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

• Caviedes, Sofía ^[1] ; De Gamboa, Genaro ^[1] ; Badillo, Edelmira ^[1]
  1. [1] Universitat Autònoma de Barcelona

     Universitat Autònoma de Barcelona

     Barcelona, España

     
• Localización: Uniciencia, ISSN-e 2215-3470, Vol. 36, Nº. 1, 2022 (Ejemplar dedicado a: Uniciencia. January-December, 2022), 20 págs.
• Idioma: español
• DOI: 10.15359/ru.36-1.41
• Títulos paralelos:
  • Conhecimento mobilizado por professores estagiários, comparando áreas de figuras 2D
  • Knowledge used by preservice teaching students when comparing areas of 2D figures
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    [Objetivo] Este estudio busca caracterizar el conocimiento matemático especializado que movilizan estudiantes para maestro, al resolver tareas que involucran la comparación de áreas de figuras planas. [Metodología] Participan 70 estudiantes para maestro que cursan el tercer año del grado de Educación Primaria, en la Universidad Autónoma de Barcelona, durante el periodo 2020-21. Los estudiantes para maestro responden un cuestionario semiestructurado de respuesta abierta que contemplaba un total de ocho tareas. Se realiza un análisis de contenido cualitativo que considera los procedimientos y las justificaciones utilizadas por los estudiantes para maestro en la resolución de dos tareas. El foco está en dos de los subdominios del modelo de Conocimiento Especializado del Profesor de Matemáticas, el Conocimiento de los Temas y de la Estructura de las Matemáticas. [Resultados] El uso de procedimientos relacionados con la descomposición, y reorganización de superficies, facilita la movilización de categorías de conocimiento especializado y el establecimiento de conexiones con otros contenidos matemáticos. La coordinación de diversos registros de representación posibilita el establecimiento de conexiones intraconceptuales en la resolución de las dos tareas presentadas. [Conclusiones] Las representaciones, en sus registros discursivo y no discursivo, se presentan como indicadores claves, pues permiten hacer explícitos los procedimientos que son utilizados por los estudiantes para maestro y, a partir de estos, las justificaciones, propiedades y principios geométricos que sustentan el proceso de resolución.

  • English

    [Objective] This study seeks to characterize the specialized mathematical knowledge that preservice teachers make use of when solving tasks that involve comparison of areas of flat figures. [Methodology] Seventy (70) preservice teachers, in the third year of the Primary Education degree at the Universidad Autónoma de Barcelona during the period 2020-21, participated in the study. Preservice teachers answered a semi-structured open-ended questionnaire, which included eight tasks. A qualitative content analysis was carried out to analyze the procedures and justifications used by preservice teachers when solving two tasks. The analysis focuses on two of the subdomains of the Mathematics Teacher’s Specialized Knowledge model, Knowledge of Topics and of the Structure of Mathematics. [Results] The use of procedures related to the decomposition and reorganization of surfaces facilitates making use of categories of specialized knowledge, and establishing connections with other types of mathematical content. Furthermore, coordination of different registers of representation makes it possible to establish intra conceptual connections in the solution of the two tasks presented. [Conclusions] Representations, in their discursive and non-discursive registers, are presented as key indicators which assist in making explicit the procedures used by preservice teachers, and based on them, the justifications, properties and geometric principles that support the resolution process.

  • português

    [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...
  • Aslan-Tutak, F. & Adams, T. (2017). A study of geometry content knowledge of elementary preservice teachers. International Electronic...
  • 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),...
  • Baturo, A. & Nason, R. (1996). Student teachers' subject matter knowledge within the domain of area measurement. Educational studies...
  • Carpenter, T. P., Fennema, E., Peterson, P. & Carey, D. (1988). Teachers' pedagogical content knowledge of students' problem solving...
  • Carrillo, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Ávila, D., ... & Ribeiro, M. (2018). The mathematics...
  • Caviedes, S., De Gamboa, G. & Badillo, E. (2019). Conexiones matemáticas que establecen maestros en formación al resolver tareas de medida...
  • Caviedes, S., De Gamboa, G. & Badillo, E. (2020). Procedimientos utilizados por estudiantes de 13-14 años en la resolución de tareas que...
  • Caviedes, S., De Gamboa, G. & Badillo, E. (2021). Mathematical objects that configure the partial area meanings mobilized in task-solving....
  • Chamberlin, M. & Candelaria, M. (2018). Learning from Teaching Teachers: A Lesson Experiment in Area and Volume with Prospective Teachers....
  • 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...
  • Duval, R. (1995). Geometrical pictures: Kinds of representation and specific processings. In Exploiting mental imagery with computers in mathematics...
  • Duval, R. (1999). Semiosis y pensamiento humano: registros semióticos y aprendizajes intelectuales (M. Vega, Trad.). Cali, Colombia: Universidad...
  • Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational studies in mathematics, 61(1-2),...
  • 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...
  • Godino, J. D., Giacomone, B., Font, V. & Pino-Fan (2018). Conocimientos profesionales en el diseño y gestión de una clase sobre semejanza...
  • Hill, H. C., Schilling, S. & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. The elementary school...
  • Hong, D. & Runnalls, C. (2020). Examining preservice teachers' responses to area conservation tasks. School Science and Mathematics,...
  • Kospentaris, G., Spyrou, P. & Lappas, D. (2011). Exploring students’ strategies in area conservation geometrical tasks. Educational Studies...
  • Krauss, S., y Blum, W. (2012). The conceptualisation and measurement of pedagogical content knowledge and content knowledge in the COACTIV...
  • 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...
  • Livy, S., Muir, T. & Maher, N. (2012). How do they measure up? Primary pre-service teachers' mathematical knowledge of area and perimeter....
  • Llinares, S. (2012). Formación de profesores de matemáticas. Caracterización y desarrollo de competencias docentes. Cuadernos, 10, 53-62....
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States....
  • Montes, M., Aguilar, A., Carrillo, J. & Muñoz-Catalán, M. (2015, febrero). MTSK: From Common and Horizon Knowledge to Knowledge of Topics...
  • 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...
  • Puig, L. & Guillén, G. (1983). Necesidad y experimentación de un nuevo modelo para el estudio de la geometría en la EGB y Escuelas de...
  • Rowland, T., Huckstep, P. & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case...
  • Runnalls, C. & Hong, D. (2020). “Well, they understand the concept of area”: Pre-service teachers’ responses to student area misconceptions....
  • Sarama, J. & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York:...
  • Scheiner, T., Montes, M., Godino, J. D., Carrillo, J. & ino-Fan, L. R. (2019). What makes mathematics teacher knowledge specialized? Offering...
  • 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...
  • Sisman, G. T. & Aksu, M. (2009). Seventh grade student’s success on the topics of area and perimeter. Elementary Education Online, 8(1),...
  • Tierney, C., Boyd, C. & Davis, G. (1990). Prospective primary teachers’ conceptions of area. In Proceedings of the 14th Conference of...
  • Zacharos, K. (2006). Prevailing educational practices for area measurement and students’ failure in measuring areas. The Journal of Mathematical...