Desarrollo de la competencia de análisis ontosemiótico de futuros profesores de matemáticas

  1. Giacomone, Belén 1
  2. Godino, Juan D. 1
  3. Wilhelmi, Miguel R. 2
  4. Blanco, Teresa F. 3
  1. 1 Universidad de Granada
    info

    Universidad de Granada

    Granada, España

    ROR https://ror.org/04njjy449

  2. 2 Universidad Pública de Navarra
    info

    Universidad Pública de Navarra

    Pamplona, España

    ROR https://ror.org/02z0cah89

  3. 3 Universidade de Santiago de Compostela
    info

    Universidade de Santiago de Compostela

    Santiago de Compostela, España

    ROR https://ror.org/030eybx10

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Journal:
Revista complutense de educación

ISSN: 1130-2496,  1988-2793

Year of publication: 2018

Volume: 29

Issue: 4

Pages: 1109-1131

Type: Article

DOI: 10.5209/RCED.54880 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Revista complutense de educación

Abstract

A suitable mathematics teaching requires the teachers’ knowledge and competence for identifying the variety of objects and meanings involved in solving school tasks. This article describes the design, implementation and retrospective analysis of a formative cycle directed to prospective mathematics teachers, which is focused on developing this onto-semiotic analysis competence. For this, some theoretical and methodological tools of the Onto-Semiotic Approach to mathematical knowledge and instruction are used. In this experience, the prospective teachers first solve some visualisation and diagrammatic reasoning mathematical tasks, and then analyse the objects and meanings put at stake in the resolution of each implemented task. In addition, the strategies that students produce in their solutions are discussed and shared in whole-class setting. The data analysis is qualitative oriented to identify significant didactical practices about the initial state of students’ personal meaning, recognition of conflicts, and progress in developing the intended onto-semiotic analysis competence. For this purpose, the students’ written responses, observer researcher’s notes, and audio recordings on the class are used as a data collection instrument. The results reveal the complexity involved in developing this onto-semiotic analysis competence, as well as its relevance to achieve high quality mathematics teaching. Finally, the retrospective analysis of the formative design carried out allows the teacher, and researcher reflecting on each of factors that condition the teaching processes, and thus determining potential improvements for future implementations.

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Funding information

La investigación presentada en este artículo fue llevada a cabo como parte de los siguientes proyectos: EDU2012-31869 y EDU2013-41141-P, Ministerios de Economía y competitividad (MINECO, España).

Funders

  • MINECO Spain
    • EDU2012-31869
    • EDU2013-41141-P

Bibliographic References

  • Batanero, C., Contreras, J. M., Díaz, C., & Sánchez, E. (2015). Prospective teachers’ semiotic conflicts in computing probabilities from a two-way table. Mathematics Education, 10(1), 3-16.
  • Batanero, C., Contreras, J. M., Díaz, C., & Sánchez, E. (2015). Prospective teachers’ semiotic conflicts in computing probabilities from a two-way table. Mathematics Education, 10(1), 3-16.
  • Chapman. O. (2014). Overall commentary: understanding and changing mathematics teachers. In J.–J. Lo, K. R. Leatham, & L. R. Van Zoest (Eds.), Research Trends in Mathematics Teacher Education (pp. 295-309). Dordrecht: Springer International Publishing.
  • Cohen, S. (2004). Teachers’ professional development and the elementary mathematics classroom: Bringing understandings to light. Mahwah, NJ: Erlbaum.
  • D'Amore, B., Font, V., & Godino, J. D. (2007). La dimensión metadidáctica en los procesos de enseñanza y aprendizaje de las matemáticas. Paradigma, 28(2), 49-77.
  • English, L. (2008). Setting an agenda for international research in mathematics education. In L. English (Ed.), Handbook of international research in mathematics education (pp. 3-19). New York, NY: Routledge.
  • Fahlgren, M., & Brunström, M. (2014). A model for task design with focus on exploration, explanation, and generalization in a dynamic geometry. Technology, knowledge and learning, 19, 287-315.
  • Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24(2), 139-162.
  • Font, V. (2011). Competencias profesionales en la formación inicial de profesores de matemáticas de secundaria. Unión, 26, 9-25.
  • Font, V., Godino, J. D., & Gallardo, J. (2013). The emergence of objects from mathematical practices. Educational Studies in Mathematics, 82, 97-124.
  • Font, V., & Ramos, A. B. (2005). Objetos personales matemáticos y didácticos del profesorado y cambio institucional: El caso de la contextualización de funciones en una Facultad de Ciencias Económicas y Sociales. Revista de Educación, 338, 309-346.
  • Godino, J. D. (2013). Indicadores de idoneidad didáctica de procesos de enseñanza y aprendizaje de las matemáticas. Cuadernos de Investigación y Formación en Educación Matemática, 11, 111-132.
  • 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.
  • 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 from different theoretical perspectives. Proceedings of the, 13th International Congress on Mathematical Education, (24-31 July 2016). Hamburg, Germany: ICME.
  • Godino, J. D., Batanero, C., Font, V., & Giacomone, B. (2016). Articulando conocimientos y competencias del profesor de matemáticas: el modelo CCDM. In C. Fernández, J. L. González, F. J. Ruiz, J. A. Macías, A. Jiménez, M. T. Sánchez, P. Hernández, T. Fernández, & A. Berciano (Eds.), Investigación en Educación Matemática XIX (pp. 272-285). Málaga, España: SEIEM.
  • Godino, J. D., Giacomone, B., Wilhelmi, M. R., Blanco, T., & Contreras, A. (2015). Configuraciones de prácticas, objetos y procesos imbricados en la visualización espacial y el razonamiento diagramático. Departamento de Didáctica de la Matemática, Universidad de Granada. Retrieved from http://www.ugr.es/~jgodino/eos/JDGodino_DiagramasEOS.pdf
  • Husu, J., Toom, A., & Patrikainen, S. (2008). Guided reflection as a means to demonstrate and develop student teachers' reflective competencies. Reflective Practice, 9(1), 37-51.
  • Kelly, A. E., Lesh, R. A., & Baek, J. Y. (Eds.). (2008). Handbook of design research in methods in education. Innovations in science, technology, engineering, and mathematics learning and teaching. New York, NY: Routledge.
  • Leung, A., & Bolite-Frant, J. (2015). Designing mathematics tasks: the role of tools. In A. Watson, & M. Ohtani (Eds.), Task design in mathematics education (pp. 191-225). New ICMI Study Series. New York: Springer.
  • Llinares, S., & Krainer, K. (2006). Mathematics (students) teachers and teacher educators as learners. In A. Gutiérrez, & P. Boero (Eds.), Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future (pp. 429-459). Rotterdam: Sense Publishers.
  • Nitsch, R., Fredebohm, A., Bruder, R., Kelava, A., Naccarella, D., Leuders, T., & Wirtz, M. (2015). Students’ competencies in working with functions in secondary mathematics education—empirical examination of a competence structure model. International Journal of Science and Mathematics Education, 13, 657-682.
  • Nolan, A. (2008). Encouraging the reflection process in undergraduate teachers using guided reflection. Australian Journal of Early Childhood, 33(1), 31-36.
  • Peirce, Ch. S. (1958). Collected papers of Charles Sanders Peirce. C. Hartshorne, & P. Weiss (Eds.). Cambridge, MA: Harvard UP.
  • Pierce, R., & Stacey, K. (2013). Teaching with new technology: Four 'early majority' teachers. Journal of Mathematics Teacher Education, 16(5), 323-347.
  • Pino-Fan, L., Godino, J. D., & Font, V. (2016). Assessing key epistemic features of didactic-mathematical knowledge of prospective teachers. The case of derivative. Journal of Mathematics Teacher Education (accepted).
  • 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 & Technology Education, 11(6), 1429-1456.
  • Radford, L. (2003). Gestures, speech, and the sprouting of signs: A semiotic-cultural approach to students' types of generalization. Mathematical Thinking and Learning, 5(1), 37-70.
  • Schoenfeld, A. H. (2010). How we think: A theory of goal-oriented decision making and its educational applications. New York, NY: Routledge.
  • Schoenfeld, A., & Kilpatrick, J. (2008). Towards a theory of proficiency in teaching mathematics. In D. Tirosh & T. L. Wood (Eds.), Tools and processes in mathematics teacher education (pp. 321-354). Rotterdam: Sense Publishers.
  • Sherry, D. (2009). The Role of Diagrams in Mathematical Arguments. Foundations of Science, 14, 59-74.
  • Shin, S-J., & Lemon, O. (2008). Diagrams. Stanford Encyclopedia of Philosophy. Retrieved from http://plato.stanford.edu/entries/diagrams/
  • Silverman, J., & Thompson, P. (2008). Toward a framework for the development of mathematical knowledge for teaching. Journal of Mathematics Teacher Education, 11(6), 499-511.
  • Sowder, J. T. (2007). The mathematical education and development of teachers. In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 157-224). Charlotte, N.C: NCTM and IAP.
  • Wittgenstein, L. (1953). Investigaciones filosóficas. Barcelona: Crítica.
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