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Critical Citizenship in Colombian Statistics Textbooks

  • Lucía Zapata-CardonaEmail author
  • Luis Miguel Marrugo Escobar
Chapter
Part of the ICME-13 Monographs book series (ICME13Mo)

Abstract

The goal of this research is to study how the statistical component of fifth-grade mathematics textbooks in Colombia contributes to the development of students’ critical citizenship. This research followed a socio-critical perspective. Content analysis was the technique used to make sense of the data produced by analyzing seven mathematics textbooks, and the units of analysis were 261 tasks in the statistical components. The results show that the contexts of the tasks were mostly hypothetical with very few tasks presented in real contexts. The tasks mainly functioned as platforms to introduce measurement calculations and application of statistical procedures. When the tasks were presented within real contexts, the conditions were not used to the fullest extent to contribute to the development of students’ critical citizenship. The tasks promoted mainly statistical and technological knowledge over reflective knowledge, failing to contribute to the students’ socio political awareness.

Keywords

Critical citizenship Statistics education Textbooks Textbook tasks 

Notes

Acknowledgements

This research was supported by The University of Antioquia Research Committee―CODI.

References

  1. Acevedo-Caicedo, M. M., & Pérez-de-Díaz, M. C. (2013). Enlace Matemáticas 5 [Mathematics Link 5]. Bogotá: Educar Editores.Google Scholar
  2. Bakker, A., & Derry, J. (2011). Lessons from inferentialism for statistics education. Mathematical Thinking and Learning, 13(1–2), 5–26.  https://doi.org/10.1080/10986065.2011.538293.CrossRefGoogle Scholar
  3. Bakker, A., van Mierlo, X., & Akkerman, S. (2012). Learning to integrate statistical and work related reasoning. In Proceedings from the 12th International Congress on Mathematical Education. Seoul, Korea.Google Scholar
  4. Barbosa, J. C. (2006). Mathematical modelling in classroom: A socio-critical and discursive perspective. ZDM—The International Journal on Mathematics Education, 38(3), 293–301.CrossRefGoogle Scholar
  5. Beltrán-Beltrán, L. P., Rodríguez-Sáenz, B. P., Suárez-Olarte, A., & Abondano-Mikán, W. (2014). Contacto Matemático 5 [Mathematics Contact 5]. Bogotá: Editorial Educativa.Google Scholar
  6. Ben-Zvi, D., & Garfield, J. (2004). Statistical literacy, reasoning, and thinking: Goals, definitions, and challenges. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 3–15). The Netherlands: Kluwer Academic Publishers.CrossRefGoogle Scholar
  7. Biembengut, M. S., & Hein, N. (2002). Modelaje y etnomatemáticas: Puntos(in) comunes [Modeling and ethnomathematics: Points (in) common]. Números, 57, 27–39.Google Scholar
  8. Borba, R., & Selva, A. (2013). Analysis of the role of the calculator in Brazilian textbooks. ZDM—The International Journal on Mathematics Education, 45(5), 737–750.  https://doi.org/10.1007/s11858-013-0517-3.CrossRefGoogle Scholar
  9. Cantoral, R. (1997). Los textos de cálculo: Una visión de las reformas y contrarreformas [The texts of calculus: A vision of reforms and counter-reforms]. Revista EMA, 2(2), 115–131.Google Scholar
  10. Chandler, D., & Brosnan, P. (1995). A comparison between mathematics textbook content and a statewide proficiency test. School Science and Mathematics, 95(3), 118–123.CrossRefGoogle Scholar
  11. Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. American Mathematical Monthly, 104, 801–823.CrossRefGoogle Scholar
  12. D’Ambrosio, U. (1999). Literacy, matheracy and technocracy: A trivium for today. Mathematical thinking and learning, 1(2), 131–153.CrossRefGoogle Scholar
  13. Duran, M. M., Sarmiento, J., Bogotá-Torres, M., Morales, C., & Fuentes, J. (2013). Matemáticas en Red 5 [Mathematics Network 5]. Bogotá: Ediciones SM.Google Scholar
  14. Etchegaray, S. C. (2010). Reflexiones y aportes para ayudar a re-pensar la enseñanza de las matemáticas [Reflections and contributions to help re-think the teaching of mathematics]. Yupana, 11–23.  https://doi.org/10.14409/yu.v1i5.258.
  15. Fan, L., Zhu, Y., & Miao, Z. (2013). Textbook research in mathematics education: Development status and directions. ZDM—The International Journal on Mathematics Education, 45(5), 633–646.  https://doi.org/10.1007/11858-013-0539-x.CrossRefGoogle Scholar
  16. Garfield, J. (2002). The challenge of developing statistical reasoning. Journal of Statistics Education, 10(3).Google Scholar
  17. Giroux, H. A. (1988). Schooling for democracy: Critical pedagogy in the modern age. London: Routledge.Google Scholar
  18. González-Astudillo, M. T., & Sierra-Vasquez, M. (2004). Metodología de análisis de libros de texto de matemáticas. Los puntos críticos en la enseñanza secundaria en España durante el siglo XX [Methodology to analyze mathematics textbooks]. Revista Enseñanza de las Ciencias, 22(3), 389–408.Google Scholar
  19. Guerrero, O. (2008). Educación matemática crítica. Influencias teóricas y aportes [Critical mathematical education: Theoretical influences and contributions]. Evaluación £ Investigación, 1(3).Google Scholar
  20. Herbel-Eisenmann, B. A. (2007). From intended curriculum to written curriculum: Examining the “Voice” of a mathematics textbook. Journal for Research in Mathematics Education, 38(4), 344–369.Google Scholar
  21. Hiebert, J., Gallimore, R., Garnier, H., Givvin, K. B., Hollingsworth, H., Jacobs, J., et al. (2003). Teaching mathematics in seven countries: Results from the TIMSS 1999 video study. Washington, DC: National Center for Education Statistics.Google Scholar
  22. Howson, G. (2013). The development of mathematics textbooks: Historical reflections from a personal perspective. ZDM—The International Journal on Mathematics Education, 45(5), 647–658.  https://doi.org/10.1007/s11858-013-0511-9.CrossRefGoogle Scholar
  23. Johansson, M. (2003). Textbooks in mathematics education: A study of textbooks as the potentially implemented curriculum. ( Unpublished doctoral dissertation) University of Lulea, Sweden.Google Scholar
  24. Jones, K., & Fujita, T. (2013). Interpretations of national curricula: The case of geometry in textbooks from England and Japan. ZDM—The International Journal on Mathematics Education, 45(5), 671–683.  https://doi.org/10.1007/s11858-013-0515-5.CrossRefGoogle Scholar
  25. Joya-Vega, A., Grande-Puentes, X., Acosta, M. L., Ramírez-Rincón, M., Buitrago-García, L., Ortiz-Wilches, L. G., et al. (2014). Los Caminos del Saber 5 [The Ways of Knowledge 5]. Bogotá: Santillana.Google Scholar
  26. Lesser, L. M. (2007). Critical values and transforming data: Teaching statistics with social justice. Journal of Statistics Education, 15(1). Retrieved from www.amstat.org/publications/jse/v15n1/lesser.html.
  27. López-Noguero, F. (2002). El análisis de contenido como método de investigación [Content analysis as research method]. XXI, Revista de Educación, 4, 167–179.Google Scholar
  28. Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13(1–2), 152–173.  https://doi.org/10.1080/10986065.2011.538301.CrossRefGoogle Scholar
  29. Mateos Montero, J. (2008). La “asignutarización” del conocimiento del medio en los textos y contextos escolares. El entorno en las aulas [The “subjectization” of knowledge of environment in the texts and school contexts. The environment in the classrooms]. Investigación en la Escuela, 65, 59–70.Google Scholar
  30. Mejía-Fonseca, C. F., Guzmán-Pineda, L. E., Vega-Reyes, A. M., & Baquero-Guevara, D. C. (2011). Zona Activa 5 [Active Zone 5]. Bogotá: Voluntad.Google Scholar
  31. Mesa, V. (2000). Conceptions of function promoted by seventh- and eighth-grade textbooks from eighteen countries. University of Georgia: Unpublished doctoral dissertation.Google Scholar
  32. Nie, B., Freedman, T., Hwang, S., Wang, N., Moyer, J., & Cai, J. (2013). An investigation of teachers’ intentions and reflection about using standards-based and traditional textbooks in the classroom. ZDM—The International Journal on Mathematics Education, 45(5), 699–711.  https://doi.org/10.1007/s11858-013-0493-7.CrossRefGoogle Scholar
  33. Österholm, M., & Bergqvist, E. (2013). What is so special about mathematical text? Analyses of common claims in research literature and of properties of textbooks. ZDM—The International Journal on Mathematics Education, 45(5), 751–763.  https://doi.org/10.1007/s11858-013-0522-6.CrossRefGoogle Scholar
  34. Otte, M. (1986). What is a text? In B. Chistiansen, A.G., Howson, & M. Otte (Eds.). Perspectives on mathematics education (pp. 173–203). Dordrecht: D. Reidel Publishing Company.CrossRefGoogle Scholar
  35. Pepin, B., Gueudet, G., & Trouche, L. (2013). Investigating textbooks as crucial interfaces between culture, policy and teacher curricular practice: Two contrasted case studies in France and Norway. ZDM—The International Journal on Mathematics Education, 45(5), 685–698.  https://doi.org/10.1007/s11858-013-0526-2.CrossRefGoogle Scholar
  36. Pfannkuch, M., & Wild, C. (2004). Towards an understanding of statistical thinking. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 17–46). The Netherlands: Kluwer Academic Publishers.CrossRefGoogle Scholar
  37. Pfannkuch, M., Budgett, S., Fewster, R., Fitch, M., Pattenwise, S., & Wild, C. (2016). Probability modeling and thinking: What can we learn from practice? Statistics Education Research Journal, 15(2), 11–37.Google Scholar
  38. Prendes-Espinosa, M. (2001). Evaluación de materiales escolares [Assessment of educational materials]. Revista Píxel Bit, 16, 1–20. http://www.sav.us.es/pixelbit/pixelbit/articulos/n16/n16art/art167.htm.
  39. Radford, L. (2006). Elementos de una teoría cultural de la objetivación [Elements of a cultural theory of objectification] (pp. 103–129). Número Especial: Revista Relime.Google Scholar
  40. Radford, L. (2016). On alienation in the mathematics classroom [Sobre la alineación en la clase de matemáticas]. International Journal of Educational Research, 79, 258–266.  https://doi.org/10.1016/j.ijer.2016.04.001.CrossRefGoogle Scholar
  41. Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211–246.CrossRefGoogle Scholar
  42. Roth, W.-M. (1996). Where is the context in contextual word problems? Mathematical practices and products in Grade 8 students’ answers to story problems. Cognition and Instruction, 14, 487–527.CrossRefGoogle Scholar
  43. Salcedo, A. (2015). Exigencia cognitiva de las actividades de estadística en textos escolares de Educación Primaria [Cognitive demand of statistical activities in primary school textbooks]. In J. M. Contreras, C. Batanero, J. D. Godino, G. R. Cañadas, P. Arteaga, E. Molina, et al. Eds.), Didáctica de la Estadística, Probabilidad y Combinatoria. Actas de las Segundas Jornadas Virtuales en Didáctica de la Estadística, Probabilidad y Combinatoria (pp. 307–315). Granada.Google Scholar
  44. Shimizu, Y., Kaur, B., Huang, R., & Clarke, D. J. (2010). Mathematical tasks in classrooms around the world. Rotterdam, The Netherlands: Sence Publishers.Google Scholar
  45. Silva-Calderon, L. H. (2014). Avanza Matemáticas 5 [Advancing Mathematics 5]. Bogotá: Norma.Google Scholar
  46. Skovsmose, O. (1992). Democratic competence and reflective knowing in mathematics. For the Learning of Mathematics, 12(2), 2–11.Google Scholar
  47. Skovsmose, O. (1999). Towards a philosophy of critical mathematics education. (P. Valero, Trad.) Bogotá: Una empresa docente.Google Scholar
  48. Stillman, G., Brown, J., Faragher, R., Geiger, V., & Galbraith, P. (2013). The role of textbooks in developing a socio-critical perspective on mathematical modeling in secondary classrooms. In G. A. Stillman (Ed.), Teaching mathematical modelling: Connection to research and practice. International perspectives on the teaching and learning of mathematical modelling (pp. 361–371). Dordrecht: Springer Science + Bussiness.  https://doi.org/10.1007/978-94-007-6540-5_30.CrossRefGoogle Scholar
  49. Travé González, G., & Pozuelos Estrada, F. (2008). Consideraciones didácticas acerca de las líneas de investigación en materiales curriculares. A modo de presentación [Didactic considerations about research in curricular materials. A presentation]. Investigación en la Escuela, 65, 3–10.Google Scholar
  50. Uribe-Cálad, J. A. (2013). Matemática Experimental 5 [Experimental Mathematics 5]. Medellín: Uros Editores.Google Scholar
  51. Usiskin, Z. (2013). Studying textbooks in an information age—A United States perspective. ZDM—The International Journal on Mathematics Education, 45(5), 713–723.  https://doi.org/10.1007/s11858-013-0514-6.CrossRefGoogle Scholar
  52. Valero, P. (2002). Consideraciones sobre el contexto y la educación matemática para la democracia [Considerations about the context and the mathematics education for democracy]. Quadrante, 11(1), 49–59.Google Scholar
  53. Xu, B. (2013). The development of school mathematics textbooks in China since 1950. ZDM—The International Journal on Mathematics Education, 45(5), 725–736.  https://doi.org/10.1007/s11858-013-0538-y.CrossRefGoogle Scholar
  54. Zapata-Cardona, L., & González-Gómez, D. (2017). Imágenes de los profesores sobre la estadística y su enseñanza [Teachers’ Images about Statistics and its Teaching]. Educación Matemática, 29(1), 61–89.  https://doi.org/10.24844/EM2901.03.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Lucía Zapata-Cardona
    • 1
    Email author
  • Luis Miguel Marrugo Escobar
    • 1
  1. 1.Universidad de AntioquiaMedellínColombia

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