Didactic Suitability of the Instructional Process on Quadrilaterals in a Book and as Implemented by Elementary School Teachers

Authors

DOI:

https://doi.org/10.15359/ru.39-1.8

Keywords:

Critical use, didactic suitability, practicing teachers, quadrilaterals, textbooks

Abstract

[Objective] The objective of the study was to analyze and compare the level of didactic suitability of instructional processes related to the study of quadrilaterals, starting with the analysis of a primary education book that addresses the topic, followed by the analysis of two lessons actually implemented by teachers who used the book as a resource, examining their actions to evaluate whether or not they improved the process outlined in the book. [Methodology] After the level of didactic suitability of the book was determined, a case study was carried out with two primary school teachers (one novice and one expert) who used the same book in the fourth year of elementary school to teach the lessons on quadrilaterals. For the analysis, the didactic suitability indicators of a general analysis guide of instructional processes were adapted to the topic of quadrilaterals, to the educational level (elementary) and to the Costa Rican curriculum. [Results] The level of suitability of the instructional process outlined in the book was medium (on a high, medium or low scale), containing some weaknesses and mathematical errors. The instructional processes implemented by both teachers were less appropriate than the ones described in the book, although there were no significant differences. There were few actions implemented by the teachers that resulted in an improvement of the instructional process used in the book. [Conclusions] The levels of adequacy of the processes implemented by the teachers were below the level of the process outlined in the book, presenting errors and weaknesses specific to the book and amplifying them. It is necessary to provide opportunities for teachers to improve their ability to use the book critically as well as their didactic-mathematical knowledge. The indicators adapted can be used to support teachers in these tasks.

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References

Arnal-Bailera, A. y Lancis, A. (2016). Análisis de progresos y dificultades en tareas de identificación del rombo en Educación primaria con GeoGebra. Revista de Didáctica de las Matemáticas, Números, 92, 105-116.

Asociación libros para todos. (2023). Matemática 4. Libros para todos.

Barrantes, M. y Barrantes, M. C. (2020). Geometría ¡prohibido no tocar! Universidad de Extremadura, Servicio de Publicaciones.

Barrantes M., y Zapata M. A. (2008). Obstáculos y errores en la enseñanza-aprendizaje de las figuras geométricas. Campo Abierto, revista de Educación, 27(1), 55-71.

Bernabeu, M., Moreno, M. y Llinares, S. (2019). Experimento de enseñanza como una aproximación metodológica a la investigación en Educación Matemática. Uni-pluriversidad, 19(2), 103-123. https://doi.org/10.17533/udea.unipluri.19.2.07

Berrerra, A. y Gonzáles, C. (2016). Los cuadriláteros en el libro oficial de educación primaria: del " Saber sabio " al " Saber para enseñar". Rev. Prod. Disc. Educ.Matem., 5(1/2), 18-29.

Beyer, C. J. y Davis, E. A. (2012). Learning to critique and adapt science curriculum materials: Examining the development of preservice elementary teachers’ pedagogical content knowledge. Science Education, 96(1), 130-157. https://doi.org/10.1002/sce.20466

Breda, A., Font, V., y Pino-Fan, L. (2018). Criterios valorativos y normativos en la didáctica de las matemáticas: El caso del constructo idoneidad didáctica. Bolema, 32(60), 255-278. https://doi.org/10.1590/1980-4415v32n60a13

Brown, M. (2009). The teacher-tool relationship: Theorizing the design and use of curriculum materials. En J. T. Remillard, B. Herbel-Eisenmann, y G. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 17-36). Routledge. https://doi.org/10.4324/9780203884645-11

Brunheira, L., y Ponte, J. P. (2019). From the classification of quadrilaterals to the classification of prisms: An experiment with prospective teachers. The Journal of Mathematical Behavior, 53, 65-80. https://doi.org/10.1016/j.jmathb.2018.06.004

Carrillo, J., Contreras, L. C., Climent, N., Montes, M.A., Escudero, D. I. y Flores, E. (2016). Didáctica de las Matemáticas para Maestros de Educación Primaria. Ediciones Paraninfo.

Castillo, M. J., Burgos, M. y Godino, J. D. (2022). Elaboración de una guía de análisis de libros de texto de matemáticas basada en la idoneidad didáctica. Educação e Pesquisa, 48, e238787. https://doi.org/10.1590/s1678-4634202248238787esp

Chen, W., Ding, M. (2018). Transition from Textbook to Classroom Instruction in Mathematics: The Case of an Expert Chinese Teacher. Front Educ China 13, 601-632. https://doi.org/10.1007/s11516-018-0031-z

Creswell, J.W. (2014). Research Design. Qualitative, quantitative and mixed methods approaches (4a ed.). Sage. https://doi10.5539/elt.v12n5p40.

De Villiers, M. (2010). Algumas reflexões sobre a Teoria de Van Hiele. Educação Matemática Pesquisa: Revista do Programa de Estudos Pós-Graduados em Educação Matemática, 12(3), 400-431.

De Villiers, M., Govender, R. y Patterson, N. (2009). Defining in geometry. En T.V. Craine y R. Rubenstein (Eds.), Understanding geometry for a changing world, Seventy-first Yearbook, (pp. 189-203). Reston: The National Council of Teachers in Mathematics.

Delgado, B. y Gómez, D. (2017). Diseño, implementación y evaluación de una unidad didáctica para la enseñanza de los cuadriláteros a estudiantes de grado 6° de la Institución Educativa Técnica Ciudad de Cali. [Tesis de Maestría]. Universidad ICESI.

Drake, C. y Sherin, M. (2009) Developing curriculum vision and trust: Changes in teachers’ curriculum strategies. En J. T. Remillard, B. A. Herbel-Eisenmann and G. M. Lloyd (eds), Mathematics Teachers at Work: Connecting Curriculum Materials and Classroom Instruction (pp. 321-337). Routledge. https://doi.org/10.4324/9780203884645-34

Fernández, T. (2013). La investigación en visualización y razonamiento espacial. Pasado, presente y futuro. En A. Berciano, G. Gutiérrez, A. Estepa y N. Climent (Eds.), Investigación en Educación Matemática XVII (pp. 19-42). SEIEM.

Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24, 139-162. https://doi.org/10.1007/BF01273689

Fujita, T. (2008). Learners’ understanding of the hierarchical classification of quadrilaterals. Proceedings of the British Society for Research into Learning Mathematics, 28(2), 31-36.

Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. Journal of Mathematical Behavior, 31, 60-72. https://doi.org/10.1016/j.jmathb.2011.08.003

Fujita, T. y Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Education, 9(1 and 2), 3-20. https://doi.org/10.1080/14794800008520167

Godino, J. D. (2013). Indicadores de la idoneidad didáctica de procesos de enseñanza y aprendizaje de las matemáticas. Cuadernos de Investigación y Formación en Educación Matemática, 11, 111-132. https://revistas.ucr.ac.cr/index.php/cifem/article/view/14720

Godino, J. D., Batanero, C. y Font, V. (2007). The onto-semiotic approach to research in mathematics education. The International Journal on Mathematics Education, 39, 127-135. https://doi.org/10.1007/s11858-006-0004-1

Godino, J. y Ruíz, F. (2003). Geometría y su didáctica para maestros. Grupo Edumat, Universidad de Granada. https://www.researchgate.net/publication/282325712_Geometr%27ia_y_su_didactica_para_maestros

Guillén, G. (2005). Análisis de la clasificación. Una propuesta para abordar la clasificación en el mundo de los sólidos. Educación matemática, 17(2), 117-152. https://doi.org/10.24844/EM1702.05

Gutiérrez, Á. y Jaime, A. (2012). Reflexiones sobre la enseñanza de la geometría en primaria y secundaria. Tecné, Episteme y Didaxis: TED, 32(2), 55-70. https://doi.org/10.17227/ted.num32-1859

Herbst, P., González, G. y Macke, M. (2005). How Can Geometry Students Understand What It Means to Define in Mathematics? The Mathematics Educator, 15(2), 17-24. https://doi.org/10.63301/tme.v15i2.1890

Hershkowitz, R. (1989). Visualization in Geometry-Two Sides of the Coin. Focus on learning problems in mathematics, 11(1), 61-76.

Hershkowitz, R. (1990). Psychological aspects of learning geometry. En P. Nesher y J. Kilpatrick (Eds). Mathematics and cognition: A research synthesis by the International Group for the Psychology of Mathematics Education (pp. 70-95). Cambridge University Press. https://doi.org/10.1017/CBO9781139013499.006

Kobiela, M., y Lehrer, R. (2015). The codevelopment of mathematical concepts and the practice of defining. Journal for Research in Mathematics Education, 46(4), 423-454. https://doi.org/10.5951/jresematheduc.46.4.0423

Kong, F., y Shi, N. (2009). Process analysis and level measurement of textbooks use by teachers. Frontiers of Education in China, 4(2), 268-285. https://doi.org/10.1007/s11516-009-0014-1

León, J. (2011). Estrategia didáctica para el desarrollo de habilidades geométricas en el primer ciclo de la Educación Primaria. [Tesis en opción al grado científico de Doctor en Ciencias Pedagógicas]. Cienfuegos: Universidad de Ciencias Pedagógicas: “Conrado Benítez García”.

León, J., y Barcia, R. (2016). Didáctica de la geometría para la escuela primaria. https://www.researchgate.net/publication/324896297_Didactica_de_la_geometria_para_la_escuela_primaria/citations

MEP. (2012). Programas de estudio de Matemáticas. Ministerio de Educación Pública. https://www.mep.go.cr/sites/default/files/programadeestudio/programas/matematica.pdf

Moise, E. y Downs, F. (1996). Geometría moderna. Addison-Wesley.

Monaghan, F. (2000). What difference does it make? Children views of the difference between some quadrilaterals. Educational Studies in Mathematics, 42(2), 179-196. https://doi.org/10.1023/A:1004175020394

Moriena, S. y Scaglia, S. (2003). Efectos de las representaciones gráficas estereotipadas en la enseñanza de la geometría. Educación Matemática, 15(1), 5-19. https://doi.org/10.24844/EM1501.1

Muñoz-Catalán, M., Montes, M., Climent, N., Contreras, L. Aguilar, A. (2013). La clasificación de las figuras planas en primaria: Una visión de progresión entre etapas y ciclos. Copiadoras Bonanza, S.L.

Nicol, C. y Crespo, S. M. (2006). Learning to teach with mathematics textbooks: How preservice teachers interpret and use curriculum materials. Educational Studies in Mathematics, 62(3), 331-355. https://doi.org/10.1007/s10649-006-5423-y

Ortega, T., y Pecharromán, C. (2015). Aprendizaje de conceptos geométricos a través de visualizaciones. Avances De Investigación En Educación Matemática, (7), 95-117. https://doi.org/10.35763/aiem.v1i7.84

Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211-246. https://doi.org/10.3102/00346543075002211

Rezat, S. (2012). Interactions of teachers’ and students’ use of mathematics textbooks. En G. Gueudet, B. Pepin, L. Trouche (Eds.), From Text to ‘Lived’ Resources Mathematics Teacher Education (Vol. 7, pp. 231-245). Springer. https://doi.org/10.1007/978-94-007-1966-8_12

Sáenz-Ludlow, A. y Athanasopoulou, A. (2008). The GSP, as a technical-symbolic tool, mediating both geometric conceptualizations and communication. En L. Radford, G. Schubring y F. Seeger (Eds.), Semiotics in mathematics education. Epistemology, history, classroom and culture (pp. 195-214). Sense Publishers. https://doi.org/10.1163/9789087905972_012

Segade, E. (2022). El desarrollo de la imagen conceptual del triángulo en el alumnado de Educación Primaria utilizando GeoGebra. [Tesis doctoral]. Universidad Da Coruña, España. http://hdl.handle.net/2183/31191

Sinclair, N., Bartolini Bussi, M. G., de Villiers, M., Jones, K., Kortenkamp, U., Leung, A. y Owens, K. (2016). Recent research on geometry education: An ICME-13 survey team report. ZDM, 48(5), 691-719. https://doi.org/10.1007/s11858-016-0796-6

Stake, R. E. (1995). The art of case study research. Thousand Oaks, CA: Sage.

Taylor (2013). Replacing the ‘teacher-proof’ curriculum with the ‘curriculum-proof’ teacher: Toward more effective interactions with mathematics textbooks. Journal of Curriculum Studies, 45(3), 295-321. https://doi.org/10.1080/00220272.2012.710253

Thompson, D. (2014). Reasoning-and-proving in the written curriculum: Lessons and implications for teachers, curriculum designers, and researchers. International Journal of Educational Research, 64, 141-148. https://doi.org/10.1016/j.ijer.2013.09.013

Törnroos, J. (2005). Mathematics textbooks, opportunity to learn and student achievement. Studies in Educational Evaluation, 31(4), 315-327. https://doi.org/10.1016/j.stueduc.2005.11.005

Tsamir, P., Tirosh, D. y Levenson, E. (2008). Entuitive nonexamples: The case of triangles. Educational Studies in Mathematics, 69(2), 81-95. https://doi.org/10.1007/s10649-008-9133-5

Usiskin, Z., Griffin, J., Witonsky, D. y Willmore, E. (2008). The classification of quadrilaterals: A study in definition. Charlotte, NC: Information Age Publishing.

Van Hiele, P. M. (1986). Structure and insight. A theory of mathematics education. Academic Press.

Walcott, C., Mohr, D. y Kastberg, S. E. (2009). Making sense of shape: An analysis of children's written responses. The Journal of Mathematical Behavior, 28(1), 30-40. https://doi.org/10.1016/j.jmathb.2009.04.001

Published

2025-11-30

Issue

Section

Original scientific papers (evaluated by academic peers)

How to Cite

Castillo Céspedes, M. J., & Vargas Gamboa, J. D. (2025). Didactic Suitability of the Instructional Process on Quadrilaterals in a Book and as Implemented by Elementary School Teachers. Uniciencia, 39(1), 1-26. https://doi.org/10.15359/ru.39-1.8