Developing reflective competence in prospective mathematics teachers by analyzing textbooks lessons

María José Castillo Céspedes; María Burgos Navarro

doi:10.29333/ejmste/12092

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María José Castillo Céspedes ¹ ^* , María Burgos Navarro ²

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¹ Department of Education of Mathematics, Faculty of Mathematics, San José, COSTA RICA² Department of Didactic of Mathematics, Faculty of Education Sciences, University of Granada, Granada, SPAIN^* Corresponding Author

Abstract

Achieving the competence to reflect on the degree of suitability of textbooks is not easy, so it is necessary to train prospective professionals in the knowledge and use of analytical tools to guide them in critically analyzing these curricular materials. In response to this research problem, this paper describes and analyses the implementation of a training intervention that aims to promote reflective competence in prospective Costa Rican teachers through the analysis of textbook lessons. The content of proportionality is chosen because of its central in the curriculum. The training activity was motivating for the participants and helped them to progress in the competence of lesson analysis. However, it is noted that the design needs to be improved in terms of time dedication, as well as attention to the necessary didactical-mathematical background knowledge on proportionality to achieve better results.

Keywords

teacher education
reflective competence
didactic suitability
textbooks
proportionality

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 18, Issue 6, June 2022, Article No: em2121

https://doi.org/10.29333/ejmste/12092

Publication date: 18 May 2022

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Article Downloads: 1018

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Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

References

Ahl, L. M. (2016). Research findings’ impact on the representation of proportional reasoning in Swedish mathematics textbooks. REDIMAT, 5(2), 180-204. https://doi.org/10.17583/redimat.2016.1987
Alvarado, M. (2014). Matemática 7, serie ser competentes [Mathematics 7, being competent series]. Santillana.
Arican, M. (2019). A diagnostic assessment to middle school students’ proportional reasoning. Turkish Journal of Education, 8(4), 237-257. https://doi.org/10.19128/turje.522839
Beltrán-Pellicer, P., Giacomone, B., & Burgos, M. (2018). Los vídeos educativos en línea desde las didácticas específicas: el caso de las matemáticas [Online educational videos according to specific didactics: the case of mathematics]. Cultura y Educación, 30(4), 633-662. https://doi.org/10.1080/11356405.2018.1524651
Breda, A., Font, V., & Pino-Fan, L. (2018). Criterios valorativos y normativos en la didáctica de las matemáticas: El caso del constructo idoneidad didáctica [Evaluative and normative criteria in didactics of mathematics: The case of didactical suitability construct]. Bolema, 32(60), 255-278. https://doi.org/10.1590/1980-4415v32n60a13
Burgos, M., Beltrán-Pellicer, P., & Godino, J. D. (2020). La cuestión de la idoneidad de los vídeos educativos de matemáticas: una experiencia de análisis con futuros maestros de educación primaria [The issue of didactical suitability in mathematics educational videos: experience of analysis with prospective primary school teachers]. Revista Española de Pedagogía, 78(275), 27-45. https://doi.org/10.22550/REP78-1-2020-07
Burgos, M., & Godino, J. D. (2020). Modelo ontosemiótico de referencia de la proporcionalidad [Ontosemiotic reference model of proportionality: Implications for curricular design in primary and secondary education]. Implicaciones para la planificación curricular en primaria y secundaria. Avances De Investigación En Educación Matemática, (18), 1-20. https://doi.org/10.35763/aiem.v0i18.255
Castillo, M. J., & Burgos, M. (2022). Reflexiones de futuros maestros sobre la idoneidad didáctica y modo de uso de una lección de libro de texto [Reflections of prospective teachers on the didactic suitability and use of a textbook lesson]. Bolema, 36(72), 555-579. https://doi.org/10.1590/1980-4415v36n72a25
Castillo, M. J., Burgos, M., & Godino, J. D. (2021). Prospective High School Mathematics Teachers’ Assessment of the Epistemic Suitability of a Textbook Proportionality Lesson. ACTA SCIENTIAE, 23(4), 169-206. https://doi.org/10.17648/acta.scientiae.6552
Castillo, M. J., Burgos, M., & Godino, J. D. (2022a). Elaboración de una guía de análisis de libros de texto de matemáticas basada en la idoneidad didáctica [Developing a guide to analyse mathematics textbooks based on the didactical suitability theory]. Educação e Pesquisa, 48, e238787.
Castillo, M. J., Burgos, M., & Godino, J. D. (2022b). Guía de análisis de lecciones de libros de texto de Matemáticas en el tema de proporcionalidad [Guidelines for the analysis of mathematics textbooks lessons on the subject of proportionality]. Uniciencia, 36(1), e15399. https://doi.org/10.15359/ru.36-1.14
Castillo, M. J., Burgos, M., & Godino. J. D. (2022c). Competencia de futuros profesores de matemáticas para el análisis de la idoneidad didáctica de una lección sobre proporcionalidad en un libro de texto [Prospective mathematics teachers’ competence for analysing the didactic suitability of a proportionality lesson in a textbook]. Revista Educación Matemática, (in press).
Cobb, P., & Gravemeijer, K. (2008). Experimenting to support and understand learning processes. In A. E. Kelly, R. A. Lesh, & J. Y. Baek (Eds.), Handbook of design research methods in education. Innovations in science, technology, engineering and mathematics learning and teaching (pp. 68-95). Lawrence Erlbaum Associates.
Cohen, L., Manion, L., & Morrison, K. (2011). Research methods in education. Routledge.
Davis, B. (2008). Is 1 a prime number? Developing teacher knowledge through concept study. Mathematics Teaching in the Middle School, Reston, 14(2), 86-91. https://doi.org/10.5951/MTMS.14.2.0086
De Bock, D., Neyens, D., & Van Dooren, W. (2017). Students’ ability to connect function properties to different types of elementary functions: An empirical study on the role of external representations. International Journal of Science and Mathematics Education, 15, 939-955. https://doi.org/10.1007/s10763-016-9724-z
De Bock, D., Van Dooren, W., Janssens, D., & Verschaffel, L. (2002). Improper use of linear reasoning: An in-depth study of the nature and the irresistibility of secondary school students’ errors. Educational Studies in Mathematics, 50, 311-334. https://doi.org/10.1023/A:1021205413749
Díaz-Levicoy, D., Giacomone, B., López-Martín, M., & Piñeiro, J. L. (2016). Estudio sobre los gráficos estadísticos en libros de texto digitales de educación primaria Española [Study on statistical graphics in digital textbooks of Spanish primary education]. Profesorado, Revista de Currículum y Formación Del Profesorado [Teachers, Journal of Curriculum and Teacher Training], 20(1), 133-156.
Escuela de Matemática de la UCR. (2015). Programa del curso Ma-0007 matemáticas en el curriculum escolar [Course program Ma-0007 mathematics in the school curriculum]. Escuela de Matemática [School of Mathematics]. https://emate.ucr.ac.cr/images/EMATE/Departamentos/Ensenanza/Programas/MA-0007.pdf
Esqué, D., & Breda, A. (2021). Valoración y rediseño de una unidad sobre proporcionalidad, utilizando la herramienta idoneidad didáctica [Assessment and redesign of a unit on proportionality using the didactical suitability tool]. Uniciencia [Uniscience], 35(1), 38-54. https://doi.org/10.15359/ru.35-1.3
Fernández, C., & Llinares, S. (2011). De la estructura aditiva a la multiplicativa: Efecto de dos variables en el desarrollo del razonamiento proporcional [From the additive to the multiplicative structure: The effect of two variables in the development of proportional reasoning]. Infancia y Aprendizaje [Childhood and Learning], 34(1), 67-80. https://doi.org/10.1174/021037011794390111
Fernández, C., & Llinares, S. (2012). Características del desarrollo del razonamiento proporcional en la educación primaria y secundaria [Characteristics of the development of proportional reasoning in primary and secondary school]. Enseñanza de las Ciencias [Science Education], 30(1), 129-142. https://doi.org/10.5565/rev/ec/v30n1.596
Fernández, C., & Yoshida, M. (2004). Lesson study. A Japanese approach to improving mathematics learning and teaching. Erlbaum.
Giacomone, B., Godino, J. D., & Beltrán-Pellicer, P. (2018). Desarrollo de la competencia de análisis de la idoneidad didáctica en futuros profesores de matemáticas [Developing the prospective mathematics teachers’ didactical suitability analysis competence]. Educação e Pesquisa [Education and Research], 44, 1-21. https://doi.org/10.1590/s1678-4634201844172011
Godino, J. D. (2013). Indicadores de la idoneidad didáctica de procesos de enseñanza y aprendizaje de las matemáticas [Indicators of didactic suitability for mathematics teaching and learning processes]. Cuadernos de Investigación y Formación en Educación Matemática [Research and Training Notebooks in Mathematics Education], 11, 111-132.
Godino, J. D. Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. The International Journal on Mathematics Education, 39(1-2), 127-135. https://doi.org/10.1007/s11858-006-0004-1
Godino, J. D., Batanero, C., Rivas, H., & Arteaga, P. (2013). Componentes e indicadores de idoneidad de programas de formación de profesores en didáctica de las matemáticas [Suitability components and indicators of teachers’ education programs in mathematics education]. REVEMAT, 8(1), 46-74. https://doi.org/10.5007/1981-1322.2013v8n1p46
Godino, J. D., Giacomone, B., Batanero, C., & Font, V. (2017). Enfoque ontosemiótico de los conocimientos y competencias del profesor de matemáticas [Onto-semiotic approach to mathematics teacher’s knowledge and competences]. Bolema, 31(57), 90-113. https://doi.org/10.1590/1980-4415v31n57a05
Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39, 372-400. https://doi.org/10.5951/jresematheduc.39.4.0372
Hodgen, J., & Johnson, D. (2004). Teacher reflection, identity and belief change in the context of primary CAME. In A. Millet, M. Brown, & A. Askew (Eds.), Primary mathematics and the developing professional (pp. 219-244). Springer. https://doi.org/10.1007/1-4020-1915-7_8
Hummes, V. B., Font, V., & Breda, A. (2019). Uso combinado del estudio de clases y la idoneidad didáctica para el desarrollo de la reflexión sobre la propia práctica en la formación de profesores de matemáticas [Combined use of the lesson study and the criteria of didactical suitability for the development of the reflection on the own practice in the training of mathematics teachers]. Acta Scientiae, 21(1), 64-82. https://doi.org/10.17648/acta.scientiae.v21iss1id4968
Izsák, A., & Jacobson, E. (2017). Preservice teachers’ reasoning about relationships that are and are not proportional: A knowledge-in-pieces account. Journal for Research in Mathematics Education, 48(3), 300-339. https://doi.org/10.5951/jresematheduc.48.3.0300
Lamon, S. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629-668). Information Age Publishing.
Lloyd, G. (2002). Mathematics teachers’ beliefs and experiences with innovative curriculum materials. The role of curriculum in teacher development. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education (pp. 149-159). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47958-3_9
Mason, J. (2002). Researching your own practice: The discipline of noticing. Routledge. https://doi.org/10.4324/9780203471876
MEP. (2012). Programas de estudio de Matemáticas [Mathematics curricula]. Ministerio de Educación Pública. https://www.mep.go.cr/sites/default/files/programadeestudio/programas/matematica.pdf
Morales-García, L., & Navarro, C. (2021). Idoneidad epistémica del significado de número natural en libros de texto Mexicanos [Epistemic suitability of the natural number meaning in Mexican textbooks]. Bolema, 35(71), 1338-1368. https://doi.org/10.1590/1980-4415v35n71a06
Morales-López, Y., & Araya-Román, D. (2020). Helping preservice teachers to reflect. Acta Scientiae, 22(1), 88-111. https://doi.org/10.17648/acta.scientiae.5641
Pino-Fan, L. R., Assis, A., & Castro, W. F. (2015). Towards a methodology for the characterization of teachers’ didactic-mathematical knowledge. Eurasia Journal of Mathematics, Science and Technology Education, 11(6), 1429-1456. https://doi.org/10.12973/eurasia.2015.1403a
Porras, V., Porras, J., & Villegas, E. (2013). Matemáticas 7° [Mathematics 7th grade]. Compas ERV.
Schön, D. (1987). Educating the reflective practitioner. Toward a new design for teaching and learning in the professions. Jossey-Bass Publishers.
Seckel, M. J., & Font, V. (2020). Competencia reflexiva en formadores del profesorado de matemática [Reflective competency in the educators of mathematics teachers]. Magis, Revista Internacional de Investigación en Educación [Magis, International Journal of Educational Research], 12(25), 127-144. https://doi.org/10.11144/Javeriana.m12-25.crfp
Shawer, S. (2017). Teacher-driven curriculum development at the classroom level: Implications for curriculum, pedagogy and teacher training. Teaching and Teacher Education, 63, 296-313. https://doi.org/10.1016/j.tate.2016.12.017
Shield, M., & Dole, S. (2013). Assessing the potential of mathematics textbooks to promote deep learning. Educational Studies in Mathematics, 82(2), 183-199. https://doi.org/10.1007/s10649-012-9415-9
Sun, J., & van Es, E. A. (2015). An exploratory study of the influence that analyzing teaching has on preservice teachers’ classroom practice. Journal of Teacher Education, 66(3), 201-214. https://doi.org/10.1177/0022487115574103
Van Dooren, W., De Bock, D., & Verschaffel, L. (2010). From addition to multiplication… and back. The development of students’ additive and multiplicative reasoning skills. Cognition and Instruction, 28(3), 360-381. https://doi.org/10.1080/07370008.2010.488306
Weiland, T., Orrill, C. H., Nagar, G. G., Brown, R. E., & Burke, J. (2021). Framing a robust understanding of proportional reasoning for teachers. Journal of Mathematics Teacher Education, 24, 179-202. https://doi.org/10.1007/s10857-019-09453-0
Yang, K., & Liu, X. (2019). Exploratory study on Taiwanese secondary teachers’ critiques of mathematics textbooks. Eurasia Journal of Mathematics, Science and Technology Education, 15(1), em1655. https://doi.org/10.29333/ejmste/99515

How to cite this article

APA

Castillo Céspedes, M. J., & Burgos Navarro, M. (2022). Developing reflective competence in prospective mathematics teachers by analyzing textbooks lessons. Eurasia Journal of Mathematics, Science and Technology Education, 18(6), em2121. https://doi.org/10.29333/ejmste/12092

Vancouver

Castillo Céspedes MJ, Burgos Navarro M. Developing reflective competence in prospective mathematics teachers by analyzing textbooks lessons. EURASIA J Math Sci Tech Ed. 2022;18(6):em2121. https://doi.org/10.29333/ejmste/12092

AMA

Castillo Céspedes MJ, Burgos Navarro M. Developing reflective competence in prospective mathematics teachers by analyzing textbooks lessons. EURASIA J Math Sci Tech Ed. 2022;18(6), em2121. https://doi.org/10.29333/ejmste/12092

Chicago

Castillo Céspedes, María José, and María Burgos Navarro. "Developing reflective competence in prospective mathematics teachers by analyzing textbooks lessons". Eurasia Journal of Mathematics, Science and Technology Education 2022 18 no. 6 (2022): em2121. https://doi.org/10.29333/ejmste/12092

Harvard

Castillo Céspedes, M. J., and Burgos Navarro, M. (2022). Developing reflective competence in prospective mathematics teachers by analyzing textbooks lessons. Eurasia Journal of Mathematics, Science and Technology Education, 18(6), em2121. https://doi.org/10.29333/ejmste/12092

MLA

Castillo Céspedes, María José et al. "Developing reflective competence in prospective mathematics teachers by analyzing textbooks lessons". Eurasia Journal of Mathematics, Science and Technology Education, vol. 18, no. 6, 2022, em2121. https://doi.org/10.29333/ejmste/12092