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Lara Escobar, R. D. ., Cárdenas Delgado, O. ., Garcés Gómez, Y. A. ., Parra, P. A. ., & López Jimenez, P. A. . (2022). Juicios metacognitivos en el aprendizaje del concepto de derivada utilizando la estrategia del laboratorio virtual. Latinoamericana De Estudios Educativos, 18(1), 169–186. https://doi.org/10.17151/rlee.2022.18.1.9
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Rubén Darío Lara Escobar
Perfil Google Scholar
Oscar Cárdenas Delgado
Yeison A. Garcés Gómez
Paulo Andrés Parra
Paula Andrea López Jimenez
Resumen
Esta investigación implementó una intervención en el aula, utilizando un laboratorio virtual como estrategia didáctica basada en la comprensión del concepto de derivada, aplicado al problema de la línea tangente. Se aplicó la metodología Pretest-Posttest para ver si existen diferencias significativas en el aprendizaje del concepto de derivada en comparación con el enfoque de enseñanza tradicional. Los resultados indican que al realizar el análisis estadístico se identifican tres categorías en relación a las competencias desarrolladas por los estudiantes: solución de ecuaciones, identificación de términos y cuestiones conceptuales. Se encontró diferencia en las varianzas de poblaciones para la competencia de resolución de ecuaciones, obteniendo mejor desempeño en el grupo experimental; las otras dos categorías muestran un desempeño similar en ambos grupos, por lo que consideramos el método propuesto como una forma alternativa de enseñar el concepto de derivada. Finalmente, se identificaron las estrategias de regulación metacognitiva aplicadas por los estudiantes durante el proceso de intervención didáctica.
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Buitrago, S., & García, L. (2011). Procesos de regulación metacognitiva en la resolución de problemas. En Memorias del 12° Encuentro Colombiano de Matemática Educativa
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Davis, P., Hersh, R., & Marchisotto, E. A. (2011). The mathematical experience. Springer Science & Business Media.
Cheung, C.-N., & Wong, W.-C. (2011). Understanding Conceptual Development Along the Implicit-Explicit Dimension: Looking Through the Lens of the Representational Redescription Model. Child Development, 82(6), 2037–2052. https://doi.org/10.1111/j.1467- 8624.2011.01657.x
Elif, A. K. A. R., Tekkaya, C., & Çakiroğlu, J. (2011). The interplay between metacognitive awareness and scientific epistemological beliefs. International Journal on New Trends in Education and Their Implications, 7.
Flavell, J. H. (1970). Developmental Studies of Mediated Memory. Advances in Child Development and Behavior, 5, 181–211. https://doi.org/10.1016/S0065-2407(08)60467-X
Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive-developmental inquiry. American Psychologist, 34(10), 906–911.
https://doi.org/10.1037/0003-066X.34.10.906
Flavell, J. H. (1999). Cognitive development: Children’s knowledge about the mind. Annual Review of Psychology, 50, 21–45. https://doi.org/10.1146/annurev.psych.50.1.21
Flavell, J. H., & Wellman, H. M. (1975). Metamemory. Institue of Child Development. https://eric.ed.gov/?id=ED115405
Frumos, F. V. (2015). Metacognitive monitoring accuracy and academic performance at university students. Journal of Innovation in Psychology, Education and Didactics, 19(2), 307-314.
García, T., Rodríguez, C., González-Castro, P., González-Pienda, J. A., & Torrance, M. (2016). Elementary students’ metacognitive processes and post-performance calibration on mathematical problem-solving tasks. Metacognition and Learning, 11(2), 139-170.
Gok, T. (2010). The General Assessment of Problem Solving Processes and Metacognition in Physics Education. International Journal of Physics & Chemistry Education,
2(2),110-122. https://doi.org/10.51724/ijpce.v2i2.186
Hacker, D. J., Dunlosky, J. & Graesser, A. C. (Eds). (1998). Metacognition in educational theory and practice. Lawrence Erlbaum Associates Publishers.
Händel, M., & Dresel, M. (2018). Confidence in performance judgment accuracy: the unskilled and unaware effect revisited. Metacognition and learning, 13(3), 265–285.
https://doi.org/10.1007/s11409-018-9185-6
Hashemi, N., Abu, M. S., Kashefi, H., Mokhtar, M., & Rahimi, K. (2015). Designing learning strategy to improve undergraduate students’ problem solving in derivatives and integrals: A conceptual framework. Eurasia Journal of Mathematics, Science and Technology Education, 11(2), 227-238. https://doi.org/10.12973/eurasia.2015.1318a
Ho, S. Y., & Lowrie, T. (2014). The model method: students’ performance and its effectiveness. Journal of Mathematical Behavior, 35, 87–100. https://doi.org/10.1016/j.jmathb.2014.06.002
Huitt, W. (1997). Metacognition. Educational Psychology Interactive. Valdosta State University.
Izzati, L. R. (2021). The effect of problem-based learning to improve students’ metacognition skills in solving mathematical problems based on cognitive style. Journal of Physics: Conference Series, 1918(4). https://doi.org/10.1088/1742-6596/1918/4/042073
Kitcher, P. (1984). The nature of mathematical knowledge. Oxford University Press.
Kline, M. (1998). El fracaso de la matemática moderna; por qué Juanito no sabe sumar, (18a ed.). Silglo veintiuno editores
Lakatos, I. (2015). Proofs and refutations: The logic of mathematical discovery. Cambridge university press.
Lan, X., & Ying, Z. (2021). Teaching Derivative Concept Using 6 Questions Cognitive Model. Journal of Didactic Mathematics, 1(3),127-137. https://doi.org/10.34007/jdm.v1i3.371
Llorens Fuster, J. L., & Pérez Carreras, P. (1996). Aplicación del modelo de van Hiele al concepto de aproximación local. Suma: Revista sobre Enseñanza y Aprendizaje de las Matemáticas, 22, 13–24. https://dialnet.unirioja.es/servlet/articulo?codigo=152347
Londoño, D. M. M., Cardozo, M. O., Ferreras, A. P., & Alzate, Ó. E. T. (2021). Los juicios metacognitivos como un campo emergente de investigación. Una revisión sistemática (2016-2020). Latinoamericana de Estudios Educativos, 17(1), 188-223.
Martin, C. S., Polly, D., & Kissel, B. (2017). Exploring the impact of written reflections on learning in the elementary mathematics classroom. Journal Of Educational Research, 110(5), 538–553. https://doi.org/10.1080/00220671.2016.1149793
Mayer, R. E. (1998). Cognitive, metacognitive, and motivational aspects of problem solving. Instructional Science, 26(1–2), 49–63.
Moshman, D. (2018). Metacognitive theories revisited. Educational Psychology Review, 30(2), 599-606. https://psycnet.apa.org/doi/10.1007/s10648-017-9413-7
Özsoy, G., & Ataman, A. (2009). The effect of metacognitive strategy training on mathematical problem solving achievement. International Electronic Journal of Elementary Education, 1(2), 68–83. https://files.eric.ed.gov/fulltext/ED508334.pdf
Pedhazur, E. J., & Schmelkin, L. P. (1991). Measurement, design, and analysis: An integrated approach (Student ed.). Lawrence Erlbaum Associates, Inc.
Polya, G. (2004). How to solve it: a new aspect of mathematical method. Princeton University press. Sandi-Urena, S., Cooper, M., & Stevens, R. (2012). Effect of cooperative problem-based lab instruction on metacognition and problem-solving skills. Journal of Chemical Education, 89(6),700-706. https://doi.org/10.1021/ed1011844
Vaccaro, A. G., & Fleming, S. M. (2018). Thinking about thinking: A coordinate-based meta-analysis of neuroimaging studies of metacognitive judgements. Brain and Neuroscience Advances, 2, 1-14. https://doi.org/10.1177/2398212818810591
Vega Urquieta, M. A., Carrillo Yañez, J. & Soto Andrade, J. (2014). Analysis according to the cognitive model following constructed learning of the concept of derivative. Bolema - Mathematics Education Bulletin, 28(48),403-429. https://doi.org/10.1590/1980-4415v28n48a20
Veenman, M. V., & Van Cleef, D. (2019). Measuring metacognitive skills for mathematics: students’ self-reports versus on-line assessment methods. ZDM: The International Journal on Mathematics Education, 51(4), 691-701.
Vinner, S. (2002). The Role of Definitions in the Teaching and Learning of Mathematics. En Tall D. (eds), Mathematics Education Library, (Vol. 11, pp. 65–81), Springer. https://doi.org/10.1007/0-306-47203-1_5
Vinner, S., & Dreyfus, T. (1989). Images and Definitions for the Concept of Function. Journal for Research in Mathematics Education, 20(4), 356–366. https://doi.org/10.2307/749441
Wewe, M. (2020). The Profile of Students’ Learning Difficulties in Concepts Mastery in Calculus Course. Desimal: Jurnal Matematika, 3(2), 161-168.
https://doi.org/10.24042/djm.v3i2.6421
Woolfolk, A. (2010). Pisicología educativa,(11a ed.). Pearson.
Ye, L., Posada, A., & Liu, Y. (2019). A Review on the Relationship Between Chinese Adolescents’ Stress and Academic Achievement: Stress and Academic Achievement. New Directions for Child and Adolescent Development, 2019(163), 81-95. https://doi.org/10.1002/cad.20265
Young, A. E., & Worrell, F. C. (2018). Comparing metacognition assessments of mathematics in academically talented students. Gifted Child Quarterly, 62(3), 259-275.
https://doi.org/10.1177/0016986218755915
Zambrano, R. A., Ávila, D. I. E., & Medrano, E. F. (2019). An introduction to the concept of derivative in high school students. Educacion Matematica, 31(1). https://doi.org/10.24844/EM3101.10
Zengin, Y. (2018). Examination of the constructed dynamic bridge between the concepts of differential and derivative with the integration of GeoGebra and the ACODESA method. Educational Studies in Mathematics, 99(3), 311–333. https://doi.org/10.1007/s10649-018-9832-5
Zubaidah Amir, M. Z. (2016). Exploration of Metacognitive Ability at Elementary School Students in Learning Mathematics. Journal of Innovative Technology and Education, 3(1), 179-184. http://dx.doi.org/10.12988/jite.2016.6834
Bringula, R. P., Basa, R. S., Dela Cruz, C., & Rodrigo, M. M. T. (2016). Effects of Prior Knowledge in Mathematics on Learner-Interface Interactions in a Learning-by-Teaching Intelligent Tutoring System. Journal of Educational Computing Research, 54(4), 462–482. https://doi.org/10.1177/0735633115622213
Buitrago, S., & García, L. (2011). Procesos de regulación metacognitiva en la resolución de problemas. En Memorias del 12° Encuentro Colombiano de Matemática Educativa
(pp. 548–559). http://funes.uniandes.edu.co/2373/
Campbell, D. T., & Stanley, J. C. (1995). Diseños experimentales y cuasiexperimentales en la investigación social. Amorrortu editores.
Davis, P., Hersh, R., & Marchisotto, E. A. (2011). The mathematical experience. Springer Science & Business Media.
Cheung, C.-N., & Wong, W.-C. (2011). Understanding Conceptual Development Along the Implicit-Explicit Dimension: Looking Through the Lens of the Representational Redescription Model. Child Development, 82(6), 2037–2052. https://doi.org/10.1111/j.1467- 8624.2011.01657.x
Elif, A. K. A. R., Tekkaya, C., & Çakiroğlu, J. (2011). The interplay between metacognitive awareness and scientific epistemological beliefs. International Journal on New Trends in Education and Their Implications, 7.
Flavell, J. H. (1970). Developmental Studies of Mediated Memory. Advances in Child Development and Behavior, 5, 181–211. https://doi.org/10.1016/S0065-2407(08)60467-X
Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive-developmental inquiry. American Psychologist, 34(10), 906–911.
https://doi.org/10.1037/0003-066X.34.10.906
Flavell, J. H. (1999). Cognitive development: Children’s knowledge about the mind. Annual Review of Psychology, 50, 21–45. https://doi.org/10.1146/annurev.psych.50.1.21
Flavell, J. H., & Wellman, H. M. (1975). Metamemory. Institue of Child Development. https://eric.ed.gov/?id=ED115405
Frumos, F. V. (2015). Metacognitive monitoring accuracy and academic performance at university students. Journal of Innovation in Psychology, Education and Didactics, 19(2), 307-314.
García, T., Rodríguez, C., González-Castro, P., González-Pienda, J. A., & Torrance, M. (2016). Elementary students’ metacognitive processes and post-performance calibration on mathematical problem-solving tasks. Metacognition and Learning, 11(2), 139-170.
Gok, T. (2010). The General Assessment of Problem Solving Processes and Metacognition in Physics Education. International Journal of Physics & Chemistry Education,
2(2),110-122. https://doi.org/10.51724/ijpce.v2i2.186
Hacker, D. J., Dunlosky, J. & Graesser, A. C. (Eds). (1998). Metacognition in educational theory and practice. Lawrence Erlbaum Associates Publishers.
Händel, M., & Dresel, M. (2018). Confidence in performance judgment accuracy: the unskilled and unaware effect revisited. Metacognition and learning, 13(3), 265–285.
https://doi.org/10.1007/s11409-018-9185-6
Hashemi, N., Abu, M. S., Kashefi, H., Mokhtar, M., & Rahimi, K. (2015). Designing learning strategy to improve undergraduate students’ problem solving in derivatives and integrals: A conceptual framework. Eurasia Journal of Mathematics, Science and Technology Education, 11(2), 227-238. https://doi.org/10.12973/eurasia.2015.1318a
Ho, S. Y., & Lowrie, T. (2014). The model method: students’ performance and its effectiveness. Journal of Mathematical Behavior, 35, 87–100. https://doi.org/10.1016/j.jmathb.2014.06.002
Huitt, W. (1997). Metacognition. Educational Psychology Interactive. Valdosta State University.
Izzati, L. R. (2021). The effect of problem-based learning to improve students’ metacognition skills in solving mathematical problems based on cognitive style. Journal of Physics: Conference Series, 1918(4). https://doi.org/10.1088/1742-6596/1918/4/042073
Kitcher, P. (1984). The nature of mathematical knowledge. Oxford University Press.
Kline, M. (1998). El fracaso de la matemática moderna; por qué Juanito no sabe sumar, (18a ed.). Silglo veintiuno editores
Lakatos, I. (2015). Proofs and refutations: The logic of mathematical discovery. Cambridge university press.
Lan, X., & Ying, Z. (2021). Teaching Derivative Concept Using 6 Questions Cognitive Model. Journal of Didactic Mathematics, 1(3),127-137. https://doi.org/10.34007/jdm.v1i3.371
Llorens Fuster, J. L., & Pérez Carreras, P. (1996). Aplicación del modelo de van Hiele al concepto de aproximación local. Suma: Revista sobre Enseñanza y Aprendizaje de las Matemáticas, 22, 13–24. https://dialnet.unirioja.es/servlet/articulo?codigo=152347
Londoño, D. M. M., Cardozo, M. O., Ferreras, A. P., & Alzate, Ó. E. T. (2021). Los juicios metacognitivos como un campo emergente de investigación. Una revisión sistemática (2016-2020). Latinoamericana de Estudios Educativos, 17(1), 188-223.
Martin, C. S., Polly, D., & Kissel, B. (2017). Exploring the impact of written reflections on learning in the elementary mathematics classroom. Journal Of Educational Research, 110(5), 538–553. https://doi.org/10.1080/00220671.2016.1149793
Mayer, R. E. (1998). Cognitive, metacognitive, and motivational aspects of problem solving. Instructional Science, 26(1–2), 49–63.
Moshman, D. (2018). Metacognitive theories revisited. Educational Psychology Review, 30(2), 599-606. https://psycnet.apa.org/doi/10.1007/s10648-017-9413-7
Özsoy, G., & Ataman, A. (2009). The effect of metacognitive strategy training on mathematical problem solving achievement. International Electronic Journal of Elementary Education, 1(2), 68–83. https://files.eric.ed.gov/fulltext/ED508334.pdf
Pedhazur, E. J., & Schmelkin, L. P. (1991). Measurement, design, and analysis: An integrated approach (Student ed.). Lawrence Erlbaum Associates, Inc.
Polya, G. (2004). How to solve it: a new aspect of mathematical method. Princeton University press. Sandi-Urena, S., Cooper, M., & Stevens, R. (2012). Effect of cooperative problem-based lab instruction on metacognition and problem-solving skills. Journal of Chemical Education, 89(6),700-706. https://doi.org/10.1021/ed1011844
Vaccaro, A. G., & Fleming, S. M. (2018). Thinking about thinking: A coordinate-based meta-analysis of neuroimaging studies of metacognitive judgements. Brain and Neuroscience Advances, 2, 1-14. https://doi.org/10.1177/2398212818810591
Vega Urquieta, M. A., Carrillo Yañez, J. & Soto Andrade, J. (2014). Analysis according to the cognitive model following constructed learning of the concept of derivative. Bolema - Mathematics Education Bulletin, 28(48),403-429. https://doi.org/10.1590/1980-4415v28n48a20
Veenman, M. V., & Van Cleef, D. (2019). Measuring metacognitive skills for mathematics: students’ self-reports versus on-line assessment methods. ZDM: The International Journal on Mathematics Education, 51(4), 691-701.
Vinner, S. (2002). The Role of Definitions in the Teaching and Learning of Mathematics. En Tall D. (eds), Mathematics Education Library, (Vol. 11, pp. 65–81), Springer. https://doi.org/10.1007/0-306-47203-1_5
Vinner, S., & Dreyfus, T. (1989). Images and Definitions for the Concept of Function. Journal for Research in Mathematics Education, 20(4), 356–366. https://doi.org/10.2307/749441
Wewe, M. (2020). The Profile of Students’ Learning Difficulties in Concepts Mastery in Calculus Course. Desimal: Jurnal Matematika, 3(2), 161-168.
https://doi.org/10.24042/djm.v3i2.6421
Woolfolk, A. (2010). Pisicología educativa,(11a ed.). Pearson.
Ye, L., Posada, A., & Liu, Y. (2019). A Review on the Relationship Between Chinese Adolescents’ Stress and Academic Achievement: Stress and Academic Achievement. New Directions for Child and Adolescent Development, 2019(163), 81-95. https://doi.org/10.1002/cad.20265
Young, A. E., & Worrell, F. C. (2018). Comparing metacognition assessments of mathematics in academically talented students. Gifted Child Quarterly, 62(3), 259-275.
https://doi.org/10.1177/0016986218755915
Zambrano, R. A., Ávila, D. I. E., & Medrano, E. F. (2019). An introduction to the concept of derivative in high school students. Educacion Matematica, 31(1). https://doi.org/10.24844/EM3101.10
Zengin, Y. (2018). Examination of the constructed dynamic bridge between the concepts of differential and derivative with the integration of GeoGebra and the ACODESA method. Educational Studies in Mathematics, 99(3), 311–333. https://doi.org/10.1007/s10649-018-9832-5
Zubaidah Amir, M. Z. (2016). Exploration of Metacognitive Ability at Elementary School Students in Learning Mathematics. Journal of Innovative Technology and Education, 3(1), 179-184. http://dx.doi.org/10.12988/jite.2016.6834
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