Prospective high school mathematics teachers’ assessment of the epistemic suitability of a proportionality textbook lesson
Tipo de documento
Lista de autores
Castillo-Cespedes, Maria Jose, Navarro, María Burgos y Godino, Juan D.
Resumen
Background: every teacher should be able to use curriculum materials to guide instructional design and make reasoned pedagogical decisions about the limitations these resources may have. Objectives: in this paper, we describe and analyse a formative intervention with prospective high school mathematics teachers, aimed at developing their competence of didactic suitability analysis of mathematics textbook lessons. Design: the methodology followed is didactic engineering, furthermore, the content analysis methodology is applied to examine the response protocols of the participants. Setting and participants: the experience was carried out within the framework of a university master's degree in compulsory secondary education and high school; the sample was made of 30 students. Data collection and analysis: we proposed these prospective teachers systematically and critically analyse a lesson on proportionality. The written reports of the lesson suitability produced by 14 work-teams are compared with the a priori analysis carried out by the researchers. Results: the results suggest that the prospective teachers usually make more descriptive and less analytical analyses even while using a guide. The participants did not clearly identify the epistemic deficiencies of the lesson, thus revealing their limited didactic-mathematical knowledge on proportionality and their lack of critical evaluation of the textbook. However, based on the analysis previously conducted, prospective teachers managed to be quite accurate in preparing their proposals for the use of the textbook lesson. Conclusions: in this article we show the interest and usefulness of providing future teachers with a tool to systematically analyse a specific textbook lesson. However, in order for future teachers to acquire the necessary skills in critical analysis of the lesson, it is necessary to reinforce their didactic-mathematical knowledge related to proportionality.
Fecha
2021
Tipo de fecha
Estado publicación
Términos clave
Didáctica francesa | Epistemología | Formación | Libros de texto | Tipos de evaluación
Enfoque
Nivel educativo
Educación secundaria básica (12 a 16 años) | Educación superior, formación de pregrado, formación de grado
Idioma
Revisado por pares
Formato del archivo
Volumen
23
Número
4
Rango páginas (artículo)
169-206
ISSN
21787727
Referencias
Ahl, L. M. (2016). Research findings’ impact on the representation of proportional reasoning in Swedish Mathematics textbooks. REDIMAT, 5(2), 180-204. http://dx.doi.org/10.17583/redimat.2016.1987 Arias, J., & Maza, S. (2015). Matemáticas, 1º ESO. Código Bruño. Avalos, B. (2011). Teacher professional development in Teaching and Teacher Education over ten years. Teaching and Teacher Education, 27(1), 10-20. https://doi.org/10.1016/j.tate.2010.08.007 Beyer, C. J., & 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 Braga, G., & Belver, J. (2016). El análisis de libros de texto: una estrategia metodológica en la formación de los profesionales de la educación. Revista Complutense de Educación, 27(1), 199-218. https://doi.org/10.5209/rev_RCED.2016.v27.n1.45688 Breda, A., Pino-Fan, L. R., & Font, V. (2017). Meta didactic-mathematical knowledge of teachers: criteria for the reflection and assessment on teaching practice. EURASIA Journal of Mathematics, Science and Technology Education, 13(6), 1893-1918. https://doi.org/10.12973/eurasia.2017.01207a Burgos, M., Beltrán-Pellicer, P., Giacomone, B., & Godino, J. (2018). Prospective mathematics teachers’ knowledge and competence analysing proportionality tasks. Educação e Pesquisa, 44, 1-22. https://doi.org/10.1590/s1678-4634201844182013 Burgos, M., Beltrán-Pellicer, P., & Godino, J. D. (2020). The issue of didactical suitability in mathematics educational videos: experience of analysis with prospective primary school teachers. Revista Española de Pedagogía, 78(275), 27-49. https://doi.org/10.22550/REP78-12020-07 Burgos, M., Castillo, M. J., Beltrán-Pellicer, P., Giacomone, B., & Godino, J. D. (2019). Análisis didáctico de una lección sobre proporcionalidad en un libro de texto de primaria con herramientas del enfoque ontosemiótico. Bolema 34(66), 40-69. https://doi.org/10.1590/19804415v34n66a03 Cohen, L., Manion, L., & Morrison, K. (2011). Research methods in education. Routledge. Cramer, K., & Post, T. (1993). Connecting research to teaching proportional reasoning. Mathematics Teacher, 86(5), 404-407. Choppin, J. (2011). Learned adaptations: Teachers’ understanding and use of curriculum resources. Journal of Mathematics Teacher Education, 14(5), 331-353. https://doi.org/10.1007/s10857-011-9170-3 Fan, L. (2013). Textbook research as scientific research: Towards a common ground on issues and methods of research on mathematics textbooks. ZDM, 45(5), 765-777. https://doi.org/10.1007/s11858-013-0530-6 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 Fernández, C., & Llinares, S. (2011). De la estructura aditiva a la multiplicativa: Efecto de dos variables en el desarrollo del razonamiento proporcional. Infancia y Aprendizaje, 34(1), 67-80. https://doi.org/10.1174/021037011794390111 Fernández, C., Llinares, C., & Valls, J. (2012). Learning to notice students' mathematical thinking through online discussions. ZDM. Mathematics Education, 44, 747-759. https://doi.org/10.1007/s11858-012-0425-y Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Reidel. Gellert, U., Becerra, R., & Chapman, O. (2013). Research Methods in Mathematics Teacher Education. In M. A. Clements, A. J. Bishop, C. Keitel-Kreidt, J. Kilpatrick & F.K.S. Leung (Eds.), Third International Handbook of Mathematics Education (Vol. 27, pp. 327-360). Springer. https://doi.org/10.1007/978-1-4614-4684-2_11 Giacomone, B., Godino, J.D., & Beltrán-Pellicer, P. (2018). Developing the prospective mathematics teachers’ didactical suitability analysis competence. Educação e Pesquisa, 44, 1-21. http://dx.doi.org/10.1590/s1678-4634201844172011 Godino, J. D., & Batanero, C. (1998). Clarifying the meaning of mathematical objects as a priority area of research in Mathematics Education. In: A. Sierpinska, & J. Kilpatrick (Ed.), Mathematics education as a research domain: A search for identity (pp. 177-195). Godino, J. D., Batanero, C., Contreras, A., Estepa, A. Lacasta, E., & Wilhelmi, M. R. (2013). Didactic engineering as design-based research in mathematics education. Proceedings of CERME8. http://cerme8.metu.edu.tr/wgpapers/WG16/WG16_Godino.pdf Godino, J. D. Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM 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. Font, V., Contreras, A., & Wilhelmi, M. R. (2016). The theory of didactical suitability: Networking a system of didactics principles for mathematics education form different theoretical perspectives. TSG51.13th International Congress on Mathematical Education. http://enfoqueontosemiotico.ugr.es/documentos/ICME13_TSG51_PA _Godino.pdf González, M., & Sierra M. (2004). Metodología de análisis de libros de texto de matemáticas. Los puntos críticos en la enseñanza secundaria en España durante el siglo XX. Enseñanza de las Ciencias, 22(3), 389408. https://www.raco.cat/index.php/Ensenanza/article/view/21990 Grossman, P., & Thompson, C. (2008). Learning from curriculum materials: Scaffolds for new teachers. Teaching and Teacher Education, 24(8), 2014 – 2026. https://doi.org/10.1016/j.tate.2008.05.002 Izsák, A., & Jacobson, E. (2017). Preservice teachers’ learning 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 Jacobs, V.R., Lamb, L.C., & Philipp, R. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202. https://www.jstor.org/stable/20720130 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. Lloyd, G. M., & Behm, S. L. (2005). Preservice elementary teachers’ analysis of mathematics instructional materials. Action in Teacher Education, 26(4), 48 – 62. https://doi.org/10.1080/01626620.2005.10463342 Mason, J. (2016). Perception, interpretation and decision making: understanding gaps between competence and performance-a commentary. ZDM, 48(1-2), 219-226. https://doi.org/10.1007/s11858016-0764-1 Monterrubio, M. C., & Ortega, T. (2012). Creación y aplicación de un modelo de valoración de textos escolares matemáticos en educación secundaria. Revista de Educación, (358), 471-496. http://www.revistaeducacion.educacion.es/doi/358_087.pdf Morales-López, Y., & Font, V. (2019). Evaluation by a teacher of the suitability of her mathematics class. Educação e Pesquisa, 45, 1-19. http://dx.doi.org/10.1590/s1678-4634201945189468 Nagar, G. G., Weiland, T., Brown, R. E., Orrill, C. H., & Burke, J. (2016). Appropriateness of proportional reasoning: Teachers’ knowledge used to identify proportional situations. In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), Proceedings of the 38th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 474–481). Nicol, C. C., & Crespo, S. M. (2006). Learning to teach with mathematics textbooks: How preservice teachers interpret and use curriculum materials. Educational Studies in Mathematics, 62, 331 – 355. https://doi.org/10.1007/s10649-006-5423-y Ramos-Rodríguez, E., Flores, P., & Ponte, J. P. (2016). An approach to the notion of reflective teacher and its exemplification on mathematics education. Systemic Practice and Action Research, 30 (1), 85-102. https://doi.org/10.1007/s11213-016-9383-6 Remillard, J. T. (2000). Can curriculum materials support teachers’ learning? Two fourth-grade teachers’ use of a new mathematics text. The Elementary School Journal, 100(4), 331–350. https://doi.org/10.1086/499645 Riley, K. J. (2010). Teachers’ understanding of proportional reasoning. En P. Brosnan, D. B. Erchick y L. Flevares (Eds.), Proceedings of the 32nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (vol. 6, pp. 1055-1061). Ruiz, E. F., & Valdemoros, M. (2004). Connections between qualitative and quantitative thinking about proportion: The case of Paulina. In M. J. Hoines & A. B. Flugestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, (Vol. 3, 201–208). Schwarz, C., Gunckel, K., Smith, E., Covitt, B., Bae, M., Enfield, M., & Tsurusaki, B. (2008). Helping elementary pre-service teachers learn to use science curriculum materials for effective science teaching. Science Education, 92(2), 345 – 377. https://doi.org/10.1002/sce.20243 Shawer, S. F. (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 Taylor (2013). Replacing the ‘teacher-proof’ curriculum with the ‘curriculumproof’ 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://www.learntechlib.org/p/203301/ Van Dooren, W., De Bock, D., Vleugels, K., & Verschaffel, L. (2010). Just answering...or thinking? Contrasting pupils' solutions and classifications of missing-value word problems. Mathematical Thinking and Learning, 12(1), 20-35. https://doi.org/10.1080/10986060903465806 Van Dooren, W., De Bock, D., Depaepe, F., Janssens, D., & Verschaffel, L. (2003). The illusion of linearity: expanding the evidence towards probabilistic reasoning. Educational Studies in Mathematics, 53(2), 113–138. https://doi.org/10.1023/A:1025516816886 Weiland, T., Orrill, C. H., Nagar, G. G., Brown, R. E., & Burke, J. (2020). 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