Research Article

Exploring the density property of rational numbers in Mexican textbooks

Isayda Lorena López-Padilla 1 * , José Antonio Juárez-López 1 , Lizzet Morales-García 1
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1 Meritorious Autonomous University of Puebla, Puebla, MEXICO* Corresponding Author
Contemporary Mathematics and Science Education, 5(2), 2024, ep24008, https://doi.org/10.30935/conmaths/14687
Published Online: 11 June 2024, Published: 01 July 2024
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ABSTRACT

In this article we present an analysis of the density property of rational numbers in eight Mexican textbooks for the first grade of secondary education. This research was qualitative and was based on the semiotic representation register theory and the technique of content analysis. In that sense, the analysis focused specifically on the treatment of definitions and examples, semiotic registers and the transformations involved in the tasks. As a result, it was found that the natural and numerical registers have the greatest presence in the definitions of the property of density, as well as in the tasks proposed to address its teaching. Likewise, few tasks were identified that allow for transformations between registers, which could be an obstacle for the student to create semiotic representations of the density property.
Keywords: density property, rational numbers, textbooks, semiotic registers

CITATION (APA)

López-Padilla, I. L., Juárez-López, J. A., & Morales-García, L. (2024). Exploring the density property of rational numbers in Mexican textbooks. Contemporary Mathematics and Science Education, 5(2), ep24008. https://doi.org/10.30935/conmaths/14687

REFERENCES

  1. Alberro, A., & García, R. (2018). Matemáticas 1 [Mathematics 1]. Correo del maestro.
  2. Ávila, A. (2008). Los profesores y los decimales. Conocimientos y creencias de un contenido de saber cuasi invisible [Teachers and decimals. Knowledge and beliefs of a quasi-invisible knowledge content]. Educación Matemática [Mathematics Education], 20(2), 5-33. https://doi.org/10.24844/EM2002.01
  3. Ávila, A. (2019). Significados, representaciones y lenguaje: Las fracciones en tres generaciones de libros de texto para primaria [Meanings, representations and language: Fractions in three generations of primary textbooks]. Educación Matemática [Mathematics Education], 31(2), 22-39. https://doi.org/10.24844/EM3102.02
  4. Ávila, A., & García, S. (2008). Los decimales más que una escritura [Decimals more than a scripture]. INEE-CINVESTAV. https://www.inee.edu.mx/wp-content/uploads/2019/01/P1D402.pdf
  5. Bosch, C., Meda, A., & Gómez, C. (2018). Matemáticas 1. Infinita secundaria [Mathematics 1. Infinite secondary]. Ediciones Castillo.
  6. Broitman, C., Itzcovich, H., & Quaranta, M. E. (2003). La enseñanza de los números decimales: El análisis del valor posicional y una aproximación a la densidad [The teaching of decimal numbers: Place value analysis and a density approximation]. Revista Latinoamericana de Investigación en Matemática Educativa [Latin American Journal of Research in Educational Mathematics], 6(1), 5-26.
  7. Campanario, J. M., & Otero, J. (2000). La comprensión de los libros de texto [The understanding of textbooks]. In F. J. Perales, & P. Cañal (Eds.), Didáctica de las ciencias experimentales [Teaching experimental sciences] (pp. 323-338). Marfil.
  8. Campbell, T. (1997). Technology, multimedia, and qualitative research in education. Journal of Research on Computing in Education, 30(2), 122-132. https://doi.org/10.1080/08886504.1997.10782219
  9. Canché, E., Domínguez, E., & Peña, M. (2018). Matemáticas 1. [Mathematics 1]. Ediciones Castillo.
  10. Chang, C., & Silalahi, S. (2017). A review and content analysis of mathematics textbooks in education research. Problems of Education in the 21st Century, 75(3), 235-251. https://doi.org/10.33225/pec/17.75.235
  11. Díaz, J. (2018). Matemáticas 1 [Mathematics 1]. Ediciones del Rio.
  12. Duval, R. (1993). Registres de représentation sémiotique [Registers of semiotic representation]. Annales de Didactique et de Sciences Cognitives [Annals of Didactics and Cognitive Sciences], 5, 37-65.
  13. Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103-131. https://doi.org/10.1007/s10649-006-0400-z
  14. Duval, R. (2012). Registros de representação semiótica e funcionamento cognitivo do pensamento [Semiotic representation registers and the cognitive functioning of thought]. Revista Eletrônica de Educação Matemática [Electronic Magazine of Mathematics Education], 7(2), 266-297. https://doi.org/10.5007/1981-1322.2012v7n2p266
  15. Escareño, F., & López, O. (2018). Matemáticas 1 [Mathematics 1]. Editorial Trillas.
  16. Fan, L. (2013). Textbook research as scientific research: Towards a common ground on issues and methods of research on mathematics textbooks, ZDM, 15, 765-777. https://doi.org/10.1007/s11858-013-0530-6
  17. Fan, L., Zhu, Y., & Miao, Z. (2013). Textbook research in mathematics education: Development status and directions. ZDM, 45(5), 633-646. https://doi.org/10.1007/s11858-013-0539-x
  18. Jiménez, V. (2018). Matemáticas 1 [Mathematics 1]. Edelvives.
  19. López, R. (2018). Matemáticas 1 [Mathematics 1]. Esfinge.
  20. Marmur, O., Moutinho, I., & Zaskis, R. (2022). On the density of Q in R: Imaginary dialogues scripted by undergraduate students. International Journal of Mathematical Education in Science and Technology, 53(6), 1297-1325. https://doi.org/10.1080/0020739X.2020.1815880
  21. Martinez, M., & Mohar, D. (2018). Matemáticas 1 [Mathematics 1]. Innova Ediciones.
  22. McMullen, J., & Van Hoof, J. (2020). The role of rational number density knowledge in mathematical development. Learning and Instruction, 65, 101228. https://doi.org/10.1016/j.learninstruc.2019.101228
  23. Putra, Z. (2020). Didactic transposition of rational numbers: A case from a textbook analysis and prospective elementary teachers mathematical and didactic knowledge. Journal of Elementary Education, 13(4), 365-394. https://doi.org/10.18690/rei.13.4.365-394.2020
  24. Reséndiz, E., & González, C. (2018). Enseñanza de fracciones en tercer grado de primaria: Análisis del discurso y prácticas pedagógicas [Teaching fractions in the third grade of primary school: Discourse analysis and pedagogical practices]. Revista Internacional de Ciencias Sociales y Humanidades [International Journal of Social Sciences and Humanities], 18(1), 109-138.
  25. Rezat, S. (2009). The utilization of mathematics textbooks as instruments for learning. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of CERME6.
  26. Rodríguez, F., Basso, A., & García, M. (2019). El análisis de textos como metodología de investigación en educación matemática [Text analysis as a research methodology in mathematics education]. In A. Ruiz (Ed.), Proceedings of the Inter-American Conference on Mathematics Education.
  27. Rodríguez, Z. (2022). Propiedad de densidad de los números racionales en libros de texto de primer grado de secundaria en México [Density property of rational number density in first grade secondary school textbooks in Mexico] [Master’s thesis, Benemérita Autonomous University of Puebla]. https://repositorioinstitucional.buap.mx/server/api/core/bitstreams/786457ab-391d-44d9-b185-eefc1c6bb0b5/content
  28. Secretaria de Educación Pública [SEP]. (2017). Aprendizajes clave para la educación integral. Plan y programas de estudio para la educación básica [Key learnings for integral education. Plan and programs of study for basic education]. Secretaría de Educación Pública [Ministry of Public Education]. https://www.sep.gob.mx/work/models/sep1/Resource/10933/1/images/Aprendizajes_clave_para_la_educacion_integral.pdf
  29. Sheydayi, A., & Dadashpoor, H. (2023). Conducting qualitative content analysis in urban planning research and urban studies. Habitat International, 139, 102878. https://doi.org/10.1016/j.habitatint.2023.102878
  30. Shield, M., & Dole, S. (2013). Assessing the potential of mathematics textbooks to promote deep learning. Educational Studies in Mathematics, 82, 183-199. https://doi.org/10.1007/s10649-012-9415-9
  31. Vamvakoussi, X., & Vosniadou, S. (2004). Understanding the structure of the set of rational numbers: A conceptual change approach. Learning and Instruction, 14(5), 453-467. https://doi.org/10.1016/j.learninstruc.2004.06.013
  32. Vamvakoussi, X., & Vosniadou, S. (2010). How many decimals are there between two fractions? Aspects of secondary school students´ understanding of rational numbers and their notation. Cognition and Instruction, 28(2), 181-209. https://doi.org/10.1080/07370001003676603
  33. Vamvakoussi, X., & Vosniadou, S. (2012). Bridging the gap between the dense and the discrete: The number line and the “rubber line” bridging analogy. Mathematical Thinking and Learning, 14(4), 265-284. https://doi.org/10.1080/10986065.2012.717378
  34. Vamvakoussi, X., Christou, K., Mertens, L., & Van Dooren, W. (2011). What fills the gap between discrete and dense? Greek and Flemish students’ understanding of density. Learning and Instruction, 21(5), 676-685. https://doi.org/10.1016/j.learninstruc.2011.03.005
  35. Van Hoof, J., Verschaffel, L., & Van Dooren, W. (2015). Inappropriately applying natural number properties in rational number tasks: Characterizing the development and secondary education. Educational Studies in Mathematics, 90, 39-56. https://doi.org/10.1007/s10649-015-9613-3