Tareas de álgebra en Secundaria: progresión formal sin demanda cognitiva en libros de texto mexicanos
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Este estudio analiza las tareas de álgebra en libros de texto oficiales de secundaria en México, con el propósito de examinar la relación entre la progresión formal de los contenidos y la demanda cognitiva que promueven. Se adopta un enfoque cualitativo de análisis documental aplicado a 78 tareas, mediante una matriz basada en el análisis didáctico, la teoría de los registros de representación y el marco de demanda cognitiva. Los resultados evidencian un predominio de tareas procedimentales y una presencia limitada de actividades de alta demanda cognitiva. Asimismo, se identifica una progresión formal del contenido que no se acompaña de un incremento en la exigencia cognitiva, lo que sugiere una estabilidad en la naturaleza de la actividad matemática promovida.
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Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52(3), 215–241. https://doi.org/10.1023/A:1024312321077
Blanton, M., y Kaput, J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36(5), 412–446. https://doi.org/10.2307/30034944
Brousseau, G. (1997). Theory of didactical situations in mathematics: Didactique des mathématiques, 1970–1990 (N. Balacheff, M. Cooper, R. Sutherland, y V. Warfield, Eds. y Trans.). Springer. https://doi.org/10.1007/0-306-47211-2
Burgos, M., Castillo, M. J., y Godino, J. D. (2023). Análisis de lecciones de libros de texto basado en las herramientas del Enfoque Ontosemiótico: Una experiencia con maestros en formación. Paradigma, 44(4), 34–58. https://doi.org/10.37618/PARADIGMA.1011-2251.2023.p34-58.id1399
Bussi, M. G., y Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artifacts and signs after a Vygotskian perspective. In L. D. English (Ed.), Handbook of International Research in Mathematics Education (2nd ed., pp. 746–783). Routledge. https://doi.org/10.4324/9780203930236.ch28
Drijvers, P., Doorman, M., Boon, P., Reed, H., y Gravemeijer, K. (2010). The teacher and the tool: Instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213–234. https://doi.org/10.1007/s10649-010-9254-5
Duval, R. (2006). A cognitive analysis of problems of comprehension in the learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131. https://doi.org/10.1007/s10649-0060400-z
Fan, L. (2013). Textbook research as scientific research: Towards a common ground on issues and methods of research on mathematics textbooks. ZDM – The International Journal on Mathematics Education, 45(5), 765–777. https://doi.org/10.1007/s11858-013-0530-6
Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? En J. J. Kaput, D. W. Carraher, y M. L. Blanton (Eds.), Algebra in the early grades (pp. 5–17). Lawrence Erlbaum Associates.
Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels: Building meaning for symbols and their manipulation. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 707–762). Information Age Publishing.
Kieran, C. (Ed.). (2018). Teaching and learning algebraic thinking with 5- to 12-year-olds: The global evolution of an emerging field of research and practice. Springer.
Küchemann, D. (1981). Algebra. En K. M. Hart (Ed.), Children’s understanding of mathematics: 11–16 (pp. 102–119). John Murray.
Namlı, Ş., y Özçakır, B. (2024). Analysing the tasks in middle school mathematics textbooks according to the levels of cognitive de
mand. TAY Journal, 8(3), 477–502. https://doi.org/10.29329/tayjournal.2024.1056.04
OECD. (2019). PISA 2018 assessment and analytical framework. OECD Publishing. https://doi.org/10.1787/b25efab8-en
Pincheira, N., y Alsina, Á. (2021). El álgebra temprana en los libros de texto de Educación Primaria: Implicaciones para la formación docente. Bolema: Boletim de Educação Matemática, 35(71), 1316–1337. https://doi.org/10.1590/1980-4415v35n71a05
Polat, S., y Dede, Y. (2023). Trends in cognitive demands levels of mathematical tasks in Turkish middle school mathematics textbooks: Algebra learning domain. International Journal for Mathematics Teaching and Learning, 24(1). 40–61. https://doi.org/10.4256/ijmtl.v24i1.476
Purnomo, Y. W., Shahrill, M., Pandansari, O., Susanti, R., y Winarni, W. (2022). Cognitive demands on geometrical tasks in Indonesian elementary school mathematics textbook. Jurnal Elemen, 8(2), 466–479. https://doi.org/10.29408/jel.v8i2.5235
Radford, L. (2014). The progressive development of early embodied algebraic thinking. Mathematics Education Research Journal, 26(2), 257–277. https://doi.org/10.1007/s13394-013-0087-2
Rezat, S., y Sträßer, R. (2014). Mathematics textbooks and how they are used. In P. Andrews y T. Rowland (Eds.), Master class in mathematics education: International perspectives on teaching and learning (pp. 51–62). Bloomsbury Academic. https://doi.org/10.5040/9781350284807.ch-005
Rezat, S., Fan, L., y Pepin, B. (2021). Mathematics textbooks and curriculum resources as instruments for change. ZDM – Mathematics Education, 53, 1189–1206. https://doi.org/10.1007/s11858-021-01309-3
Rico, L., Lupiáñez, J. L., y Molina, M. (Eds.). (2013). Análisis didáctico en educación matemática: Metodología de investigación, formación de profesores e innovación curricular. Comares.
Schoenfeld, A. H. (2017). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. Journal of Education, 196(2), 1–38. https://doi.org/10.1177/002205741619600202
Secretaría de Educación Pública. (2024). Libros de texto gratuitos: Matemáticas secundaria (Serie Nueva Escuela Mexicana). SEP.
Secretaría de Educación Pública. (2022). Marco curricular común de la educación básica 2022. SEP.
https://www.gob.mx/basica/documentos/marco-curricular-comun-2022
Smith, M. S., y Stein, M. K. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics Teaching in the Middle School, 3(4), 268–275. https://doi.org/10.5951/MTMS.3.4.0268
Stein, M. K., Smith, M. S., Henningsen, M. A., y Silver, E. A. (2009). Implementing standards-based mathematics instruction: A casebook for professional development. Teachers College Press.
Stylianides, A. J. (2009). Reasoning-and-proving in school mathematics textbooks. Mathematical Thinking and Learning, 11(4), 258–288. https://doi.org/10.1080/10986060903253954
Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge University Press.