Professional noticing and hypothetical learning trajectories in the teaching practice of pre-service teachers
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The teaching practicum in initial teacher education should consider the use and appropriation of professional knowledge. This article argues that the use of Hypothetical Learning Trajectories (HLT) in the pedagogical practice of pre-service mathematics teachers fosters the development of their professional noticing of students’ mathematical thinking and the curriculum. In this context, HLT serve not only as a theoretical framework for professional noticing but also as methodological tools and curricular resources. Consequently, this study identifies potential research avenues for exploring professional noticing through the use of HLT from multiple perspectives. It is recommended that HLT be incorporated into pre-service mathematics teacher education courses because of their potential to enhance professional noticing and to refine both theoretical and practical aspects of teaching and learning processes.
- Mathematics education
- Professional vision
- Pre-service teacher education
- Teaching practicum
- Hypothetical learning trajectories (HLTs)
Amador, J. (2020). Noticing as a Tool to Analyze Mathematics Instruction and Learning. En O. Chapman y L. Salvador (Eds.), International Handbook of Mathematics Teacher Education (Vol. 2, pp. 311–336). https://doi.org/10.1163/9789004418967_012
Amador, J. M. (2019). Preservice Teachers' Use of Curricular Resources for Mathematics Lesson Design. Mathematics Teacher Education and Development, 21(1), 51–81. https://eric.ed.gov/?id=EJ1216048
Amador, J. M. (2022). Mathematics teacher educator noticing: examining interpretations and evidence of students’ thinking. Journal of Mathematics Teacher Education, 25(2), 163–189. https://doi.org/10.1007/s10857-020-09483-z
Amador, J., Males, L., Earnest, D., y Dietiker, L. (2017). Curricular Noticing: Theory on and Practice of Teachers’ Curricular Use. En E. Schack, M. Fisher, y J. Wilhelm (Eds.), Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks (pp. 427–443). Springer International Publishing. https://doi.org/10.1007/978-3-319-46753-5_25
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
Bosch, M., y Gascón, J. (2009). Aportaciones de la Teoría Antropológica de lo Didáctico a la formación del profesorado de matemáticas de Secundaria. En M. González, M. González, y J. Murillo (Eds.), Investigación en educación matemática XIII (pp. 89–114). SEIEM. http://educmath.inrp.fr/Educmath/
Cárcamo, A., y Fuentealba, C. (2023). Un modelo para la construcción de trayectorias hipotéticas de aprendizaje Preliminares. Bolema: Boletim de Educação Matemática, 37 (76), 577–701. https://doi.org/10.1590/1980-4415v37n76a10
Decreto 2450 de 2015 [Ministerio de Educación Nacional]. Por el cual se reglamentan las condiciones de calidad para el otorgamiento y renovación del registro calificado de los programas académicos de licenciatura y los enfocados a la educación, y se adiciona el Decreto 1075 de 2015, Único Reglamentario del Sector Educación. 17 de diciembre de 2015. https://www.alcaldiabogota.gov.co/sisjur/normas/Norma1.jsp?i=64184
Downton, A., y Sullivan, P. (2020). Models of in-service mathematics teacher education professional development. En S. Lerman (Ed.), Encyclopedia of Mathematics Education (2ª ed., pp. 627–631). Springer. https://doi.org/10.1007/978-3-030-15789-0_115
Edgington, C. (2012). Teachers' uses of a learning trajectory to support attention to students' mathematical thinking [Tesis de doctorado no publicada]. North Carolina State University. http://search.proquest.com/docview/1346014792?accountid=17192
Ellis, A., Ozgur, Z., Kulow, T., Dogan, M., y Amidon, J. (2016). An exponential growth learning trajectory: Students’ emerging understanding of exponential growth through covariation. Mathematical Thinking and Learning, 18(3), 151–181. https://doi.org/10.1080/10986065.2016.1183090
Fernández, C., y Choy, B. (2020). Theoretical Lenses to Develop Mathematics Teacher Noticing. En International Handbook of Mathematics Teacher Education (Vol. 2, pp. 337–360). Brill. https://doi.org/10.1163/9789004418967_013
Fernández, C., Sánchez-Matamoros, G., Valls, J., y Callejo, M. (2018). Noticing students’ mathematical thinking: Characterization, development and contexts. Avances de Investigación en Educación Matemática, 13, 39–61. https://doi.org/10.35763/aiem.v0i13.229
Godino, J., y Llinares, S. (2008). Competencia docente en el análisis de procesos instructivos y desarrollo de una “mirada profesional”. Aportes desde el interaccionismo simbólico. En A. Avila (Ed.), Rutas de la Educación Matemática (pp. 19–37). Sociedad Mexicana de Investigación y Divulgación de la Educación Matemática.
González-Forte, J., Ivars, P., y Fernández, C. (2021). Un estudio sobre la mirada curricular en estudiantes para profesor de matemáticas. En R. Satorre (Coord.), REDES-INNOVAESTIC 2021, Libro de actas (pp. 42-43). Universidad de Alicante.
Ivars, P., y Fernández, C. (2023). Snapshots of curricular noticing: planning a subtraction algorithm lesson in primary education. En M. Ayalon, B. Koichu, R. Leikin, L. Rubel. y M. Tabach (Eds.), Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 107–114). PME.
Jacobs, V., Lamb, L., y Philipp, R. (2010). Professional Noticing of Children’s Mathematical Thinking. En Journal for Research in Mathematics Education (Vol. 41, pp. 169–202). National Council of Teachers of Mathematics. https://doi.org/10.2307/20720130
Kang, R. (2022). Preparing Middle and High School Teachers for Effectively Teaching Mathematical Modeling through Curricular and Professional Noticing [Tesis Doctoral no publicada]. University of Georgia.
Lesh, R., y Kelly, A. (2000). Multitiered Teaching Experiments. En R. Lesh y A. Kelly (Eds.), Handbook of Research Design in Mathematics and Science Education (pp. 197–230). Lawrence Erlbaum Associates Publishers. https://doi.org/https://doi.org/10.4324/9781410602725
Llinares, S. (2013). El desarrollo de la competencia docente “mirar profesionalmente” la enseñanza-aprendizaje de las matemáticas. Educar em Revista, 50, 117–133. https://doi.org/10.1590/s0104-40602013000400009
Llinares, S. (2020). Tools and ways of thinking in mathematics teacher education: An introduction. En International Handbook of Mathematics Teacher Education (Vol. 2, pp. 1-19). Brill. https://doi.org/10.1163/9789004418967_001
Males, L., Earnest, D., Amador, J., y Dietiker, L. (2015). Examining K-12 prospective teachers’ curricular noticing. En T. Bartell, K. Bieda, R. Putnam, K. Bradfield, y H. Dominguez (Eds.), Proceedings of the 37th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 88–95). East Lansing, MI: Michigan State University.
Males, L., y Setniker, A. (2019). An examination of prospective secondary teachers’ curricular noticing when planning. En Paper presentation at the annual meeting of the American Educational Research Association. https://par.nsf.gov/servlets/purl/10134823
Ministerio de Educación Nacional. (2016). La práctica como escenario de aprendizaje. https://www.mineducacion.gov.co/1759/articles-357388_recurso_1.pdf
Olson, T. (2014). Articulated learning trajectories: A framework for mathematical content analyses. En A. Maloney, J. Confrey y K. Nguyen (Eds.), Learning over time: Learning trajectories in mathematics education (pp. 187–226). Information Age Publishing.
Resolución 18583 de 2017 [Ministerio de Educación Nacional]. Por la cual se ajustan las características específicas de calidad de los programas de Licenciatura para la obtención, renovación o modificación del registro calificado, y se deroga la Resolución 2041 de 2016. 15 de septiembre de 2017. https://www.alcaldiabogota.gov.co/sisjur/normas/Norma1.jsp?i=71384&dt=S
Rezat, S. (2024) Research on curriculum resources in mathematics education: a survey of the field. ZDM Mathematics Education, 1–15. https://doi.org/10.1007/s11858-024-01559-x
Ruíz-Higueras, L., y García, F. (2011). Análisis de las praxeologías didácticas: implicaciones en la formación de maestros. En M. Bosch, J. Gascón, A. Ruiz Olarría, M. Artaud, A. Bronner, Y. Chevallard, G. Cirade y C. Ladage (Eds.), Un panorama de la TAD, CRM Documents (pp. 431–464). Centre de Recerca Matemàtica.
Schoen, R., LaVenia, M., y Ozsoy, G. (2019). Teacher beliefs about mathematics teaching and learning: Identifying and clarifying three constructs. Cogent Education, 6(1). https://doi.org/10.1080/2331186X.2019.1599488
Simon, M. (1995). Reconstructing Mathematics Pedagogy from a Constructivist Perspective. Journal for Research in Mathematics Education, 26(2), 114–145. https://doi.org/10.5951/jresematheduc.26.2.0114
Wickstrom, M., y Langrall, C. (2020). The case of Mrs. Purl: Using a learning trajectory as a tool for teaching. Journal of Mathematics Teacher Education, 23(1), 97–125. https://doi.org/10.1007/s10857-018-9412-8
Wilkie, K. J. (2020). Investigating students’ attention to covariation features of their constructed graphs in a figural pattern generalisation context. International Journal of Science and Mathematics Education, 18(2), 315–336. https://doi.org/10.1007/s10763-019-09955-6
Wilson, P., Mojica, G., y Confrey, J. (2013). Learning trajectories in teacher education: Supporting teachers’ understandings of students’ mathematical thinking. The Journal of Mathematical Behavior, 32(2), 103–121. https://doi.org/10.1016/j.jmathb.2012.12.003
Wilson, P., Sztajn, P., Edgington, C., y Myers, M. (2015). Teachers’ uses of a learning trajectory in student-centered instructional practices. Journal of Teacher Education, 66(3), 227–244. https://doi.org/10.1177/002248711557410
Zapatera-Llinares, A. (2015). La competencia “mirar con sentido” de estudiantes para maestro (epm) analizando el proceso de generalización en alumnos de Educación Primaria [Tesis de doctorado no publicada]. Universidad de Alicante.
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