Los sistemas inteligentes en educación matemática: Un contexto de investigación para el desarrollo del currículo de matemáticas

• Autores: Carlos de Castro Hernández
• Localización: Investigación en Educación Matemática XXVIII. / coord. por María Burgos , María Consuelo Cañadas Santiago , José María Marbán Prieto , Irene Polo Blanco , 2025, ISBN 978-84-09-75766-4, pág. 109
• Idioma: español
• Títulos paralelos:
  • Intelligent systems in mathematics education: A context for research into thedevelopment of mathematics curriculum
• Enlaces
  • Texto Completo Libro
• Resumen
  • español

    Los sistemas educativos adaptativos e inteligentes basados en la web plantean retos específicos parala transferencia de resultados de investigación en Educación Matemática debido a la especificidadde su contexto. Tras explicar las necesidades y restricciones propias del ámbito de transferencia, sedescribe cómo se han aplicado la metodología de la investigación basada en el diseño y la teoría delas trayectorias de aprendizaje en matemáticas. También se expone cómo se han aplicado principios,basados en la investigación, de un alcance bastante general en Educación Matemática, como elandamiaje, el uso de representaciones, la retroalimentación, los ejemplos resueltos y lascomparaciones de estrategias, con ejemplos de la aplicación Smartick Matemáticas

  • English

    Web-based adaptive and intelligent educational systems pose specific challenges for the transfer ofresearch findings in Mathematics Education due to the specificity of their context. After outlining thespecific requirements and constraints of this transfer domain, the application of design-basedresearch methodology and the theory of learning trajectories in mathematics is described. The use ofbroadly applicable, research-based principles in Mathematics Education—such as scaffolding, theuse of representations, feedback, worked examples, and strategy comparisons—is also discussed. Allof this is illustrated through the Smartick Math application.

• Referencias bibliográficas
  • Ainsworth, S. (1999). The functions of multiple representations. Computers & Education, 33(2-3), 131-152. https://doi.org/10.1016/S0360-1315(99)00029-9
  • Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and instruction, 16(3),...
  • Ainsworth, S. (2014). The multiple representation principle in multimedia learning. En R.E. Mayer (Ed.), The Cambridge handbook of multimedia...
  • Anghileri, J. (2006). Scaffolding practices that enhance mathematics learning. Journal of Mathematics Teacher Education, 9(1), 33-52. https://doi.org/10.1007/s10857-006-9005-9
  • Bachelard, G. (1938/1999). La formación del espíritu científico: Contribución a un psicoanálisis del conocimiento objetivo (22ª ed.). Siglo...
  • Bakker, A., Smit, J. y Wegerif, R. (2015). Scaffolding and dialogic teaching in mathematics education: introduction and review. ZDM – Mathematics...
  • Barana, A, Marchisio, M. y Sacchet, M. (2021). Interactive feedback for learning mathematics in a digital learning environment. Education...
  • Baroody, A. J. (2017). The use of concrete experiences in early childhood mathematics instruction. Advances in Child Development and Behavior,...
  • Barton, C. (2018). How I wish I’d taught maths: Lessons learned from research, conversations with experts, and 12 years of mistakes. John...
  • Beishuizen, M. (1993). Mental strategies and materials or models for addition and subtraction up to 100 in Dutch second grades. Journal for...
  • Bohan, H. J. y Shawaker, P. B. (1994). Using manipulatives effectively: A drive down rounding road. The Arithmetic Teacher, 41, 5, 246-248....
  • Booth, J. L., McGinn, K. M., Barbieri, C., Begolli, K. N., Chang, B., Miller-Cotto, D., Young, L. K. y Davenport, J. L. (2017). Evidence for...
  • Brusilovsky, P. y Peylo, C. (2003). Adaptive and intelligent web-based educational systems. International Journal of Artificial Intelligence...
  • Burns, H. L. y Capps, C. G. (2013). Foundations of intelligent tutoring systems: An introduction. En M. C. Polson y J. J. Richardson (Eds.),...
  • Carbonneau, K. J., Marley, S. y Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives....
  • Clements, D. H. y Sarama J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81-89. Clements,...
  • Confrey J. (2019). Future of education and skills 2030: Curriculum analysis: A synthesis of research on learning trajectories/progressions...
  • Confrey, J., Maloney, A. P. y Nguyen, K. H. (2014). Introduction: Learning trajectories in mathematics. En A. P. Maloney, J. Confrey y K....
  • González, M. J. (1997). Aprendizaje por analogía: Análisis del proceso de Inferencia Analógica para la adquisición de nuevos conocimientos....
  • Hodgen, J., Foster, C., Marks, R. y Brown, M. (2018). Evidence for review of mathematics teaching: Improving mathematics in key stages two...
  • Kahraman, H. T., Sagiroglu, S. y Colak, I. (2010). Development of adaptive and intelligent web-based educational systems. En T. Unwin, D....
  • Maloney, A. P., Confrey, J. y Nguyen, K. H. (Eds.) (2014). Learning over time: Learning trajectories in mathematics education. Information...
  • Molina, M., Castro, E., Molina, J. L. y Castro, E. (2011). Un acercamiento a la investigación de diseño a través de los experimentos de enseñanza....
  • Moyer-Packenham, P. S. y Westenskow, A. (2013). Effects of virtual manipulatives on student achievement and mathematics learning. International...
  • Opfer, J. E. y Siegler, R. S. (2007). Representational change and children’s numerical estimation. Cognitive Psychology, 55(3), 169-195. https://doi.org/10.1016/j.cogpsych.2006.09.002
  • Prediger, S. y Zwetzschler, L. (2013). Topic-specific design research with a focus on learning processes: The case of understanding algebraic...
  • Rittle-Johnson, B. y Star, J. R. (2009). Compared with what? The effects of different comparisons on conceptual knowledge and procedural flexibility...
  • Rohrer, D., Dedrick, R. F. y Stershic, S. (2015). Interleaved practice improves mathematics learning. Journal of Educational Psychology, 107(3),...
  • Rohrer, D., Dedrick, R. F. y Hartwig, M. K. (2020). The scarcity of interleaved practice in mathematics textbooks. Educational Psychology...
  • Santos, L. y Pinto, L. (2009). Lights and shadows of feedback in mathematics learning. En Tzekaki, M., Kaldrimidou, M. y Sakonidis, C. (Eds.),...
  • Skolowski, A. (2018). The Effects of Using Representations in Elementary Mathematics: Meta-Analysis of Research. IAFOR Journal of Education,...
  • Söderström, S. y Palm, T. (2024). Feedback in mathematics education research: A systematic literature review. Research in Mathematics Education,...
  • Sowell, E.J. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 20(5), 498-505....
  • Star, J. R. y Rittle-Johnson, B. (2009). Making algebra work: Instructional strategies that deepen student understanding, within and between...
  • Thompson, I. (1999). Mental calculation strategies for addition and subtraction. Part 1. Mathematics in school, 28(5), 2-4. http://www.jstor.org/stable/30215422
  • van Loon-Hillen, N., van Gog, T. y Brand-Gruwel, S. (2010). Effects of worked examples in a primary school mathematics curriculum. Interactive...
  • Wood, D., Bruner, J. S. y Ross, G. (1976). The role of tutoring in problem-solving. Journal of Child Psychology and Psychiatry and Allied...
  • Zapata-Ross, M. (2018). La universidad inteligente. Revista de Educación a Distancia (RED), 18(57). https://revistas.um.es/red/article/view/327431
  • Zhu, X. y Simon, H.A. (1987). Learning mathematics from examples and by doing. Cognition and Instruction, 4(3), 137-166. https://doi.org/10.1207/s1532690xci0403_1