Dificultad de los problemas aritméticos verbales de los libros de texto singapurenses y españoles

  1. Santiago Vicente
  2. Lieven Verschaffel
  3. Marta Ramos
Aldizkaria:
Avances de investigación en educación matemática: AIEM

ISSN: 2254-4313

Argitalpen urtea: 2022

Zenbakia: 22

Orrialdeak: 137-156

Mota: Artikulua

Beste argitalpen batzuk: Avances de investigación en educación matemática: AIEM

Laburpena

De acuerdo con TIMSS 2019 (INEE, 2020), los alumnos singapurenses son capaces de resolver problemas verbales más difíciles que los alumnos españoles. Puesto que en ambos países los libros de texto son el recurso principal que utiliza la mayoría de los profesores para enseñar a sus alumnos a resolver pro-blemas, es posible que existan algunas diferencias en relación con la dificultad semántico-matemática de los problemas aritméticos verbales que presentan los libros de texto de Singapur y España. Por este motivo, se realizó una comparación cuantitativa del nivel de dificultad semántico-matemática de los problemas de los libros de la editorial española Santillana y de la principal editorial singapurense (Marshall Cavendish). Los libros de Singapur contenían problemas más difíciles que los españoles, si bien en todos los libros la gran mayoría de los problemas eran fáciles. Las diferencias encontradas podrían ser el reflejo de algunas diferencias en los currículos de Singapur y España.

Erreferentzia bibliografikoak

  • Bermejo, V. (2012). Cómo enseñar matemáticas para aprender mejor. CCS.
  • Cai, J., & Jiang, C. (2017). An Analysis of Problem-Posing Tasks in Chinese and US Ele-mentary Mathematics Textbooks. International Journal of Science and Mathematics Education, 15, 1521–1540. https://doi.org/10.1007/s10763-016-9758-2
  • Carpenter, T.P., & Moser, J.M. (1984). The acquisition of addition and subtraction con-cepts. En R. Lesh & M. Landau (Eds.), The acquisition of mathematical concepts and processes (pp. 7–44). Academic Press.
  • Clark, A. (2013). Singapore math: A visual approach to word problems. Houghton Mifflin Harcourt. http://www.hmhco.com/~/media/sites/home/education/global/pdf/white-papers/mathematics/elementary/math-in-focus/mif_model_drawing_lr.pdf?la=en
  • Cohen, J. (1988). Statistical power and analysis for the behavioral sciences. Lawrence Erlbaum Associates, Inc. https://doi.org/10.1002/bs.3830330104
  • Daroczy G., Wolska M., Meurers W.D., & Nuerk H.C (2015). Word problems: a review of linguistic and numerical factors contributing to their difficulty. Frontiers in Psy-chology, 6, 348. https://doi.org/10.3389/fpsyg.2015.00348
  • Greer, B. (1992). Multiplication and division as models of situations. En D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 276–295). Macmillan.
  • Hansen, T.I. (2018). Textbook Use. En E. Fuchs & A. Bock (Eds.), The Palgrave Handbook of Textbook Studies (pp. 369-398). Palgrave Macmillan.
  • Haylock, D., & Cockburn, A. (2004). Understanding mathematics in the lower primary years. Paul Chapman Publishing.
  • Heller, J., & Greeno, J. (1978). Semantic processing in arithmetic word problem solving. Comunicación presentada en la Midwestern Psychological Association Conven-tion, Chicago.
  • Instituto Nacional de Evaluación Educativa [INEE] (2020). TIMSS 2019. Estudio interna-cional de tendencias en Matemáticas y Ciencias. Ministerio de Educación, Cultura y Deporte.
  • Knight, B.A. (2015). Teachers use of textbooks in the digital age. Cogent Education, 2(1). https://doi.org/10.1080/2331186X.2015.1015812
  • Lewis, A. B., & Mayer, R. E. (1987). Students' miscomprehension of relational statements in arithmetic word problems. Journal of Educational Psychology, 79(4), 363–371. https://doi.org/10.1037/0022-0663.79.4.363
  • Lindquist, M., Philpot, R., Mullis, I., & Cotter, K.E. (2017). TIMSS 2019 Mathematics Framework. En I.V.S. Mullis & M.O. Martin (Eds.), TIMSS 2019 Assessment Frame-works. http://timssandpirls.bc.edu/timss2019/frameworks/
  • López, E.M., Guerrero, A.C., Carrillo, J., & Contreras, L.C. (2015). La resolución de problemas en los libros de texto: Un instrumento para su análisis. Avances en Investigación en Educación matemática, 8, 73–94.
  • Martínez, J., & Sánchez, C. (2013). Resolución de problemas y Método ABN. Wolters Kluwer Educación.
  • Marton, F. (2015). Necessary conditions of learning. Routledge.
  • Moseley, B., & Brenner, M. E. (2009). A comparison of curricular effects on the integra-tion of arithmetic and algebraic schemata in pre-algebra students. Instructional Science, 37(1), 1-20. https://doi.org/10.1007/s11251-008-9057-6
  • Mullis, I., Martin, M., & Foy, P. (2008). TIMSS 2007 international mathematics report: Findings from IEA’s Trends in International Mathematics and Science Study at the fourth and eighth grade. TIMSS and PIRLS International Study Center, Boston Col-lege. http://pirls.bc.edu/timss2007/mathreport.html
  • Mullis, I.V.S., Martin, M.O., Foy, P., & Arora, A. (2012). TIMSS 2011 International Results in Mathematics. TIMSS & PIRLS International Study Center, Boston College. https://timssandpirls.bc.edu/timss2011/downloads/T11_IR_Mathematics_FullBook.pdf
  • Mullis, I., Martin, M., Foy, P., Kelly, D., & Fishbein, B. (2020). TIMSS 2019 International Results in Mathematics and Science. TIMSS and PIRLS International Study Center, Boston College. https://timssandpirls.bc.edu/timss2019/international-results/
  • Musa, N., & Malone, J. (2012). Problem Categorisation in Ratio. A Closer Look. En J. Dindyal, L. P. Cheng & S. F. Ng (Eds.), Mathematics education: Expanding horizons, Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia. MERGA.
  • Ng, S. F., Lee, K., Ang, S. Y., & Khng, F. (2006). Model method: Obstacle or bridge to learn-ing symbolic algebra. En W. Bokhorst-Heng, M. Osborne & K. Lee (Eds.), Redesign-ing pedagogies: Reflections fromtheory and praxis (pp. 227–242). Sense publishers.
  • Oates, T. (2014). Why textbooks count. Cambridge assessments. http://www.cambridgeassessment.org.uk/Images/181744-why-textbooks-count-tim-oates.pdf
  • Orrantia, J., González, L.B., & Vicente, S. (2005). Un análisis de los problemas aritméticos en los libros de texto de Educación Primaria. Infancia Y Aprendizaje, 28(4), 429-451. https://doi.org/10.1174/021037005774518929
  • Rao, N., Ng, S. S. N., & Pearson, E. (2010). Preschool pedagogy: A fusion of traditional Chinese beliefs and contemporary notions of appropriate practice. En C. Chan & N. Rao (Eds.), Revisiting the Chinese learner. CERC studies in comparative education (pp. 255–279). Springer. https://doi.org/10.1007/978-90-481-3840-1_9
  • Riley, M., & Greeno, J. (1988). Developmental analysis of understanding language about quantities of solving problems. Cognition y Instruction, 5, 49–101. https://doi.org/10.1207/s1532690xci0501_2
  • Schmidt, W., McKnight, C., Houang, R., Wang, H., Wiley, D., Cogan, L., & Wolfe, R. (2001). Why schools matter: A cross-national comparison of curriculum and learning. Jossey-Bass.
  • Schoenfeld, A.H. (1991). On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. En J.F. Voss, D.N. Perkins & J.W. Segal (Eds.), Informal reasoning and education (pp. 311–343). Lawrence Erl-baum Associates.
  • Siegler, R., & Oppenzato, C. (2021). Missing Input: How Imbalanced Distributions of Textbook Problems Affect Mathematics Learning. Child Development Perspectives, 15(2), 76-82. https://doi.org/10.1111/cdep.12402
  • Sievert, H., van den Ham, A.K., & Heinze, A. (2021). Are first graders’ arithmetic skills related to the quality of mathematics textbooks? A study on students’ use of arith-metic principles. Learning and Instruction, 71(101401), 1–14. https://doi.org/10.1016/j.learninstruc.2020.101401.
  • Sievert, H., van den Ham, A.K., Niedermeyer, I., & Heinze, A. (2019). Effects of mathemat-ics textbooks on the development of primary school children’s adaptive expertise in arithmetic. Learning and Individual Differences, 74(101716), 1–13. https://doi.org/10.1016/j.lindif.2019.02.006
  • Tarim, K. (2017). Problem solving levels of elementary school students on mathematical word problems and the distribution of these problems in textbooks. Çukurova Uni-versity. Faculty of Education Journal, 46(2), 639-648. https://doi.org/10.14812/cuefd.306025
  • Tárraga, R., Tarín, J., & Lacruz, I. (2021). Analysis of word problems in primary education mathematics textbooks in Spain. Mathematics, 9(17), 2123. https://doi.org/10.3390/math9172123
  • Törnroos, J. (2005). Mathematics textbooks, opportunity to learn and student achieve-ment. Studies in Educational Evaluation, 31(4), 315–327. https://doi.org/10.1016/j.stueduc.2005.11.005
  • Vergnaud, G. (1991). El niño, las matemáticas y la realidad. Trillas.
  • Van Dooren, W., Verschaffel, L., Greer, B., & De Bock, D. (2006). Modelling for life: Devel-oping adaptative expertise in Mathematical modelling from early age. En L. Ver-schaffel, F. Dochy, M. Boekaerts y S. Vosniadou (Eds.), Instructional psychology: Past, present and future trends (pp. 91–109). Elsevier.
  • Van Zanten, M., & Van den Heuvel-Panhuizen, M. (2018). Opportunity to learn problem solving in Dutch primary school mathematics textbooks. ZDM The International Journal on Mathematics Education, 50(7), 827-838. https://doi.org/10.1007/s11858-018-0973-x
  • Verschaffel, L., Depaepe, F., & Van Dooren, W. (2020). Word problems in mathematics education. En S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 908–911). Springer.
  • Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Swets y Zeitlinger Publishers. https://doi.org/10.1023/A:1004190927303
  • Verschaffel, L., Greer, B., & De Corte, E. (2007). Whole number concepts and operations. En F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 557-628). Information Age Publishing.
  • Vicente, S., Manchado, E., & Verschaffel, L. (2018). Resolución de problemas aritméticos verbales. Un análisis de los libros de texto españoles. Cultura y Educación, 30, 71-104, https://doi.org/10.1080/11356405.2017.1421606
  • Vicente, S., Sánchez, R., & Verschaffel, L. (2020). Word problem solving approaches in mathematics textbooks: a comparison between Singapore and Spain. European Journal of Psychology of Education, 35, 567–587. https://doi.org/10.1007/s10212-019-00447-3.
  • Vicente, S., Verschaffel, L., & Múñez, D. (2021). Comparación del nivel de autenticidad de los problemas aritméticos verbales de los libros de texto españoles y singapuren-ses. Cultura y Educación, 33(1), 106-133. https://doi.org/10.1080/11356405.2020.1859738
  • Vicente, S., Verschaffel, L., Sánchez, R., & Múñez, D. (2022). Arithmetic word problem solving. Analysis of Singaporean and Spanish textbooks. Educational Studies in Mathematics, 111, 375-397. https://doi.org/10.1007/s10649-022-10169-x
  • Xin, Y.P. (2007). Word problem solving tasks in textbooks and their relation to student performance. The Journal of Educational Research, 6, 347–359. https://doi.org/10.3200/JOER.100.6.347-360
  • Yang, D.Y., & Sianturi, I. A. J. (2020) Analysis of algebraic problems intended for elemen-tary graders in Finland, Indonesia, Malaysia, Singapore, and Taiwan. Educational Studies, 1-23. http://dx.doi.org/10.1080/03055698.2020.1740977
  • Cai, J., & Jiang, C. (2017). An Analysis of Problem-Posing Tasks in Chinese and US Ele-mentary Mathematics Textbooks. International Journal of Science and Mathematics Education, 15, 1521–1540. https://doi.org/10.1007/s10763-016-9758-2