Geometric Reasoning Promoted in Tasks of Secondary Education Textbooks in Chile

Authors

DOI:

https://doi.org/10.35763/aiem27.5881

Keywords:

Textbooks, Mathematical instruction, Geometric reasoning, Geometric concepts, Primary objects

Abstract

The characterization of the processes underlying geometric reasoning promoted by Chilean secondary school textbooks is studied. For this, the tasks corresponding to the thematic axis of geometry are considered. A content analysis is carried out, using tools of the ontosemiotic approach to mathematical knowledge and instruction, to identify the mathematical objects and processes that are promoted in the textbook tasks. The results show that, although the tasks analyzed promote some type of process (visualization, measurement, construction, representation, and deduction), the measurement process that brings into play arithmetic-algebraic procedures predominates, which is detrimental to geometric reasoning in the geometrical labeled practices of the textbooks.

Downloads

Download data is not yet available.

References

Aké, L. P. (2013). Evaluación y desarrollo del razonamiento algebraico elemental en maestros en formación (Tesis de doctorado sin publicar). Universidad de Gra-nada, España.

Arce, D. (2019). Cuaderno de actividades matemáticas 7º básico. SM.

Barrantes, M., López, M., & Fernández, M. A. (2015). Análisis de las representacio-nes geométricas en los libros de texto. PNA, 9(2), 107–127.

Battista, M. T. (2007). The development of geometric and spatial thinking. En F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 943–908). Information Age Publishing.

Battista, M. T., Frazee, L. M., & Winer, M. L. (2018). Analyzing the relation between spatial and geometric reasoning for elementary and middle school students. En K. S. Mix & M. T. Battista (Eds.), Visualizing mathematics: Research in math-ematics education (pp. 195–228). Springer. https://doi.org/10.1007/978-3-319-98767-5_10

Charalambous, C. Y., Delaney, S., Hsu, H. Y., & Mesa, V. (2010). A comparative anal-ysis of the addition and subtraction of fractions in textbooks from three coun-tries. Mathematical Thinking and Learning, 12(2), 117–151. https://doi.org/10.1080/10986060903460070

Chico, J., & Montes, M. Á. (2023). Representaciones semióticas de la multiplicación y división en libros de texto de educación primaria. Bolema: Boletim de Educa-ção Matemática, 37(75), 296–316. https://doi.org/10.1590/1980-4415v37n75a14

Clements, D. H., & Sarama, J. (2011). Early childhood teacher education: The case of geometry. Journal of Mathematics Teacher Education, 14(2), 133–148. https://doi.org/10.1007/s10857-011-9173-0

Cohen, L., Manion, L., & Morrison, K. (2007). Research methods in education (6th ed.). Routledge.

Díaz, E., Ortiz, N., Norambuena, P., Morales, K., Rebolledo, M., & Barrera, R. (2020). Texto del estudiante de matemática 2° medio. SM.

Díaz, E., Ortiz, N., Morales, K., & Verdejo, A. (2020). Cuaderno de actividades mate-máticas 2º medio. SM.

Dimmel, J. K., & Herbst, P. G. (2015). The semiotic structure of geometry diagrams: How textbook diagrams convey meaning. Journal for Research in Mathematics Education, 46(2), 147–195. https://doi.org/10.5951/jresematheduc.46.2.0147

Duval, R. (2017). Understanding the mathematical way of thinking–The registers of se-miotic representations. Springer. https://doi.org/10.1007/978-3-319-56910-9

Font, V., Godino, J. D., & Gallardo, J. (2013). The emergence of objects from mathe-matical practices. Educational Studies in Mathematics, 82, 97–124. https://doi.org/10.1007/s10649-012-9411-0

Fresno, C., Torres, C., & Ávila, J. (2020). Texto del estudiante de matemática 1° medio. Santillana.

Fujita, T., & Jones, K. (2003). The place of experimental tasks in geometry teaching: Learning from the textbooks design of the early 20th century. Research in Mathematics Education, 5, 47–62. https://doi.org/10.1080/14794800008520114

Gal, H., & Linchevski, L. (2010). To see or not to see: Analyzing difficulties in ge-ometry. Educational Studies in Mathematics, 74(2), 163–183. https://doi.org/10.1007/s10649-010-9232-y

Godino, J. D., Batanero, C., & Font, V. (2019). The onto-semiotic approach: Implica-tions for the prescriptive character of didactics. For the Learning of Mathemat-ics, 39(1), 38–43.

Godino, J. D., Wilhelmi, M., Blanco, T., Contreras, Á., & Giacomone, B. (2016). Aná-lisis de la actividad matemática mediante dos herramientas teóricas: Regis-tros de representación semiótica y configuración ontosemiótica. Avances de Investigación en Educación Matemática, 10, 91–110. https://doi.org/10.35763/aiem.v0i10

González, M., & Sierra, M. (2004). Metodología de análisis de libros de texto de ma-temáticas: Los puntos críticos en la enseñanza secundaria en España durante el siglo XX. Enseñanza de las Ciencias, 22(3), 389–408.

Hadar, L. L. (2017). Opportunities to learn: Mathematics textbooks and students’ achievements. Studies in Educational Evaluation, 55, 153–166. https://doi.org/10.1016/j.stueduc.2017.10.002

Hershkowitz, R., Duval, R., Bussi, M. G. B., Boero, P., Lehrer, R., Romberg, T., Berthelot, R., Salin, M. H., & Jones, K. (1998). Reasoning in geometry. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century: An ICMI study (pp. 29–83). Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5226-6_3

Hershkowitz, R., Arcavi, A., & Bruckheimer, M. (2001). Reflections on the status and nature of visual reasoning – the case of the matches. International Journal of Mathematical Education in Science and Technology, 32(2), 255–265. https://doi.org/10.1080/00207390010010917

Iturra, F., Manosalva, C., Romero, D., & Ramírez, M. (2019). Texto del estudiante de matemática 7° básico. SM.

Jones, K., & Fujita, T. (2013). Interpretations of national curricula: The case of ge-ometry in textbooks from England and Japan. ZDM Mathematics Education, 45, 671–683. https://doi.org/10.1007/s11858-013-0515-5

Lugo-Armenta, J. G., & Pino-Fan, L. R. (2021). Niveles de razonamiento inferencial para el estadístico T Student. Bolema: Boletim de Educação Matemática, 35(71), 1776–1802. https://doi.org/10.1590/1980-4415v35n71a25

Ministerio de Educación de Chile (MINEDUC). (2015). Bases curriculares Séptimo bási-co a Segundo medio. Unidad de Currículum y Evaluación.

Otten, S., Gilbertson, N. J., Males, L. M., & Clark, D. L. (2014). The mathematical na-ture of reasoning—and proving opportunities in geometry textbooks. Mathe-matical Thinking and Learning, 16(1), 51–79. https://doi.org/10.1080/10986065.2014.857802

Pino-Fan, L. R., Godino, J. D., & Font, V. (2018). Assessing key epistemic features of didactic mathematical knowledge of prospective teachers: The case of the derivative. Journal of Mathematics Teacher Education, 21, 63–94. https://doi.org/10.1007/s10857-016-9349-8

Presmeg, N. (2008). Spatial abilities research as a foundation for visualization in teaching and learning mathematics. En P. Clarkson & N. Presmeg (Eds.), Criti-cal issues in mathematics education: Major contributions of Alan Bishop (pp. 83–95). Springer.

Rubio, N. (2012). Competencia del profesorado en el análisis didáctico de prácticas, ob-jetos y procesos matemáticos (Tesis de doctorado sin publicar). Universitat de Barcelona, España.

Seah, R., & Horne, M. (2020). The influence of spatial reasoning on analysing about measurement situations. Mathematics Education Research Journal, 32, 365–386. https://doi.org/10.1007/s13394-020-00327-w

Sepúlveda, A. (2020). Cuaderno de actividades matemática 1° medio. Santillana.

Stylianides, G. J. (2009). Reasoning and proving in school mathematics textbooks. Mathematical Thinking and Learning, 11(4), 258–288. https://doi.org/10.1080/10986060903253954

Torres, C., & Caroca, M. (2019a). Texto del estudiante de matemática 8° básico. Santi-llana.

Torres, C., & Caroca, M. (2019b). Cuaderno de actividades matemática 8° básico. Santi-llana.

Whitely, W., Sinclair, N., & Davis, B. (2015). What is spatial reasoning? En B. Davis & Spatial Reasoning Study Group (Eds.), Spatial reasoning in the early years: Principles, assertions and speculations (pp. 139–150). Routledge. https://doi.org/10.4324/9781315762371

Downloads

Published

2025-05-02

How to Cite

Morales-Ramírez, G., Pino-Fan, L. R., Lugo Armenta, J. G., & Caviedes Barrera, S. L. (2025). Geometric Reasoning Promoted in Tasks of Secondary Education Textbooks in Chile. Advances of Research in Mathematics Education, (27), 67–85. https://doi.org/10.35763/aiem27.5881

Issue

No. 27 (2025)

Section

Artículos

License

Copyright (c) 2025 Guadalupe Morales-Ramírez, Luis Roberto Pino-Fan, Jesús Guadalupe Lugo Armenta, Sofía Luisa Caviedes Barrera

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The articles published in this journal are under a license Creative Commons: By 4.0 España from  number 21 (2022).

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and keep the acknowledgement of authorship.
  2. The texts published in this journal are – unless indicated otherwise – covered by the Creative Commons Attribution 4.0 international licence. You may copy, distribute, transmit and adapt the work, provided you attribute it (authorship, journal name, publisher) in the manner specified by the author(s) or licensor(s). The full text of the licence can be consulted here: http://creativecommons.org/licenses/by-nc/4.0.
  3. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  4. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).

Funding data

Most read articles by the same author(s)