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.
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Notes
- 1.
This is a translation by the authors. The expression in Spanish is Formación ciudadana.
- 2.
Skovsmose uses the context of motoring to clarify the differences among technological and reflective knowledge. Technological knowledge is related to the skills required to construct and repair a car while the reflective knowledge is related to the skills required to drive a car and to assess the social consequences of car production. “Technological knowledge itself is unable to predict and analyse the results of its own production; reflections are needed. The competence in constructing cars is not sufficient for the evaluation of the social consequences of car production” (Skovsmose 1992, p.7).
- 3.
Translation from the authors.
- 4.
Catalogue was available on line, at the beginning of 2014, in the following link http://aplicaciones2.colombiaaprende.edu.co/textos_escolares/contenidos/resultado_busqueda.php. However, the link is not available anymore.
- 5.
One of the bookstores has its catalogue available on-line. Catalogue visited on February 11, 2014 http://www.panamericana.com.co/categorias/categoria.aspx?p=reN6vDa2UjMBxvdrQqQYWeLel8MiV6lZ
References
Acevedo-Caicedo, M. M., & Pérez-de-Díaz, M. C. (2013). Enlace Matemáticas 5 [Mathematics Link 5]. Bogotá: Educar Editores.
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.
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.
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.
Beltrán-Beltrán, L. P., Rodríguez-Sáenz, B. P., Suárez-Olarte, A., & Abondano-Mikán, W. (2014). Contacto Matemático 5 [Mathematics Contact 5]. Bogotá: Editorial Educativa.
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.
Biembengut, M. S., & Hein, N. (2002). Modelaje y etnomatemáticas: Puntos(in) comunes [Modeling and ethnomathematics: Points (in) common]. Números, 57, 27–39.
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.
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.
Chandler, D., & Brosnan, P. (1995). A comparison between mathematics textbook content and a statewide proficiency test. School Science and Mathematics, 95(3), 118–123.
Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. American Mathematical Monthly, 104, 801–823.
D’Ambrosio, U. (1999). Literacy, matheracy and technocracy: A trivium for today. Mathematical thinking and learning, 1(2), 131–153.
Duran, M. M., Sarmiento, J., Bogotá-Torres, M., Morales, C., & Fuentes, J. (2013). Matemáticas en Red 5 [Mathematics Network 5]. Bogotá: Ediciones SM.
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.
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.
Garfield, J. (2002). The challenge of developing statistical reasoning. Journal of Statistics Education, 10(3).
Giroux, H. A. (1988). Schooling for democracy: Critical pedagogy in the modern age. London: Routledge.
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.
Guerrero, O. (2008). Educación matemática crítica. Influencias teóricas y aportes [Critical mathematical education: Theoretical influences and contributions]. Evaluación £ Investigación, 1(3).
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.
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.
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.
Johansson, M. (2003). Textbooks in mathematics education: A study of textbooks as the potentially implemented curriculum. ( Unpublished doctoral dissertation) University of Lulea, Sweden.
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.
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.
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.
López-Noguero, F. (2002). El análisis de contenido como método de investigación [Content analysis as research method]. XXI, Revista de Educación, 4, 167–179.
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.
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.
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.
Mesa, V. (2000). Conceptions of function promoted by seventh- and eighth-grade textbooks from eighteen countries. University of Georgia: Unpublished doctoral dissertation.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211–246.
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.
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.
Shimizu, Y., Kaur, B., Huang, R., & Clarke, D. J. (2010). Mathematical tasks in classrooms around the world. Rotterdam, The Netherlands: Sence Publishers.
Silva-Calderon, L. H. (2014). Avanza Matemáticas 5 [Advancing Mathematics 5]. Bogotá: Norma.
Skovsmose, O. (1992). Democratic competence and reflective knowing in mathematics. For the Learning of Mathematics, 12(2), 2–11.
Skovsmose, O. (1999). Towards a philosophy of critical mathematics education. (P. Valero, Trad.) Bogotá: Una empresa docente.
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.
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.
Uribe-Cálad, J. A. (2013). Matemática Experimental 5 [Experimental Mathematics 5]. Medellín: Uros Editores.
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.
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.
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.
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.
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This research was supported by The University of Antioquia Research Committee―CODI.
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Zapata-Cardona, L., Marrugo Escobar, L.M. (2019). Critical Citizenship in Colombian Statistics Textbooks. In: Burrill, G., Ben-Zvi, D. (eds) Topics and Trends in Current Statistics Education Research. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-030-03472-6_17
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