Desarrollo de un marco para evaluar la comprensión del estudiante en la generalización de patrones figurativos
DOI:
https://doi.org/10.30827/pna.v18i1.16566Palabras clave:
Generalización de patrones figurativos, Marco de desarrollo, Representación de estructuras, Teoría APOSResumen
Los patrones figurativos tienen una capacidad única para promover el pensamiento funcional. Este estudio tuvo como objetivo identificar las construcciones mentales de los estudiantes de 7º grado en Generalización de Patrones Figurativos (FPG) mediante el uso de la teoría de Acción, Proceso, Objeto y Esquema (APOS) para desarrollar un marco para evaluar la comprensión de la FPG. Una muestra de 220 estudiantes completó una prueba diseñada en el marco APOS y 19 estudiantes participaron en una entrevista semiestructurada. Los resultados mostraron que existen niveles de acción emergentes y parciales antes de la etapa de acción y niveles de proceso/objeto pre, emergentes y parciales antes de la etapa de proceso/objeto.
Descargas
Citas
Arnon, I. (1998). In the Mind's Eye: How Children Develop Mathematical Concepts -Extending Piaget's Theory- the Case of Fractions in Grade Four (Dissertation). Haifa, University of Haifa, Israel.
Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Roa Fuentes, S., Trigueros, M., & Weller, K. (2014). APOS Theory: A framework for research and curriculum development in the mathematics education. Springer-Verlag. DOI: https://doi.org/10.1007/978-1-4614-7966-6
Baker, B., Cooley, L., & Trigueros, M. (2000). The schema triad—a calculus example. Journal for Research in Mathematics Education, 31, 557-578. DOI: https://doi.org/10.2307/749887
Blanton, M. L. & Kaput, J. J. (2011). Functional thinking as a route into algebra in the elementary grades. ZDM-International Reviews on Mathematical education, 37(1), 34-42. https://doi.org/10.1007/BF02655895 DOI: https://doi.org/10.1007/BF02655895
Carraher, D. W. & Schliemann, A. D. (2019). Early algebraic thinking and the US mathematics standards for grades K to 5. Infancia y Aprendizaje, 42(3), 479-522. https://doi.org/10.1080/02103702.2019.1638570 DOI: https://doi.org/10.1080/02103702.2019.1638570
Chua, B. L. (2009). Features of generalising task: Help or hurdle to expressing generality? Australian Mathematics Teacher, 65(2), 18-24.
Chua, B. L. & Hoyles, C. (2012). The effect of different pattern formats on secondary two students’ ability to generalise. In T. Y. Tso, (Ed.), Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2 (pp. 155-162). PME.
Chua, B. L. & Hoyles, C. (2014). Modalities of rules and generalizing strategies of year 8 students for a quadratic pattern. In C. Nicol, P. Liljedahl, S. Oesterle, & D. Allan (Eds.) Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (pp.305-312). PME.
Copley, J. V. (2000). The young child and mathematics. National Association for the Education of Young Children.
Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 95-123). Kluwer. DOI: https://doi.org/10.1007/0-306-47203-1_7
Dubinsky, E., Arnon, I., & Weller, K. (2013). Preservice Teachers’ Understanding of the Relation between a Fraction or Integer and its Decimal Expansion: The Case of 0.9 ̂ and 1. Canadian Journal of science, mathematics and Technology education, 13(3), 232-258. https://doi.org/10.1080/14926156.2013.816389 DOI: https://doi.org/10.1080/14926156.2013.816389
Gronow, M., Mulligan, J., & Cavanagh, M. (2022). Teachers’ understanding and use of mathematical structure. Mathematics Education Research Journal 34, 215-240. https://doi.org/10.1007/s13394-020-00342-x DOI: https://doi.org/10.1007/s13394-020-00342-x
Huntzinger, E. M. (2008). Exploring generalization through pictorial growth patterns. In C. E. Greenes & R. Rubenstein (Eds.), Algebra and algebraic thinking in school mathematics (pp. 279-293). NCTM.
Jones, D. & Bush, W. S. (1996). Mathematical structures: Answering the “Why” questions. The Mathematics Teacher, 89, 716-722. DOI: https://doi.org/10.5951/MT.89.9.0716
Kaput, J., Carraher, D. W., & Blanton, M. L. (Eds.) (2007). Algebra in the early grades. Lawrence Erlbaum Associates.
Lannin, J. K., Barker, D. D., & Townsend, B. E. (2006). Algebraic generalization strategies: factors influencing student strategy selection. Mathematics Education Research Journal, 18(3), 3-28. DOI: https://doi.org/10.1007/BF03217440
Mason, J. (1996). Expressing generality and roots of algebra. In N. Bdnarz, C. Kieran & L. Lee (Eds), Approaches to algebra: perspective for research and teaching (pp.65-86). Kluwer. DOI: https://doi.org/10.1007/978-94-009-1732-3_5
Mason, J., Stephens, M., & Watson, A. (2009). Appreciating mathematical structures for all. Mathematics Education Research Journal, 21(2), 10-32. https://doi.org/10.1007/BF03217543 DOI: https://doi.org/10.1007/BF03217543
Mulligan, J., Prescott, A., & Mitchelmore, M. (2004). Children’s development of structure in early mathematics. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th conference of the International Group for the Psychology in Mathematics Education. PME.
Mulligan, J. & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33-49. https://doi.org/10.1007/BF03217544 DOI: https://doi.org/10.1007/BF03217544
Markworth, K. A. (2010). Growing and growing: Promoting functional thinking with geometric growing patterns (Dissertation). Chapel Hill, University of North Carolina, USA.
NCTM (2000). Principles and Standards for School Mathematics. The National Council of Teachers of Mathematics.
Oliveira, H., Polo-Blanco, I., & Henriques, A. (2021). Exploring prospective elementary mathematics teachers’ knowledge: A focus on functional thinking. Journal on Mathematics Education, 12(2), 257-278. https://doi.org/10.22342/jme.12.2.13745.257-278 DOI: https://doi.org/10.22342/jme.12.2.13745.257-278
Piaget, J. (1975). Piaget’s theory (Translated by G. Cellerier & J. Langer). In P. B. Neubauer (Ed.), The process of child development (pp. 164-212). Jason Aronson.
Papic, M. M., Mulligan, J. T., & Mitchelmore, M. C. (2009). The growth of mathematical patterning strategies in preschool children. In M. Tzekaki, M. Kaldrimidou, H. Sakonidis (Eds), Proceedings of the 33th Conference of the International Group for the Psychology of Mathematics Education - in search for theories in mathematics education (pp. 329-336). PME.
Papic, M., Mulligan, J., & Mitchelmore, M. (2011). Assessing the development of preschoolers’ mathematical patterning. Journal for Research in Mathematics Education, 42(3), 237-268. https://doi.org/10.5951/jresematheduc.42.3.0237 DOI: https://doi.org/10.5951/jresematheduc.42.3.0237
Rivera, F. (2011). Toward a visually-oriented school mathematics curriculum: Research, theory, practice, and issues. Springer. DOI: https://doi.org/10.1007/978-94-007-0014-7
Rivera, F. (2013). Teaching and learning patterns in school mathematics: Psychological and pedagogical considerations. Springer Science & Business Media. DOI: https://doi.org/10.1007/978-94-007-2712-0
Samson, D. A. (2007). An Analysis of the Influence of Question Design on Pupils’ Approaches to Number Pattern Generalisation Tasks. (Master Thesis). Grahamstown, Rhodes University, South Africa. DOI: https://doi.org/10.4102/pythagoras.v0i66.79
Samson, D. A. (2011). The Heuristic Significance of Enacted Visualisation. (Dissertation). Grahamstown, Rhodes University, South Africa.
Smith, E. (2008). Representational thinking as a framework for introducing functions in the elementary curriculum. In J. J. Kaput, D. W. Carrher, M. L. Blanton (Eds), Algebra in the Early Grades (pp. 133-163). Routledge. DOI: https://doi.org/10.4324/9781315097435-6
Sutarto, Nusantara, T., Subanji, Hastuti, I. D., & Dafik (2018). Global conjecturing process in pattern generalization problem. Journal of Physics: Conference Series 1008, 012060. https://doi.org/10.1088/1742-6596/1008/1/012060 DOI: https://doi.org/10.1088/1742-6596/1008/1/012060
Sutarto, Nusantara, T., Subanji, & Sisworo (2016). Local conjecturing process in the solving of pattern generalization problem. Educational Research and Reviews, 11(8), 732-742. https://doi.org/10.5897/ERR2016.2719
Weller, K., Arnon, I., & Dubinsky, E. (2009). Preservice teachers’ understanding of the relation between a fraction or integer and its decimal expansion. Canadian Journal of Science, Mathematics and Technology Education, 9(1), 5-28. https://doi.org/10.1080/14926150902817381 DOI: https://doi.org/10.1080/14926150902817381
Wilkie, K. J., & Clarke, D. M. (2016). Developing students’ functional thinking in algebra through different visualisations of a growing pattern’s structure. Mathematics Education Research Journal, 28(2), 223-243. https://doi.org/10.1007/s13394-015-0146-y DOI: https://doi.org/10.1007/s13394-015-0146-y
Yuniati, S., Nusantara, T., Subanji, & Made Sulandra (2020). Stages in partial functional thinking in the form of liner functions: APOS theory. Humanities & Social Sciences Reviews, 8(3), 536-544. https://doi.org/10.18510/hssr.2020.8358 DOI: https://doi.org/10.18510/hssr.2020.8358
Descargas
Publicado
Versiones
- 2023-10-23 (2)
- 2023-10-23 (1)
Número
Sección
Licencia
Derechos de autor 2023 PNA. Revista de Investigación en Didáctica de la Matemática
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-SinDerivadas 4.0.