Generalization in fifth graders within a functional approach

  1. Pinto, Eder 1
  2. Cañadas, María C. 1
  1. 1 Universidad de Granada
    info

    Universidad de Granada

    Granada, España

    ROR https://ror.org/04njjy449

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

ISSN: 1887-3987

Año de publicación: 2018

Volumen: 12

Número: 3

Páginas: 173-184

Tipo: Artículo

DOI: 10.30827/PNA.V12I3.6643 DIALNET GOOGLE SCHOLAR lock_openDIGIBUG editor

Otras publicaciones en: PNA: Revista de investigación en didáctica de la matemática

Resumen

This article discusses evidence of 24 fifth graders’ (10-11 year olds’) ability to generalize when solving a problem which involves a linear function. Analyzed in the context of the functional approach of early algebra, the findings show that 3 students generalized both when solving specific instances and when asked to provide the general formula; while 15 students generalized only when asked to define the general formula. The results are described in terms of the functional relationship identified, the types of representation used to express them and the type of questions in which students generalized their answers. Most of the pupils who generalized did so based on the correspondence between pairs of values in the function at issue.Generalización de estudiantes de quinto de primaria desde un enfoque funcional En este artículo presentamos evidencias de generalización de 24 estudiantes de quinto de primaria (10-11 años) al resolver un problema que involucra una función lineal. Desde el enfoque funcional del early algebra, los hallazgos muestran que 3 estudiantes generalizaron al trabajar con casos particulares y cuando se les pide expresar la regla general; mientras que 16 estudiantes solo lo hicieron cuando les pedimos expresar la regla general. Describimos los resultados en términos de la relación funcional identificada, los tipos de representaciones que emplearon para expresar dichas relaciones y el tipo de pregunta en la cual los estudiantes generalizaron. La mayoría de los estudiantes que generalizaron establecieron una relación de correspondencia entre los pares de valores de la función. 

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Información de financiación

This study forms part of National R&D Projects EDU2013-41632-P and EDU2016-75771-P funded by the Spanish Ministry of Economy and Competitiveness; the first author was supported by a PhD scholarship granted by Chilean Government through the CONICYT, folio 72160307-2015.

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