Pensamiento funcional de estudiantes de 2º de primariaestructuras y representaciones

  1. Torres, María Dolores 1
  2. María C. Cañadas 1
  3. Antonio Moreno 1
  1. 1 Universidad de Granada
    info

    Universidad de Granada

    Granada, España

    ROR https://ror.org/04njjy449

Journal:
PNA: Revista de investigación en didáctica de la matemática

ISSN: 1887-3987

Year of publication: 2022

Volume: 16

Issue: 3

Pages: 215-236

Type: Article

DOI: 10.30827/PNA.V16I3.23637 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

More publications in: PNA: Revista de investigación en didáctica de la matemática

Sustainable development goals

Abstract

This work is part of a broader investigation that is being developed in the field of algebraic thinking of elementary school students in Spain. We focus here on identifying the structures (identified regularities) and representations that appear during the generalization process of some students when students work with generalization tasks. For this purpose, we implemented generalization tasks involving linear functions in a case study within a teaching experiment with three students in the 2nd year of primary school (7-8 years old). We emphasize that the number of structures and the way of generalizing the structure depend on the tasks posed in each case. The generalizations of all students have been represented by verbal and/or numerical representations.

Bibliographic References

  • Ayala-Altamirano, C. y Molina, M. (2020). International Journal of Science and Mathematics Education, 18, 1271–1291. https://doi.org/10.1007/s10763-019-10012-5.
  • Blanton, M. y Kaput, J. (2004). Elementary grades students’ capacity for functional thinking. En M. Hoines y A. Fuglestad (Eds.), Proceedings of the 28th International Conference for the Psychology of Mathematics Education (Vol. 2, pp. 135-142). Bergen University College.
  • Blanton, M., Levi, L., Crites, T. y Dougherty, B. (2011). Developing essential understanding of algebraic thinking for teaching mathematics in Grades 3-5. NCTM.
  • Brizuela, B. M., Blanton, M. L., Sawrey, K., Newman-Owens, A. y Gardiner, A. M. (2015). Children’s use of variables and variable notation to represent their algebraic ideas. Mathematical Thinking and Learning, 17(1), 34-63. https://doi.org/10.1080/10986065.2015.981939.
  • Cai, J. (2005). US and Chinese teachers’ constructing, knowing and evaluating representations to teach mathematics. Mathematical Thinking and Learning, 7(2), 135-169.
  • Cañadas, M. C., Castro E. y Castro, E. (2008). Patrones, generalización y estrategias inductivas de estudiantes de 3º y 4º de Educación Secundaria Obligatoria en el problema de las baldosas. PNA, 2(3), 137-151.
  • Cañadas, M. C. y Figueiras, L. (2011). Uso de representaciones y generalización de la regla del producto. Infancia y Aprendizaje, 34(4), 409-425.
  • Cañadas, M. C. y Fuentes, S. (2015). Pensamiento funcional de estudiantes de primero de educación primaria: Un estudio exploratorio. En C. Fernández, M. Molina y N. Planas (Eds.), Investigación en Educación Matemática XIX (pp. 211-220). SEIEM.
  • Cañadas, M. C. y Molina, M. (2016). Una aproximación al marco conceptual y principales antecedentes delpensamiento funcional en las primeras edades. En E. Castro, E. Castro, J. L. Lupiáñez, J. F. Ruiz y M. Torralbo (Eds.), Investigación en Educación Matemática. Homenaje a Luis Rico (pp. 209-218). Comares.
  • Carraher, D. W. y Schliemann, A. (2016). Powerful ideas in elementary school mathematics. En L. English y D. Kirshner (Eds.), Handbook of international research in Mathematics Education. Third edition (pp. 191-218). Routledge.
  • Carraher, D., Martinez, M. y Schliemann, A. (2008). Early algebra and mathematical generalization. The International Journal on Mathematics Education (ZDM), 40(1), 3-22.
  • Cooper, T. J. y Warren, E. (2011). Years 2 to 6 students’ ability to generalise: Models, representations and theory for teaching and learning. En J. Cai (Ed.), Early algebraization. Advances in mathematics education (pp. 187-214). Springer.
  • Doorman, M. y Drijvers, P. (2011). Algebra in functions. En P. Drijvers (Ed.), Secondary algebra education (pp. 119-135). Sense Publishers.
  • Duval, R. (2006). The cognitive analysis of problems of comprehension in the learning of mathematics. Educational Studies in Mathematics, (61), 103-131.
  • Drijvers, P., Dekker, T. y Wijers, M. (2011). Patterns and formulas. En P. Drijvers (Ed.), Secondary Algebra Education (pp. 89-100). Sense Publishers.
  • Hewitt, D. (2019). “Never carry out any arithmetic”: the importance of structure in developing algebraic thinking. Paper presented at The Eleventh Congress of the European Society for Research in Mathematics Education. Utrecht, the Netherlands: Freudenthal Group y Freudenthal Institute, Utrecht University and ERME.
  • Kaput, J. J. (1991). Notations and representations as mediators of constructive processes. En E. V. Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 53-74). Springer.
  • Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? En J. J. Kaput, D. W. Carraher y M. L. Blanton (Eds.), Algebra in the early grades (pp. 5-17). Routledge.
  • Kieran, C. (1989). The early learning of algebra: A structural perspective. En S. Wagner y C. Kieran (Eds.), Research issues in the learning and teaching of algebra (Vol. 4, pp. 33-56). NCTM.
  • Kolloffel, B., Eysink, T. H. S., De Jong, T. y Wilhelm, P. (2009). The effects of representational format on learning combinatory from an interactive computer simulation. Instructional Science, 37(6), 503-517.
  • Martínez, M. y Brizuela, B. M. (2006). A third grader's way of thinking about linear function tables. The Journal of Mathematical Behavior, 25(4), 285-298.
  • Mason, J. (1996). Expressing generality and roots of algebra. En N. Bednarz, C. Kieran y L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 65-86). Kluwer.
  • Merino, E., Cañadas, M. C. y Molina, M. (2013). Estrategias utilizadas por alumnos de primaria en una tarea de generalización basada en un ejemplo genérico. En A. Berciano, A. Gutiérrez, A. Estepa y N. Climent (Eds.), Investigación en Educación Matemática XVII (pp. 383-392). SEIEM.
  • Ministerio de Educación, Cultura y Deporte. (2014). Real Decreto 126/2014 de 28 de febrero, por el que se establece el currículo básico de la Educación Primaria [Royal Decree 126/2014 of February 28, which establishes the basic curriculum of Primary Education]. BOE, 52, 19349–19420.
  • Molina, M., Castro, E., Molina, J. L. y Castro, E. (2011). Un acercamiento a la investigación de diseño a través de los experimentos de enseñanza. Enseñanza de las ciencias, 29(1), 75-88.
  • Mulligan, J. y 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.
  • Mulligan, J., Prescott, A. y Mitchelmore, M. (2006). Integrating concepts and processes in early mathematics: the australian pattern and structure mathematics awareness project (PASMAP). En J. Novotná, H. Moraová, M. Krátká y N. Stehlíková (Eds.), Proceedings of the 30th conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 209-216). PME.
  • NCTM. (2007). Principios e normas para a matemática escolar. A.P.M e I.I.E.
  • Papic, M., Mulligan, J., y Mitchelmore, M. (2011). Assessing the development of preschoolers’ mathematical patterning. Journal for Research in Mathematics Education, 42(3), 237. https://doi.org/10.5951/jresematheduc.42.3.0237.
  • Pincheira, N. G. y Alsina, À. (2021). Hacia una caracterización del álgebra temprana a partir del análisis de los currículos contemporáneos de Educación Infantil y Primaria. Educación Matemática, 33(1), 153-180.
  • Pinto, E. (2019). Generalización de estudiantes de 3º a 6º de Educación Primaria en un contexto funcional del álgebra escolar. [Tesis Doctoral, Universidad de Granada]. https://digibug.ugr.es/handle/10481/71860
  • Pinto, E. y Cañadas, M. C. (2017). Estructuras y generalización de estudiantes de tercero y quinto de primaria: un estudio comparativo. En J. M. Muñoz-Escolano, A. Arnal-Bailera, P. Beltrán-Pellicer, M. L. Callejo y J. Carrillo (Eds.), Investigación en Educación Matemática XXI (pp. 407-416). SEIEM
  • Pólya, G. (1966). Matemáticas y razonamiento plausible. Tecnos.
  • Radford, L. (2002). The seen, the spoken and the written: A semiotic approach to the problem of objectification of mathematical knowledge. For the Learning of Mathematics, 22(2), 14-23.
  • 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.
  • Radford, L. (2018). The emergence of symbolic algebraic thinking in primary school. En C. Kieran (Ed.), Teaching and learning algebraic thinking with 5- to 12-year-olds: The global evolution of an emerging field of research and practice (pp. 3-25). Springer. https://doi.org/10.1007/978-3-319-68351-5_1.
  • Rivera, F. (2017). Abduction and the emergence of necessary mathematical knowledge. En L. Magnani y T. Bertolotti (Eds.), Springer handbook of model-based xcience. Springer. doi:10.1007/978-3-319-30526-4_25
  • Rivera, F.D. y Becker, J. (2003). The effects of figural and numerical cues on the induction processes of preservice elementary mathematics teachers. En N. Pateman, B. Dougherty y J. Zilliox (Eds.), Proceedings of the 2003 Joint Meeting of PME and PMENA (pp. 4-63 -70). University of Hawaii.
  • Stacey, K. (1989) Finding and using patterns in linear generalising problems. Educational Studies Mathematics, 20, 147–164.
  • Stephens, A., Ellis, A., Blanton, M. y Brizuela, B. (2017). Algebraic thinking in the elementary and middle grades. En J. Cai (Ed.), Compendium for research in mathematics education. Third handbook of research in mathematics education. (pp. 386–420). NCTM.
  • Torres, M. D., Cañadas, M. C. y Moreno, A. (2018). Estructuras, generalización y significado de letras en un contexto funcional por estudiantes de 2º de primaria. En L. J. Rodríguez-Muñiz, L. Muñiz-Rodríguez, A. Aguilar-González, P. Alonso, F. J. García García y A. Bruno (Eds.), Investigación en Educación Matemática XXII (pp. 574-583). SEIEM.
  • Torres, M. D., Cañadas, M. C. y Moreno, A. (2021). Estructuras en las formas directa e inversa de una función por estudiantes de 7-8 años. Uniciencia, 35(2), 1-16. http://dx.doi.org/10.15359/ru.35-2.16.
  • Torres, M. C., Moreno, A. y Cañadas, M. C. (2021). Generalization process by second grade students. Mathematics, 9, 1109. https://doi.org/10.3390/math9101109.
  • Ureña, J. (2021). Representaciones de generalización y estrategias empleadas en la resolución de tareas que involucran relaciones funcionales. Una investigación con estudiantes de primaria y secundaria. [Tesis doctoral, Universidad de Granada]. https://digibug.ugr.es/handle/10481/66412?show=full
  • Ureña, J., Ramírez, R. y Molina, M. (2019). Representations of the generalization of a functional relationship and the relation with the interviewer’s mediation. Journal for the Study of Education and Development, 42(3), 570-614, https://doi.org/10.1080/02103702.2019.1604020
  • Warren, E., Miller, J. y Cooper, T. J. (2013). Exploring young students’ functional thinking. PNA, 7(2), 75-84.