Extra-mathematical Connections Made by Prospective Elementary School Teachers when Designing Geometric Homework Assignments
DOI:
https://doi.org/10.35763/aiem25.6441Keywords:
Extra-mathematical connections, Teacher training, Geometry, Primary school, Ontosemiotic approachAbstract
We describe the extra-mathematical connections that emerge when a group of 250 prospective elementary school teachers are confronted with two professional tasks that deal with different geometric notions. The analysis considers the theory of extra-mathematical connections and the tool of the Ontosemiotic Approach (epistemic configurations) to evidence the emergence of generic metaphorical and interdisciplinary connections; the former referred to the constitution of a metaphor as a tool to access from an extra-mathematical idea to an intra-mathematical object; while the latter refers to the use of elements belonging to a particular discipline and therefore extra-mathematical, to understand an intra-mathematical object. The results and conclusions revolve around the evidence presented on the emergence of such connections. It contributes to the reflection on the theory of extra-mathematical connections, and it shows the potential of the design of school tasks in the training processes of Primary Education teachers.
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Alsina, Á. (2014). Procesos matemáticos en Educación Infantil: 50 ideas clave. Números, 86, 5-28.
Businskas, A. M. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections. [Tesis doctoral no publicada]. Simon Fraser University, Canadá.
Chamoso, J., & Cáceres, M. (2019). Creación de tareas por futuros docentes de matemáticas a partir de contextos reales. Cuadernos de Investigación y Formación en Educación Matemática, 18, 59-69.
Coxford, A. F. (1995). The case for connections. En P. A. House & A. F. Coxford (Eds.), Connecting mathematics across the curriculum (pp. 3-12). National Council of Teachers of Mathematics.
da Ponte, J. P. (2004). Problemas e investigaciones en la actividad matemática de los alumnos. En J. Giménez, L. Santos, & J. P. Ponte (Eds.), La actividad matemática en el aula (pp. 25-34). Graó.
de Gamboa, G., & Figueiras, L. (2014). Conexiones en el conocimiento matemático del profesor: propuesta de un modelo de análisis. En M. T. González, M. Codes, D. Arnau & T. Ortega (Eds.), Investigación en Educación Matemática XVIII (pp. 337-344). SEIEM.
Eli, J., Mohr-Schroeder, M., & Lee, C. (2011). Exploring mathematical connections of prospective Middle-grades teachers through card-sorting tasks. Mathematical Education Research Journal, 23(3), 297-319. https://doi.org/10.1007/s13394-011-0017-0
Evitts, T. (2004). Investigating the mathematical connections that preservice teachers use and develop while solving problems from reform curricula. [Unpublished doctoral dissertation]. Pennsylvania State University College of Education. EE.UU.
Font, V., Godino, J. D., & Gallardo, J. (2013). The emergence of objects from mathematical practices. Educational Studies in Mathematics, 82, 97-124. https://doi.org/10.1007/s10649-012-9411-0
García-García, J. G. (2019). Escenarios de exploración de conexiones matemáticas. Números: Revista de didáctica de las matemáticas, 100, 129-133.
García-García, J., & Dolores-Flores, C. (2018). Intra-mathematical connections made by high school students in performing Calculus tasks. International Journal of Mathematical Education in Science and Technology, 49(2), 227-252. https://doi.org/10.1080/0020739X.2017.1355994
García-García, J., & Dolores-Flores, C. (2020). Exploring pre-university students’ mathematical connections when solving Calculus application problems. International Journal of Mathematical Education in Science and Technology, 52(6), 912-936. https://doi.org/10.1080/0020739X.2020.1729429
Godino, J., & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos. Recherches en didactique des Mathématiques, 14(3), 325-355.
Godino, J., Batanero, C., & Font, V. (2007). The Ontosemiotic approach to research in mathematics education. ZDM–The International Journal on Mathematics Education, 39(1-2), 127-135. https://doi.org/10.1007/s11858-006-0004-1
Godino, J., Giacomone, B., Font, V., & Pino-Fan, L. (2018). Conocimientos profesionales en el diseño y gestión de una clase sobre semejanza de triángulos. Análisis con herramientas del modelo CCDM. AIEM- Avances de Investigación En Educación Matemática, 13, 63-83. https://doi.org/10.35763/aiem.v0i13.224
Hernández, R., Fernández, C., & Baptista, P. (2010) Metodología de la Investigación (5ª ed.). McGraw-Hill.
Kenedi, A. K., Helsa, Y., Ariani, Y., Zainil, M., & Hendri, S. (2019). Mathematical connection of elementary school students to solve mathematical problems. Journal on Mathematics Education, 10(1), 69-80. https://doi.org/10.22342/jme.10.1.5416.69-80
Lakoff, G., & Núñez, R. (2000) Where Mathematics comes from. How the embodied mind brings Mathematics into being. Basic Books.
National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. Autor.
Rebello, N., Cui, L., Bennett, A., Zollman, D., & Ozimek, D. (2017). Transfer of learning in problem solving in the context of mathematics and physics. In D. Jonassen (Ed.), Learning to Solve Complex Scientific Problems (1st edition, pp. 223-246). Routledge. https://doi.org/10.4324/9781315091938-10
Rodríguez-Nieto, C., Rodríguez-Vásquez, F., & Font, V. (2020). A new view about connections: the mathematical connections established by a teacher when teaching the derivative. International Journal of Mathematical Education in Science and Technology, 53(6), 1231-1256. https://doi.org/10.1080/0020739X.2020.1799254
Rodríguez-Nieto, C., Rodríguez-Vásquez, F., Font, V., & Morales, A. (2021). Una visión desde la red de teorías TAC-EOS sobre el papel de las conexiones matemáticas en la comprensión de la derivada. Revemop, 3, 1-32. https://doi.org/10.33532/revemop.e202115
Sullivan, P., Clarke, D., Clarke, B., & O’Shea, H. (2010). Exploring the relationship between task, teacher actions, and student learning. PNA, 4(4), 133-142. https://doi.org/10.30827/pna.v4i4.6163
Vanegas, Y., & Giménez, J. (2018). Conexões extramatemáticas na formação inicial de docentes. Estudos Avançados, 32(94), 153-169. https://doi.org/10.1590/s0103-40142018.3294.0012
Wittmann, E. C. (2021). Connecting Mathematics and Mathematics Education: Collected Papers on Mathematics Education as a Design Science. Springer.
Yin, R. (2014) Case Study Research: design and methods. Sage Publications.
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