Resolución de problemas aritméticos verbales. Un análisis de los libros de texto españoles

  1. Santiago Vicente 1
  2. Eva Manchado 1
  3. Lieven Verschaffel 2
  1. 1 Universidad de Salamanca
    info

    Universidad de Salamanca

    Salamanca, España

    ROR https://ror.org/02f40zc51

  2. 2 KU Leuven
    info

    KU Leuven

    Lovaina, Bélgica

    ROR https://ror.org/05f950310

Journal:
Culture and Education, Cultura y Educación

ISSN: 1135-6405,  1578-4118

Year of publication: 2018

Volume: 30

Issue: 1

Pages: 87-104

Type: Article

DOI: 10.1080/11356405.2017.1421606 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Culture and Education, Cultura y Educación

Abstract

This study analyses whether the primary school mathematics textbooks from two Spanish publishers show a varied instructional diet of addition and multiplication problems at different levels of complexity. To do so, it analyses the problems in all the primary grades by the publishers Santillana and SM according to two levels of complexity: (a) procedural (number of steps needed to solve the problem); and (b) semantic/mathematical (addition or multiplication structures, with their different subtypes). The results show that: (a) these problems are so simple that the books themselves cannot be regarded as a sufficient tool to teach students to solve the more complex problems; and (b) if we compare them with previous studies, the design of the problems has hardly changed in 10 years. These results show that the variety of problems in books should be expanded both procedurally and semantically/mathematically, and teachers should be given assistance to compensate for these shortcomings when using these textbooks in class

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Bibliographic References

  • Apple, M. (1992). The text and cultural politics. Educational Researcher, 21(7), 4–11.
  • Carpenter, P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (1999). Children’s mathematics. Cognitively guided instruction. Portsmouth, NH: Heinemann.
  • Carpenter, T. P., & Moser, J. M. (1984). The acquisition of addition and subtraction concepts. In: R. Lesh, & M. Landau (Eds.), The acquisition of mathematical concepts and processes (pp. 7–44). New York, NY: Academic Press.
  • Chapin, S., & Johnson, A. (2000). Math matters: Understanding the Math You Teach, grades K-6. Sausalico, CA: Mach Solucions Publications.
  • Cummins, D. D., Kintsch, W., Reusser, K., & Weimer, R. (1988). The role of understanding in solving word problems. Cognitive Psychology, 20, 405–438.
  • García, A., Jiménez, J. E., & Hess, S. (2006). Solving arithmetic word problems: An analysis of classification as a function of difficulty in children with and without arithmetic LD. Journal of Learning Disabilities, 39, 270–281.
  • Greer, B. (1992). Multiplication and division as models of situations. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 276–295). New York, NY: Macmillan.
  • Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87, 18–32.
  • Heller, J. I., & Greeno, J. G. (1978). Semantic processing in arithmetic word problem solving. Paper presented at the Midwestern Psychological Association Convention, Chicago.
  • Hiebert, J., Gallimore, R., Garnier, H., Givvin, K. B., Hollingsworth, H., Jacobs, J., … Stigler, P.(2003). Teaching mathematics in seven countries. Results from the TIMSS 1999 video study. Washington, DC: National Center for Education Statistics (NCES).
  • Mayer, R. E., Sims, V., & Tajika, H. (1995). A comparison of how textbooks teach mathematical problem solving in Japan and the United States. American Educational Research Journal, 32, 443–460.
  • 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. Chestnut Hill, MA: TIMSS and PIRLS International Study Center, Boston College. Retrieved from http://pirls.bc.edu/timss2007/mathreport.html
  • Orrantia, J., González, L. B., & Vicente, S. (2005). Analysing arithmetic word problems in Primary Education text books. Infancia y Aprendizaje, 28, 429–451.
  • Puig, L., & Cerdán, F. (1995). Problemas aritméticos escolares. Madrid: Editorial Síntesis.
  • Riley, M. S., & Greeno, J. G. (1988). Developmental analysis of understanding language about quantities of solving problems. Cognition & Instruction, 5, 49–101.
  • Rosales, J., Orrantia, J., Vicente, S., & Chamoso, J. (2008a). Arithmetic problem solving in the classroom: What do teachers do when they work jointly with students? Cultura y Educación, 20, 423–439.
  • Rosales, J., Orrantia, J., Vicente, S., & Chamoso, J. (2008b). Studying mathematics problem-solving classrooms. A comparison between the discourse of in-service teachers and student teachers. European Journal of Psychology of Education, 23, 275–294.
  • Rosales, J., Vicente, S., Chamoso, J., Múñez, D., & Orrantia, J. (2012). Teacher student interaction in joint word problem solving. The role of situational and mathematical knowledge in mainstream classrooms. Teaching and Teacher Education, 28, 1185–1195.
  • Sánchez, M. R., & Vicente, S. (2015). Modelos y procesos de resolución de problemas aritméticos verbales propuestos por los libros de texto de matemáticas españoles. Cultura y Educación, 27, 695–725.
  • Schoenfeld, A. H. (1991). On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. In J. F. Voss, D. N. Perkins, & J. W. Segal (Eds.), Informal reasoning and education (pp. 311–343). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Stewart, V. (2011). Singapore: Rapid improvement followed by strong performance. In OECD (Ed.),Lessons from PISA for the United States: Strong performers and successful reformers in education (pp. 159–175). Paris: OECD Publications.
  • Stigler, J. W., & Hiebert, J. (1999). The teaching gap. New York, NY: Free Press.
  • Stigler, J. W., Fuson, K. C., Ham, M., & Kim, M. S. (1986). An analysis of addition and subtraction word problems in American and Soviet elementary mathematics textbooks. Cognition and Instruction, 3, 153–171.
  • Vergnaud, G. (1991). El niño, las Matemáticas y la realidad. México: Trillas.
  • Verschaffel, L., De Corte, E., & Pauwels, A. (1992). Solving compare problems: An eye movement test of Lewis and Mayer’s consistency hypothesis. Journal of Educational Psychology, 84, 85–94.
  • Verschaffel, L., Depaepe, F., & Van Dooren, W. (2014). Word problems in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 641–645). Dordrecht: Springer.
  • Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse: Swets & Zeitlinger Publishers.
  • Vicente, S., Rosales, J., Chamoso, J. M., & Múñez, D. (2013). Analyzing educational practice in Spanish Primary education mathematics classes: A tentative explanation for students’ mathematical ability. Cultura y Educación, 25, 535–548.
  • Xin, Y. P. (2007). Word problem solving tasks in textbooks and their relation to student performance. The Journal of Educational Research, 6, 347–359.
  • Chapman, O. (2006). Classroom practices for context of mathematics word problems. Educational Studies in Mathematics, 62, 211–230.
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