Conocimiento movilizado por estudiantes para maestro, al comparar áreas de figuras 2D

  1. Caviedes, Sofía 1
  2. De Gamboa, Genaro 1
  3. Badillo, Edelmira 1
  1. 1 Universitat Autònoma de Barcelona
    info

    Universitat Autònoma de Barcelona

    Barcelona, España

    ROR https://ror.org/052g8jq94

Revista:
Uniciencia

ISSN: 2215-3470

Año de publicación: 2022

Título del ejemplar: Uniciencia. January-December, 2022

Volumen: 36

Número: 1

Tipo: Artículo

DOI: 10.15359/RU.36-1.41 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

Otras publicaciones en: Uniciencia

Resumen

[Objetivo] Este estudo visa caracterizar o conhecimento matemático especializado mobilizados por professores estagiários na resolução de tarefas que envolvem a comparação de áreas de figuras planas.  [Metodologia] Participaram 70 professores estagiários do terceiro ano do ensino fundamental na Universidade Autônoma de Barcelona, durante o período de 2020-21. Os professores estagiários respondem a um questionário aberto semi-estruturado com um total de oito tarefas. É realizada uma análise de conteúdo qualitativo que considera os procedimentos e justificativas utilizadas pelos professores estagiários na resolução de duas tarefas. O foco está em dois dos subdomínios do modelo de Conhecimento Especializado do Professor de Matemática, Conhecimento dos Temas e da Estrutura da Matemática. [Resultado] O uso de procedimentos relacionados à decomposição e reorganização de superfícies facilita a mobilização de categorias de conhecimento especializado e o estabelecimento de conexões com outros conteúdos matemáticos. A coordenação de vários registros de representação permite estabelecer conexões intraconceituais na resolução das duas tarefas apresentadas. [Conclusões] As representações, em seus registros discursivos e não discursivos, são apresentadas como indicadores-chave, pois explicitam os procedimentos utilizados pelos professores estagiários e, a partir deles, as justificativas, propriedades e princípios geométricos que sustentam o processo de resolução.

Referencias bibliográficas

  • References Aguilar-González, Á., Muñoz-Catalán, M. C. & Carrillo, J. (2018). An example of connections between the mathematics teacher’s conceptions and specialised knowledge. EURASIA Journal of Mathematics, Science and Technology Education, 15(2), 1-15. https://doi.org/10.29333/ejmste/101598
  • Aslan-Tutak, F. & Adams, T. (2017). A study of geometry content knowledge of elementary preservice teachers. International Electronic Journal of Elementary Education, 7(3), 301-318. https://files.eric.ed.gov/fulltext/EJ1068059.pdf
  • Bailey, K. (2007). Methods of Social Research. New York: The free press.
  • Ball, D. L., Thames, M. & Phelps, G. (2008). Content Knowledge for Teaching: What Makes It Special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
  • Baturo, A. & Nason, R. (1996). Student teachers' subject matter knowledge within the domain of area measurement. Educational studies in mathematics, 31(3), 235-268. https://doi.org/10.1007/BF00376322
  • Carpenter, T. P., Fennema, E., Peterson, P. & Carey, D. (1988). Teachers' pedagogical content knowledge of students' problem solving in elementary arithmetic. Journal for research in mathematics education, 19(5), 385-401. https://web.phys.ksu.edu/current/seminar/f10/pckcarpenter.pdf
  • Carrillo, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Ávila, D., ... & Ribeiro, M. (2018). The mathematics teacher’s specialised knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236-253. https://doi.org/10.1080/14794802.2018.1479981
  • Caviedes, S., De Gamboa, G. & Badillo, E. (2019). Conexiones matemáticas que establecen maestros en formación al resolver tareas de medida y comparación de áreas. Praxis, 15(1), 69-87. https://doi.org/10.21676/23897856.2984
  • Caviedes, S., De Gamboa, G. & Badillo, E. (2020). Procedimientos utilizados por estudiantes de 13-14 años en la resolución de tareas que involucran el área de figuras planas. Bolema, 34(68). https://doi.org/10.1590/1980-4415v34n68a09
  • Caviedes, S., De Gamboa, G. & Badillo, E. (2021). Mathematical objects that configure the partial area meanings mobilized in task-solving. International Journal of Mathematical Education in Science and Technology, 1-20. https://doi.org/10.1080/0020739X.2021.1991019
  • Chamberlin, M. & Candelaria, M. (2018). Learning from Teaching Teachers: A Lesson Experiment in Area and Volume with Prospective Teachers. Mathematics Teacher Education and Development, 20(1), 86-111. https://eric.ed.gov/?id=EJ1173370
  • Cohen, L., Manion, L. & Morrison, K. (2000). Research methods in education, 5th ed, Routledge falmer, London.
  • D'Amore, B. & Fandiño, M. (2007). Relaciones entre área y perímetro: convicciones de maestros y de estudiantes. Revista Latinoamericana de Investigación en Matemática Educativa, 10(1), 39-68.
  • Duval, R. (1995). Geometrical pictures: Kinds of representation and specific processings. In Exploiting mental imagery with computers in mathematics education (pp. 142-157). Berlin: Springer. https://doi.org/10.1007/978-3-642-57771-0_10
  • Duval, R. (1999). Semiosis y pensamiento humano: registros semióticos y aprendizajes intelectuales (M. Vega, Trad.). Cali, Colombia: Universidad del Valle.
  • Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational studies in mathematics, 61(1-2), 103-131. https://doi.org/10.1007/s10649-006-0400-z
  • Duval, R. (2017). Understanding the mathematical way of thinking – The registers of semiotic representations. Cham: Springer. https://doi.org/10.1007/978-3-319-56910-9
  • Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: Reidel.
  • Godino, J. D., Batanero, C. & Font, V. (2019). The Onto-Semiotic Approach: Implications for the Prescriptive Character of Didactics. For the Learning of Mathematics, 39(1), 38-43. https://eric.ed.gov/?id=EJ1211459
  • Godino, J. D., Giacomone, B., Font, V. & Pino-Fan (2018). Conocimientos profesionales en el diseño y gestión de una clase sobre semejanza de triángulos: análisis con herramientas del modelo CCDM. Avances de investigación en Educación Matemática. (13), 63-83. https://doi.org/10.35763/aiem.v0i13.224
  • Hill, H. C., Schilling, S. & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. The elementary school journal, 105(1), 11-30. https://doi.org/10.1086/428763
  • Hong, D. & Runnalls, C. (2020). Examining preservice teachers' responses to area conservation tasks. School Science and Mathematics, 120(5), 262-272. https://doi.org/10.1111/ssm.12409
  • Kospentaris, G., Spyrou, P. & Lappas, D. (2011). Exploring students’ strategies in area conservation geometrical tasks. Educational Studies in Mathematics, 77(1), 105-127. https://doi.org/10.1007/s10649-011-9303-8
  • Krauss, S., y Blum, W. (2012). The conceptualisation and measurement of pedagogical content knowledge and content knowledge in the COACTIV study and their impact on student learning. Journal of Education, (56), 45-66. http://doi.org/10.5283/epub.34256
  • Krippendorff, K. (2004) Content Analysis: An Introduction to its Methodology. California: Sage.
  • Liñan, M., Barrera, V. & Infante, J. (2014). Conocimiento especializado de los estudiantes para maestro: la resolución de un problema con división de fracciones. Escuela Abierta, 17(1), 41-63. https://doi.org/10.29257/EA17.2014.04
  • Livy, S., Muir, T. & Maher, N. (2012). How do they measure up? Primary pre-service teachers' mathematical knowledge of area and perimeter. Mathematics Teacher Education and Development, 14(2), 91-112. https://files.eric.ed.gov/fulltext/EJ1018652.pdf
  • Llinares, S. (2012). Formación de profesores de matemáticas. Caracterización y desarrollo de competencias docentes. Cuadernos, 10, 53-62. http://funes.uniandes.edu.co/21400/1/Llinares2012Formacion.pdf
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates. https://doi.org/10.4324/9780203856345
  • Montes, M., Aguilar, A., Carrillo, J. & Muñoz-Catalán, M. (2015, febrero). MTSK: From Common and Horizon Knowledge to Knowledge of Topics and Structures. En B. Ubuz, C. Haser, y M. Mariotti (Eds.), Proceedings of the 8th Congress of the European Society for Research in Mathematics Education (pp. 3185-3194). Antalya: ERME. http://www.mathematik.tu-dortmund.de/~erme/doc/CERME8/CERME8_2013_Proceedings.pdf
  • Piaget, J., Inhelder, B. & Szeminska, A. (1981). The Child’s Conception of Geometry. New York: Norton and Company.
  • Policastro, M., Mellone, M., Ribeiro, M. & Fiorentini, D. (2019, febrero). Conceptualising tasks for teacher education: from a research methodology to teachers’ knowledge development. En Eleventh Congress of the European Society for Research in Mathematics Education. Utrecht: ERME. https://hal.archives-ouvertes.fr/hal-02430487
  • Puig, L. & Guillén, G. (1983). Necesidad y experimentación de un nuevo modelo para el estudio de la geometría en la EGB y Escuelas de Magisterio. Memoria de Investigación. https://redined.educacion.gob.es/xmlui/handle/11162/83753
  • Rowland, T., Huckstep, P. & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of mathematics teacher education, 8(3), 255-281. https://doi.org/10.1007/s10857-005-0853-5
  • Runnalls, C. & Hong, D. (2020). “Well, they understand the concept of area”: Pre-service teachers’ responses to student area misconceptions. Mathematics Education Research Journal, 32(4), 629-651. https://doi.org/10.1007/s13394-019-00274-1
  • Sarama, J. & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York: Routledge. https://doi.org/10.4324/9780203883785
  • Scheiner, T., Montes, M., Godino, J. D., Carrillo, J. & ino-Fan, L. R. (2019). What makes mathematics teacher knowledge specialized? Offering alternative views. International Journal of Science and Mathematics Education, 17(1), 153-172. https://doi.org/10.1007/s10763-017-9859-6
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
  • Simon, M. & Blume, G. (1994). Building and understanding multiplicative relationships: A study of prospective elementary teachers. Journal for Research in Mathematics Education, 25(5), 472-494. https://doi.org/10.5951/jresematheduc.25.5.0472
  • Sisman, G. T. & Aksu, M. (2009). Seventh grade student’s success on the topics of area and perimeter. Elementary Education Online, 8(1), 243-253. https://doi.org/10.16986/huje.2018045388
  • Tierney, C., Boyd, C. & Davis, G. (1990). Prospective primary teachers’ conceptions of area. In Proceedings of the 14th Conference of the International Group for the Psychology of Mathematics Education, 2, 307-314. https://files.eric.ed.gov/fulltext/ED411138.pdf
  • Zacharos, K. (2006). Prevailing educational practices for area measurement and students’ failure in measuring areas. The Journal of Mathematical Behavior, 25(3), 224-239. https://doi.org/10.1016/j.jmathb.2006.09.003
Fuente de los datos: Dialnet