Representaciones de la generalización de una relación funcional y el vínculo con la mediación del entrevistador

• Jason Ureña ^[1] ; Rafael Ramírez ^[2] ; Marta Molina ^[2]
  1. [1] Universidad de Granada

     Universidad de Granada

     Granada, España

     
  2. [2] Universidad de Salamanca

     Universidad de Salamanca

     Salamanca, España

     
• Localización: Journal for the Study of Education and Development, Infancia y Aprendizaje, ISSN-e 1578-4126, ISSN 0210-3702, Vol. 42, Nº 3, 2019 (Ejemplar dedicado a: Pensamiento algebraico temprano : estudios desde diversas perspectivas, enfoques y regiones), págs. 591-614
• Idioma: español
• DOI: 10.1080/02103702.2019.1604020
• Títulos paralelos:
  • Representations of the generalization of a functional relationship and the relation with the interviewer’s mediation
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• Dialnet Métricas: 5 Citas
• Resumen
  • español

    En este estudio descriptivo se analiza la capacidad de generalizar y de representar generalizaciones exhibida por estudiantes de cuarto grado de primaria. El estudio adopta un diseño experimental basado en una entrevista semiestructurada en torno a una tarea basada en la relación funcional lineal y = x + 2. El papel de la mediación de la entrevistadora en las representaciones de las generalizaciones realizadas por los estudiantes se determina en función de las interacciones de los estudiantes con ella. Se definen cuatro formas de representación de la generalización de una relación funcional. Los resultados confirman la importancia de la mediación para ayudar a los estudiantes a mejorar su capacidad de reconocer, representar y generalizar las relaciones funcionales.

  • English

    The ability to generalize and represent generalizations exhibited by eight fourth-grade students was analysed in this descriptive study, designed around a semi-structured interview involving a task based on the linear functional relationship y = x + 2. The relation of the interviewer’s mediation on students’ representations of generalizations was determined on the grounds of students’ interactions with her. Four forms to represent the generalization of a functional relationship were defined. The findings confirm the importance of mediation in helping students strengthen their ability to recognize, represent and generalize functional relationships.

• Referencias bibliográficas
  • Blanton, M. (2008). Algebra and the elementary classroom. Transforming thinking to practice. Portsmouth, NH: Heinemann.
  • Blanton, M., Brizuela, B., Gardiner, A., Sawrey, K., & Newman-Owens, A. (2015). A learning trajectory in 6-year-old’s thinking about generalizing...
  • Blanton, M., & Kaput, J. (2004). Elementary grades student´s capacity for functional thinking. In M. Hoines, & A. Fugslestad (Eds.),...
  • Blanton, M., & Kaput, J. (2011). Functional thinking as a route into algebra in the elementary grades. In J. Cai, & E. Knuth (Eds.),...
  • Blanton, M., Levi, L., Crites, T., & Dougherty, B. J. (Eds.). (2011). Developing essential understanding of algebraic thinking for teaching...
  • Cañadas, M. C., & Molina, M. (2016). Una aproximación al marco conceptual y principales antecedentes del pensamiento funcional en las...
  • Carraher, D., Martínez, M., & Schliemann, A. (2008). Early Algebra and mathematical generalization. ZDM Mathematics Education, 40, 3–22.
  • Carraher, D., Schliemann, A. D., & Brizuela, B. (2003). Treating operations as functions. Paper presented at the Psychology of Mathematics...
  • Castro, E., Cañadas, M. C., & Molina, M. (2010). El razonamiento inductivo como generador de conocimiento matemático [Inductive reasoning...
  • Hitt, F., & González-Martín, A. S. (2016). Generalization, covariation, functions, and calculus. In Á. Gutiérrez, G. C. Leder, & P....
  • Kaput, J. (2008). What is algebra? What is algebraic reasoning? In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the early grades...
  • Mason, J., Graham, A., & Johnston-Wilder, S. (2005). Developing thinking in algebra. London: The Open University and Paul Chapman Publishing.
  • Mason, J., Graham, A., Pimm, D., & Gowar, N. (1985). Routes to roots of algebra. Milton Keynes: The Open University Press.
  • Mason, J., & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15, 277–287.
  • Mata-Pereira, J., & Da Ponte, J.-P. (2017). Enhancing students’ mathematical reasoning in the classroom: Teacher actions facilitating...
  • McEldoon, K. L., & Rittle-Johnson, B. (2010). Assessing elementary students’ functional thinking skills: The case of function tables....
  • Merino, E., Cañadas, M. C., & Molina, M. (2013). Uso de representaciones y patrones por alumnos de quinto de educación primaria en una...
  • Ministerio de Educación, Cultura y Deporte. (2014). Real Decreto 126/2014, de 28 de febrero, por el que se establece el currículo básico de...
  • Molina, M., Ambrose, R., & Del Rio, A. (2018). First encounter with variables by first and third grade spanish students. In C. Kieran...
  • Pinto, E., Cañadas, M.C., Moreno, A., & Castro, E. (2016, September). Relaciones funcionales que evidencian estudiantes de tercero de...
  • Polya, G. (1989). ¿Cómo plantear y resolver problemas? [How to solve it?]. Mexico, DF: Trillas.
  • Ponte, J. P., Mata-Pereira, J., & Quaresma, M. (2013). Ações do professor na condução de discussões matemáticas [Teacher actions in the...
  • Radford, L. (2001, July). Factual, contextual and symbolic generalization in algebra. In M. van Den Heuvel-Panhuizen (Ed.), Proceedings of...
  • Radford, L. (2010). Layers of generality and types of generalization in pattern activities. PNA, 4, 37–62.
  • Radford, L. (2018). The emergence of symbolic algebraic thinking in primary school. In C. Kieran (Ed.), Teaching and Learning Algebraic Thinking...
  • Smith, E. (2008). Representational thinking as a framework for introducing functions in the elementary curriculum. In J. Kaput, D. Carraher,...
  • Soller, A. (2001). Supporting social interaction in an intelligent collaborative learning system. International Journal of Artificial Intelligence...
  • Stephens, A., Ellis, A., Blanton, M. L., & Brizuela, B. M. (2017). Algebraic thinking in the elementary and middle grades. In J. Cai (Ed.),...
  • Warren, E. (2006, July). Teacher actions that assist young students write generalizations in words and in symbols. In J. Novotná, M. Krátka,...
  • Warren, E., Trigueros, M., & Ursini, S. (2016). Research on the learning and teaching of algebra. In Á. Gutiérrez, G. C. Leder, &...