Representations of Numerical Sequences in Mexican Secondary School Textbooks
DOI:
https://doi.org/10.53103/cjess.v4i3.234Keywords:
Numerical Sequences, Representations, Mathematics Textbooks, Early Algebra, Secondary EducationAbstract
The study of numerical sequences usually focuses on the use of symbols or finding generalizations, that is, a more formal notation. However, there is several research on the different representations, but little research in representations that we consider as drawings and illustrations and that, in general, are commonly used in textbooks when both a numerical sequence and a figurative sequence are shown. The present research with a qualitative approach sought to identify the representations of sequences contained in Middle school textbooks. Nine textbooks were analyzed using the theoretical-methodological proposal known as Mathematical Content Analysis, where 28 different figures were found to represent a numerical sequence. The findings showed that there are three types of representations in the textbooks analyzed: abstract figures, real figures, and pictorial figures. The results show that the representations that appear most frequently in textbooks are pictorial figures.
Downloads
References
Castro, E. (2013). Exploración de patrones numéricos mediante configuraciones puntuales: estudio con escolares de primer ciclo de secundaria (12-14 años). Granada: Universidad de Granada. http://hdl.handle.net/10481/25009
Duval, R. (2012). Registers of semiotic representation and cognitive functioning of thought. REVEMAT, 7(2), 266-297. https://doi.org/10.5007/1981-1322.2012v7n2p266
English, L. D., & Warren, E. A. (1998). Introducing the variable through pattern exploration. Mathematics Teacher, 91(2), 166–170. https://doi.org/10.5951/MT.91.2.0166
Eves, H. (1976). An introduction to history of mathematics. New York: Saunder College.
Faria, A. R., Viseu, F., Gomes, A., & Aires, A. P. (2022). Representations in the learning of Sequences and Regularities by Third-grade Portuguese Students. International Electronic Journal of Elementary Education, 14(2), 147-161. https://doi.org/10.26822/iejee.2022.235
Ferrini-Mundy, J., Lappan, G., & Phillips, E. (1997). Experiences with Patterning. Teaching Children Mathematics, 3(6), 282-288. https://doi.org/10.5951/TCM.3.6.0282
Freudenthal, H. (1991). Revisiting Mathematics Education. Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47202-3
Goldin, G. A. (2014). Mathematical representations. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp.409–413). The Netherlands: Springer. https://doi.org/10.1007/978-94-007-4978-8_103
Lupiañez, J. L. (2016). Sistemas de representación. En L. Rico, & A. J. Moreno (Eds.). Elementos de didáctica de la matemática para el profesor de Secundaria (pp 119-138). Granada: Pirámide.
Medrano, A., Xolocotzin, U., & Flores-Macías, R. (2022). Un análisis de la producción de representaciones al solucionar problemas de álgebra temprana en estudiantes de primaria. Educación Matemática, 34(3), 10-41. https://doi.org/10.24844/EM3403.01
National Council of Teachers of Mathematics [NCTM]. (2000). Principles and Standards for School Mathematics. Reston: NCTM.
Nuñez-Gutiérrez, K., & Cabañas-Sánchez, G. (2023). Sucesiones matemáticas en el currículo de México en secundaria. Bolema: Boletim De Educação Matemática, 37(77), 1234-1257. https://doi.org/10.1590/1980-4415v37n77a15
Ozsoy, G. (2018). Pre-service Teachers’ Use of Visual Representations. International Electronic Journal of Elementary Education, 11(1), 49-54. https://doi.org/10.26822/iejee.2018143960
Palatnik, A., & Koichu, B. (2017). Sense making in the context of algebraic activities. Educational Studies in Mathematics, 95(3), 245–262. https://doi.org/10.1007/s10649-016-9744-1
Radford, L. (2003). Gestures, speech, and the sprouting of signs: A semiotic-cultural approach to students’ types of generalization. Mathematical Thinking and Learning, 5(1), 37–70. https://doi.org/10.1207/S15327833MTL0501_02
Radford, L. (2014). On the role of representations and artifacts in knowing and learning. Educational Studies in Mathematics, 85(3), 405–422. https://doi.org/10.1007/s10649-013-9527-x
Rico, L. (1997). Los organizadores del currículo de matemáticas. En L. Rico; E. Castro., E. Castro., M. Coriat., A. Marín., L. Puig., M. Sierra., & M. M. Socas. (Eds.), La educación matemática en la enseñanza secundaria (pp. 39-59). España: Horsori.
Rico, L., Castro, E., & Romero, I. (1996). The role of representation systems in the learning of numerical structures. En A. Gutiérrez., L. Puig. (Eds.), Proceedings of the twentieth international conference for the psychology of mathematics education (pp. 87-102). Valencia: Universidad de Valencia.
Rico, L. & Moreno, A. J. (2016). Elementos de didáctica de la matemática para el profesor de Secundaria. España: Pirámide.
Rivera, F. D. (2010). Visual templates in pattern generalization activity. Educational Studies in Mathematics, 73(3), 297–328. https://doi.org/10.1007/s10649-009-9222-0
Rivera, F. D., & Becker, J. R. (2005). Figural and numerical modes of generalizing in algebra. Mathematics Teaching in the Middle School, 11(4), 198–203. https://doi.org/10.5951/MTMS.11.4.0198
Secretaría de Educación Pública. (2011). Plan de estudios 2011. Recuperado de https://www.gob.mx/cms/uploads/attachment/file/20177/Plan_de_Estudios_2011_f.pdf
Secretaría de Educación Pública (2017). Aprendizaje Clave Para La Educación Integral: Plan Y Programa De Estudio Para La Educación Básica. Recuperado de https://www.sep.gob.mx/work/models/sep1/Resource/10933/1/images/Aprendizajes_clave_para_la_educacion_integral.pdf
Secretaría de Educación Pública (2022). Plan de estudios para la educación preescolar, primario y secundaria 2022. Recuperado de https://educacionbasica.sep.gob.mx/wp-content/uploads/2023/07/Plan_de_Estudios_para_la_Educacion_Preescolar_Primaria_y_Secundaria.pdf
Schmelkes, C., & Shmelkes, N. E. (2010). Manual para la represnetación de anteproyectos e informantes de investigación. Reino Unido: OXFORD.
Stacey, K. (1989). Finding and using patterns in linear generalising problems. Educational Studies in Mathematics, 20(2), 147–164. https://doi.org/10.1007/BF00579460
Steen, L. A. (1988). The science of patterns. Science, 240(4852), 611-616.
Walkowiak, T. A. (2014). Elementary and middle school students’ analyses of pictorial growth patterns. The Journal of Mathematical Behavior, 33(2014), 56-71. https://doi.org/10.1016/j.jmathb.2013.09.004
Wilkie, K. J. (2016). Students’ use of variables and multiple representations in generalizing functional relationships prior to secondary school. Educational Studies in Mathematics, 93(3), 333–361. https://doi.org/10.1007/s10649-016-9703-x
Wilkie, K. J., & Clarke, D. M. (2016). Developing students’ functional thinking in algebra through different visualisations of a growing pattern’s structure. Mathematics Education Research Journal, 28, 223-243. https://doi.org/10.1007/s13394-015-0146-y
Wilkie, K. J. (2021). Seeing quadratics in a new light: Secondary mathematics pre-service teachers’ creation of figural growing patterns. Educational Studies in Mathematics, 106(1), 91–116.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Yasmin Cruz Hernandez, José Antonio Juárez López, Carolina Napp Avelli, Lizzet Morales García
This work is licensed under a Creative Commons Attribution 4.0 International License.
All articles published by CJESS are licensed under the Creative Commons Attribution 4.0 International License. This license permits third parties to copy, redistribute, remix, transform and build upon the original work provided that the original work and source is appropriately cited.
