Construyendo conocimiento especializado en geometríaun experimento de enseñanza en formación inicial de maestros

  1. Miguel Ángel Montes Navarro 1
  2. Nuria Climent 1
  3. Luis Carlos Contreras 1
  1. 1 Universidad de Huelva
    info

    Universidad de Huelva

    Huelva, España

    ROR https://ror.org/03a1kt624

Journal:
Aula abierta

ISSN: 0210-2773

Year of publication: 2022

Issue Title: Miscelánea

Volume: 51

Issue: 1

Pages: 27-36

Type: Article

More publications in: Aula abierta

Abstract

This work aims to characterize the specialized knowledge built in a primary teachers initial training class by means of a task based on video analysis. We designed a first phase consisting in a small scale teaching experiment with three students, used to define the referents that would allow to redesign the task in the second phase. This second phase scaled up the experiment to group of students in a teacher training program. The task was based on the visualization and discussion of a video about building a definition of ‘polygon’. After the analysis, conducted using the Mathematics Teacher’s Specialized Knowledge model, we identified the knowledge mobilized by prospective teachers about the definition of ‘polygon’ and its elements, about the mathematical practice of defining, about resources and examples to define ‘polygon’, about learning difficulties related to that content, and about its presence in primary school syllabi, consistent with research literature. This work ends with reflections about how the task allows to build elements of specialized knowledge

Bibliographic References

  • Alsawaie, O. N., y Alghazo, I. M. (2010). The effect of video-based approach on prospective teachers’ ability to analyze mathematics teaching. Journal of Mathematics Teacher Education, 13(3), 223-241. DOI: 10.1007/s10857-009-9138-8
  • Ball, D. L., Thames, M. H., y Phelps, G. (2008). Content knowledge for teaching: What makes its special? Journal of Teacher Education, 59(5), 389-407. DOI: 10.1177/0022487108324554
  • Barrantes, M., López, M. y Fernández, M. A. (2015). Análisis de las representaciones geométricas en los libros de texto. PNA, 9(2), 107-127. DOI: 10.30827/pna.v9i2.6105
  • Carrillo, J., y Climent, N. (2008). From professional tasks in collaborative environments to educational tasks in mathematics teacher education. En B. Clarke, B. Grevholm y R. Millman (eds.), Tasks in Primary Mathematics Teacher Education: Purpose, Use and Exemplars (Vol. 4, pp. 215-234). Springer. DOI: 10.1007/978-0-387-09669-8_15
  • Carrillo, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Ávila, D., Vasco, D., Rojas, N., Flores, P., Aguilar-González, A., Ribeiro, M., y Muñoz-Catalán, M. C. (2018). The Mathematics Teacher’s Specialised Knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236-253. DOI: 10.1080/14794802.2018.1479981
  • Climent, N., Montes, M., Contreras, L. C., Carrillo, J., Liñán, M., Muñoz-Catalán, M. C, Barrera, V., y León, F. (2016). Construcción de conocimiento sobre características de aprendizaje de las Matemáticas a través del análisis de vídeos. Avances de Investigación En Educación Matemática, 9, 85-103. DOI: 10.35763/aiem.v0i9.108
  • Cobb, P., y Gravemeijer, K. (2008). Experimenting to support and understand learning processes. En A.E. Kelly, R. A. Lesh y J. Baek (eds.), Handbook of design research Methods in Education. Innovation in Science, technology, Engineering and Mathematics Learning and Teaching (pp. 68-95). Lawrence Erlbaum Associates. DOI:10.4324/9781315759593.
  • Codes, M., Climent, N., Oliveros, I. (2019). Prospective primary teachers’ knowledge about the mathematical practice of defining. En U. T. Jankvist, M. Van den Heuvel-Panhuizen y M. Veldhuis (eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME 11) (pp. 3871-3878). Freudenthal Group & Freudenthal Institute, Utrecht University y ERME.
  • De Villiers, M. (1998). To teach definitions in geometry or teach to define? En A. Oliver, y K. Newstead (ed.), Proceedings of the 22th Conference of the International Group for the Psychology of Mathematics Education. 2 (pp. 248-255). University of Stellenbosch.
  • De Villiers, M., Govender, R., y Patterson, N. (2009). Defining in Geometry. En T. Craine, y R. Rubinstein (eds.), Understanding Geometry for a Changing World (pp. 189-203). NCTM.
  • Escudero-Ávila, D., Gomes, J., Muñoz-Catalán, M.C., Flores-Medrano, E., Flores, P., Rojas, N., Aguilar, A. (2015). Aportaciones metodológicas de investigaciones con MTSK. En J. Carrillo, L.C. Contreras y M. Montes (Eds.), Reflexionando sobre el conocimiento del profesor. Actas de las II Jornadas del Seminario de Investigación de Didáctica de la Matemática de la Universidad de Huelva (pp. 60-68). SGSE.
  • Fernández, C., Sánchez-Matamoros, G., Valls, J., y Callejo, M. L. (2018). Noticing students’ mathematical thinking: characterization, development and contexts. Avances de Investigación en Educación Matemática, 13, 39-61.
  • Fortuny, J. M., y Rodríguez, R. (2012). Aprender a mirar con sentido: facilitar la interpretación de las interacciones en el aula. Avances de Investigación en Educación Matemática, 1, 23-37.
  • García, F. J., Maas, K., y Wake, G. (2010). Theory meets practice: Working pragmatically within diferent cultures and traditions. En R. Lesh, P. Galbraith, C. Haines y A. Hurford (eds.), Modeling Students’ Mathematical Modeling Competencies (pp. 445-457). Springer. https://doi.org/10.1007/978-1-4419-0561-1
  • Grevholm, B., Millman, R., y Clarke, B. (2009). Function, Form, and Focus: The role of Tasks in Elementary Mathematics Teacher Education. En B. Clarke, B. Grevholm y R. Millman (eds.), Tasks in Primary Mathematics Education: Purpose, Use and Exemplars (pp. 1-5). New York. DOI: 10.1007/978-0-387-09669-8_1
  • Lampert, M., y Ball, D.L. (1998). Teaching, Multimedia and Mathematics: Investigations of Real Practice. Teachers College Press, Columbia University.
  • Lin, F.L., y Rowland, T. (2016). Pre-Service and In-Service Mathematics Teachers’ Knowledge and Professional Development. En Á. Gutiérrez, G.C. Leder y P. Boero (eds.), The Second Handbook of Research on the Psychology of Mathematics Education (pp. 483-519). Sense Publishers. DOI:10.1007/978-94-6300-561-6_14
  • Mason, J. (2021). Learning about noticing, by, and through, noticing. ZDM Mathematics Education, 53, 231–243. DOI: 10.1007/s11858-020-01192-4
  • Millman, R., Svec, K., y Williams, D. (2009). Tasks using video clips of children in a content Mathematics course for future elementary school teachers. En B. Clarke, B. Grevholm y R. Millman (eds.), Tasks in Primary Mathematics Teacher Education: Purpose, Use, and Exemplars (pp. 105-112). Springer. DOI: 10.1007/978-0-387-09669-8_8
  • Molina, M., Castro, E., Molina, J.L., y Castro, E. (2011). Un acercamiento a la investigación de diseño a través de los experimentos de enseñanza. Enseñanza de las Ciencias, 29(1), 75-88. https://doi.org/10.5565/rev/ec/v29n1.435
  • Montes, M., Carrillo, J., Contreras, L. C., Liñán-García, M. M., y Barrera-Castarnado, V. J. (2019). Estructurando la formación inicial de Profesores de Matemáticas: una propuesta desde el modelo MTSK. En E. Badillo, N. Climent, C. Fernández y M. T. González (eds.), Investigación sobre el profesor de matemáticas: formación, práctica de aula, conocimiento y competencia profesional (pp. 157-176). Ediciones Universidad de Salamanca.
  • Rowland, T., Turner, F., Thwaites, A., y Huckstep, P. (2009). Developing primary mathematics teaching. Reflecting on practice with the Knowledge Quartet. SAGE. DOI: 10.4135/9781446279571
  • Shulman, L.S. (1986). Those who understand. Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. DOI: 10.3102/0013189X015002004
  • Star, J. R., y Strickland, S. K. (2008). Learning to observe: Using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education, 11(2), 107-125. DOI: 10.1007/s10857-007-9063-7
  • Ulusoy, F. (2020). Prospective Early Childhood and Elementary School Mathematics Teachers’ Concept Images and Concept Definitions of Triangles. International Journal of Science and Mathematics Education, 1-22. https://doi.org/10.1007/s10763-020-10105-6
  • van Es, E. A., y Sherin, M. G. (2010). The influence of video clubs on teachers’ thinking and practice. Journal of Mathematics Teacher Education, 13(2), 155–176. DOI: 10.1007/s10857-009-9130-3
  • Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. En D. Tall (ed.), Advanced Mathematical Thinking (pp. 65-81). Kluwer Academic Publishers. DOI:10.1007/0-306-47203-1_5
  • Vinner, S., y Hershkowitz, R. (1983). On concept formation in geometry. ZDM, 83, 20-25. DOI: 10.1007/BF00452223
  • Ward, R. A. (2004). An Investigation of K-8 Preservice Teachers' Concept Images and Mathematical Definitions of Polygons. Issues in Teacher Education, 13(2), 39-56.
  • Watson, A., y Mason, J. (2005). Mathematics as a constructive activity: Learners generating examples. Erlbaum. DOI: 10.4324/9781410613714
  • Zakaryan, D., y Ribeiro, M. (2019). Mathematics teachers’ specialized knowledge: a secondary teacher's knowledge of rational numbers. Research in Mathematics Education, 21(1), 25-42. DOI:10.1080/14794802.2018.1525422
  • Zaslavsky, O., Harel, G., y Manaster, A. (2006). A teacher’s treatment of examples as reflection of her knowledge-base. En J. Novotná, H. Moraová, M. Krátká y N. Stehliková (Eds.), Proceedings of the 30th conference of the international group for the psychology of mathematics education (Vol. 5, pp. 457-464).
  • Zaslavsky, O., y Shir, K. (2005). Students’ Conception of a Mathematical Definition. Journal for Research in Mathematics Education, 36(4), 317-346. DOI:10.2307/30035043