Modelo VMEEA: marco integral para la enseñanza efectiva de las Matemáticas
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https://doi.org/10.71112/jts98c87Palabras clave:
enseñanza de matemáticas, modelo instruccional, competencia matemática, vocabulario matemático, pedagogía efectivaResumen
La enseñanza de las matemáticas enfrenta desafíos significativos en cuanto a efectividad pedagógica y logro estudiantil. Este artículo presenta el Modelo VMEEA (Vocabulario, Metodología, Explicación, Ejecución, Aplicación), un marco conceptual secuencial que integra cinco componentes esenciales para la instrucción matemática efectiva. Basado en teorías de aprendizaje cognitivo, principios de neurociencia educativa y mejores prácticas documentadas, el modelo VMEEA proporciona una estructura sistemática que facilita tanto la planificación docente como el desarrollo progresivo de la competencia matemática estudiantil. Se discuten los fundamentos teóricos de cada componente, se presentan estrategias específicas de implementación y se proponen áreas para investigación futura.
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Ball, D. L., Thames, M. H., & Bass, H. (2017). Knowing and using mathematics in teaching. En F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 433–456). Information Age Publishing.
Bay-Williams, J. M., & Livers, S. D. (2021). Supporting mathematical language development. Teaching Children Mathematics, 27(4), 236–244.
Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? En S. J. Cho (Ed.), Proceedings of the 12th International Congress on Mathematical Education (pp. 73–96). Springer. https://doi.org/10.1007/978-3-319-12688-3_9
Boaler, J. (2016). Mathematical mindsets: Unleashing students' potential through creative math, inspiring messages and innovative teaching. Jossey-Bass.
Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. Teachers College Record, 110(3), 608–645. https://doi.org/10.1177/016146810811000302
Bressoud, D., Ghedamsi, I., Martinez-Luaces, V., & Törner, G. (2016). Teaching and learning of calculus. Springer. https://doi.org/10.1007/978-3-319-32975-8
Bruner, J. S. (2017). Toward a theory of instruction (Rev. ed.). Belknap Press.
Chapin, S. H., O'Connor, C., & Anderson, N. C. (2021). Classroom discussions in math: A teacher's guide for using talk moves to support the Common Core and more (4th ed.). Math Solutions.
Clark, R. C., & Mayer, R. E. (2016). E-learning and the science of instruction: Proven guidelines for consumers and designers of multimedia learning (4th ed.). Wiley. https://doi.org/10.1002/9781119239086
Cook, S. W., Friedman, H. S., Duggan, K. A., Cui, J., & Popescu, V. (2017). Hand gesture and mathematics learning: Lessons from an avatar. Cognitive Science, 41(2), 518–535. https://doi.org/10.1111/cogs.12344
Creswell, J. W., & Poth, C. N. (2018). Qualitative inquiry and research design: Choosing among five approaches (4th ed.). SAGE Publications.
Darling-Hammond, L., Hyler, M. E., & Gardner, M. (2017). Effective teacher professional development. Learning Policy Institute. https://doi.org/10.54300/122.311
Dehaene, S. (2020). How we learn: Why brains learn better than any machine… for now. Viking.
Dignath, C., & Büttner, G. (2018). Teachers' direct and indirect promotion of self-regulated learning in primary and secondary school mathematics classes. Metacognition and Learning, 13(2), 127–157. https://doi.org/10.1007/s11409-018-9181-x
Drake, S. M., & Reid, J. L. (2018). Integrated curriculum as an effective way to teach 21st century capabilities. Asia Pacific Journal of Educational Research, 1(1), 31–50. https://doi.org/10.30777/APJER.2018.1.1.03
Fisher, D., & Frey, N. (2021). Better learning through structured teaching: A framework for the gradual release of responsibility (3rd ed.). ASCD.
Franklin, C., Bargagliotti, A., Case, C., Kader, G., Scheaffer, R., & Spangler, D. (2017). The statistical education of teachers. American Statistical Association.
Fyfe, E. R., McNeil, N. M., & Borjas, S. (2015). Benefits of concreteness fading for children's mathematics understanding. Learning and Instruction, 35, 104–120. https://doi.org/10.1016/j.learninstruc.2014.10.004
Gagné, R. M. (2016). The conditions of learning and theory of instruction (5th ed.). Wadsworth Publishing.
Geary, D. C. (2020). Cognitive foundations of mathematical development. En D. H. Schunk & J. A. Greene (Eds.), Handbook of self-regulation of learning and performance (2nd ed., pp. 391–408). Routledge.
Gravemeijer, K., Stephan, M., Julie, C., Lin, F. L., & Ohtani, M. (2017). What mathematics education may prepare students for the society of the future? International Journal of Science and Mathematics Education, 15(S1), 105–123. https://doi.org/10.1007/s10763-017-9814-6
Hattie, J. (2018). Visible learning: A synthesis of over 800 meta-analyses relating to achievement (2nd ed.). Routledge. https://doi.org/10.4324/9780203887332
Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81–112. https://doi.org/10.3102/003465430298487
Heritage, M. (2018). Assessment for learning as support for student self-regulation. Australian Educational Researcher, 45(1), 51–63. https://doi.org/10.1007/s13384-018-0261-3
Kang, S. H. K. (2016). Spaced repetition promotes efficient and effective learning. Policy Insights from the Behavioral and Brain Sciences, 3(1), 12–19. https://doi.org/10.1177/2372732215624708
Kazemi, E., & Hintz, A. (2020). Intentional talk: How to structure and lead productive mathematical discussions (2nd ed.). Stenhouse Publishers.
Leinwand, S., Brahier, D., Huinker, D., Berry, R. Q., Dillon, F., Larson, M. R., Leiva, M. A., Schielack, J. F., & Smith, M. S. (2020). Principles to actions: Ensuring mathematical success for all (2nd ed.). National Council of Teachers of Mathematics.
Lesh, R., Galbraith, P. L., Haines, C. R., & Hurford, A. (2015). Modeling students' mathematical modeling competencies. Springer. https://doi.org/10.1007/978-94-007-6271-8
Monroe, E. E., & Orme, M. P. (2017). Working with words in mathematics. Rowman & Littlefield.
National Council of Teachers of Mathematics. (2020). Catalyzing change in early childhood and elementary mathematics: Initiating critical conversations. NCTM.
Organisation for Economic Co-operation and Development. (2019). PISA 2018 results (Volume I): What students know and can do. OECD Publishing. https://doi.org/10.1787/5f07c754-en
Paas, F., & Sweller, J. (2021). Cognitive load theory: New directions and challenges. Applied Cognitive Psychology, 34(4), 768–779. https://doi.org/10.1002/acp.3730
Powell, S. R., & Driver, M. K. (2015). The influence of mathematics vocabulary instruction embedded within addition tutoring. Learning Disability Quarterly, 38(4), 221–233. https://doi.org/10.1177/0731948714564574
Riccomini, P. J., Smith, G. W., Hughes, E. M., & Fries, K. M. (2015). The language of mathematics. Reading & Writing Quarterly, 31(3), 235–252. https://doi.org/10.1080/10573569.2015.1030995
Rittle-Johnson, B., Fyfe, E. R., Hofer, K. G., & Farran, D. C. (2017). Early math trajectories. Child Development, 88(5), 1727–1742. https://doi.org/10.1111/cdev.12662
Rittle-Johnson, B., & Koedinger, K. R. (2005). Designing knowledge scaffolds. Cognition and Instruction, 23(3), 313–349. https://doi.org/10.1207/s1532690xci2303_1
Rohrer, D. (2015). Student instruction should be distributed over long time periods. Educational Psychology Review, 27(4), 635–643. https://doi.org/10.1007/s10648-015-9332-4
Rohrer, D., Dedrick, R. F., & Stershic, S. (2015). Interleaved practice improves mathematics learning. Journal of Educational Psychology, 107(3), 900–908. https://doi.org/10.1037/edu0000001
Schleicher, A. (2019). PISA 2018: Insights and interpretations. OECD Publishing.
Schleppegrell, M. J. (2017). The language of schooling: A functional linguistics perspective. Routledge. https://doi.org/10.4324/9781315092591
Schmidt, W. H., & Houang, R. T. (2018). Curricular coherence and the Common Core State Standards for Mathematics. Educational Researcher, 41(8), 294–308. https://doi.org/10.3102/0013189X12464517
Schoenfeld, A. H. (2016). Learning to think mathematically. Journal of Education, 196(2), 1–38. https://doi.org/10.1177/002205741619600202
Sousa, D. A. (2015). How the brain learns mathematics (2nd ed.). Corwin Press.
Star, J. R., et al. (2015). Teaching strategies for improving algebra knowledge (NCEE 2014-4333). National Center for Education Evaluation.
Staples, M. E., Bartlo, J., & Thanheiser, E. (2017). Justification as a teaching and learning practice. Journal of Mathematical Behavior, 44, 29–48.
Stigler, J. W., & Hiebert, J. (2016). Lesson study, improvement, and cultural routines. ZDM Mathematics Education, 48(4), 581–587. https://doi.org/10.1007/s11858-016-0787-7
Sweller, J., van Merriënboer, J. J. G., & Paas, F. (2019). Cognitive architecture and instructional design. Educational Psychology Review, 31(2), 261–292. https://doi.org/10.1007/s10648-019-09465-5
Tomlinson, C. A. (2017). How to differentiate instruction in academically diverse classrooms (3rd ed.). ASCD.
Usiskin, Z. (2021). Van Hiele levels and achievement in secondary school geometry. Journal for Research in Mathematics Education, 13(5), 424–432.
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2018). Elementary and middle school mathematics: Teaching developmentally (10th ed.). Pearson.
Webb, N. M., et al. (2019). Engaging with others' mathematical ideas. International Journal of Educational Research, 63, 79–93. https://doi.org/10.1016/j.ijer.2013.02.001
Wiliam, D. (2018). Embedded formative assessment (2nd ed.). Solution Tree Press.
Witzel, B. S., Ferguson, C. J., & Mink, D. V. (2019). Number sense (2nd ed.). Corwin.
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Derechos de autor 2026 Edwin Rivera Rivera (Autor/a)
Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.
