Difficulty level of arithmetic word problems in Singaporean and Spanish textbooks
DOI:
https://doi.org/10.35763/aiem22.4412Keywords:
Word problems (mathematics)Arithmetic, Textbook content, Task difficulty, Primary EducationAbstract
According to TIMSS-2019 (INEE, 2020), Singaporean students are able to solve more difficult word problems than Spanish students. Since in both countries textbooks are the main resource used by most teachers to teach their students to solve problems, it is possible that there are some differences in the semantic-mathematical difficulty of arithmetic word problems presented in Singaporean and Spanish textbooks. For this reason, a quantitative comparison of the level of semantic-mathematical difficulty of the problems in books from the Spanish publisher Santillana and the leading Singaporean publisher (Marshall Cavendish) was carried out. The Singaporean books contained more difficult problems than the Spanish ones, although in all books most of the problems were easy. The differences found could reflect some differences in the curricula of Singapore and Spain.
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References
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 proble-mas en los libros de texto: Un instrumento para su análisis. Avances en Investiga-ción 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
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