las tareas asignadas obtuvieron buenos resultados en la evaluación institucional, mostrando buena correlación entre esta evaluación y los resultados de la prueba. Se analiza la importancia de exponer a los futuros profesores de matemáticas a metodologías de enseñanza no tradicionales. Finalmente, se presentan sugerencias para mejorar esta propuesta dentro del marco delaprendizaje activo.

  • English

    Results of a didactic experience for teaching functions using the flipped classroom strategy in a Precalculus course for future mathematics teachers in a public national university are described. The students had to follow, as pre-class assignments, web-based explanatory videos, completing a simple application exercise, individually explaining their results in a short video that they had to send to the teacher for evaluation. Using an ex post facto research approach, the learning results of this experience were evaluated by applying the Precalculus Concept Assessment test at the beginning and end of the instruction, obtaining a satisfactory normalized gain g = 0.48. The instruction was not effective in aspects related to the behavior of the rate of change of one variable functions and in applications to and modeling of everyday situations, including their use in other disciplines. Students that completed the assigned work performed well on the institutional evaluation, showing a good correlation between this evaluation and the test results. The importance of subjecting prospective math teachers to non-traditional teaching is discussed. Finally, suggestions are made to improve this proposal within the framework of active learning.

• Referencias bibliográficas
  • Ausubel, D. P. (1968). Educational Psychology: A Cognitive View. Holt, Rinehart; Winston.
  • Beichner, R. (1994). Testing Student Interpretation of Kinematics Graphs. American Journal of Physics, 62(8), 750-762. https://doi.org/10.1119/1.17449
  • Bennoun, S., & Holm, T. (2020). Establishing Consistent Active Learning in a Calculus I Course. PRIMUS. https://doi.org/ 10. 1080/ 10511970....
  • Bergmann, J., & Sams, A. (2012). Flip Your Classroom: Reach Every Student in Every Class Every Day. International Society for Technology...
  • Bressoud, D., Mesa, V., & Rasmussen, C. (Eds.). (2015). Insights and Recommendations from the MAA National Study of College Calculus....
  • Carlson, M. P., Madison, B., & West, R. D. (2015). A Study of Students’ Readiness to Learn Calculus. International Journal of Research...
  • Carlson, M. P., Oehrtman, M. C., & Engelke, N. (2010). The Precalculus Concept Assessment (PCA) Instrument: A Tool for Assessing Students’...
  • Chickering, A. W., & Gamson, Z. F. (1991). Seven Principles for Good Practice in Undergraduate Education. New Directions for Teaching...
  • Crouch, C. H., & Mazur, E. (2001). Peer Instruction: Ten Years of Experience and Results. American Journal of Physics, 69, 970-977. https://doi.org/10.1119/1.1374249
  • Crowl, T. (1993). Fundamentals of Educational Research. McGraw-Hill.
  • del Arco, I., Mercadé-Melé, P., Ramos-Pla, A., & Flores-Alarcia, Ò. (2022). Bibliometric Analysis of the Flipped Classroom Pedagogical...
  • Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active Learning Increases...
  • Hake, R. R. (1998). Interactive-Engagement vs Traditional Methods: A Six-ThousandStudent Survey of Mechanics Test Data for Introductory Physics...
  • Miller, R. L., Santana-Vega, E., & Terrell, M. S. (2006). Can Good Questions and Peer Discussion Improve Calculus Instruction? PRIMUS,...
  • O’Flaherty, J., & Phillips, C. (2015). The Use of Flipped Classrooms in Higher Education: A Scoping Review. Internet and Higher Education,...
  • PhysPort. (2025a). Assessments. https://www.physport.org/assessments/
  • PhysPort. (2025b). Assessments. https://www.physport.org/assessments/assessment.cfm?A=PCA
  • Prieto, A., Barbarroja, J., Álvarez, S., & Corell, A. (2021). Eficacia del Modelo de Aula Invertida en la Enseñanza Universitaria: Una...
  • Shulman, L. S. (1987). Knowledge and Teaching: Foundations of the New Reform. Harvard Educational Review, 57(1), 1-22. https://doi.org/10.17763/haer.57.1.j463w79r56455411
  • Smith, S., & Banilower, E. (2012). Extended Paper for PCK Summit. http://pcksummit.bscs.org/sites/default/files/SmithBanilowerEP.pdf
  • Tanujaya, B., & Mumu, J. (2019). Implementation of Think-Pair-Share to Mathematics Instruction. Journal of Education and Learning (EduLearn),...
  • Terrell, M. (2023). Good Questions Project. https://pi.math.cornell.edu/~GoodQuestions/materials.html
  • Thompson, P. W., & Carlson, M. P. (2017). Variation, Covariation, and Functions: Foundational Ways of Thinking Mathematically. En J. Cai...
  • Vygotsky, L. S. (1978). Mind in Society: The Development of Higher Mental Processes. Harvard University Press.
  • Watson, C. N., Duran, P., Castillo, A., Fuller, E., Potvin, G., & Kramer, L. (2023). The Supportive Role of Active Learning in a Calculus...