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Generalization: strategies and representations used by sixth to eighth graders in a functional context

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Abstract

We conducted a descriptive exploratory study in which we analyzed 313 sixth to eighth grade students’ answers to a word problem, accompanied by diagrams, involving generalization in an algebraic functional context. In this research, we jointly addressed two objectives: (a) to determine the strategies deployed by students to generalize and (b) to identify the types of representation used to express their generalizations. We integrated how regularities are produced, evidenced in structures and represented by students. One of the most prominent findings was that functional strategy was used by almost all the students who generalized. They expressed the generalization using verbal, symbolical, or multiple representations. Ways of expressing regularities that are not restricted to algebraic symbolism are also shown. Although the potential to identify functional relationships was observed in sixth graders, seventh and eighth school students were able to represent more varied and structurally complex relationships. However, no relevant differences in generalization strategies were found between students of different ages with and without previous algebraic training.

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Funding

It was funded by Spain’s National Research Agency (Spanish initials, AEI) and the European Regional Development Fund (ERDF) under projects EDU2016-75771-P, EDU2017-84377-R (AEI/ERDF, EU), and PID2020-113601 GB-I00.

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Authors and Affiliations

  1. Departamento de Educación Matemática, Escuela de Matemática, Universidad de Costa Rica, San José, Costa Rica

    J. Ureña

  2. Facultad de Ciencias de la Educación, Universidad de Granada, Campus Cartuja, 18071, Granada, Spain

    R. Ramírez & M. C. Cañadas

  3. Universidad de Salamanca, E.U. de Educación y Turismo de Ávila, Travesía Madrigal de las Altas Torres, 3, 05003, Ávila, Spain

    M. Molina

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  1. J. Ureña
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  4. M. C. Cañadas
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Contributions

Jason Ureña: conceptualization, data analysis, original draft preparation, and writing—review and editing. Rafael Ramírez: conceptualization, methodology, task design, data collection, supported and validated the analysis, and writing—review and editing. Marta Molina: methodology, supported and validated the analysis, and writing—review and editing. María C. Cañadas: methodology, task design, data collection, supported and validated the analysis, and writing—review and editing.

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Correspondence to J. Ureña.

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This study was conducted in the context of the first author’s pursuit of a PhD, from the University of Costa Rica.

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Ureña, J., Ramírez, R., Molina, M. et al. Generalization: strategies and representations used by sixth to eighth graders in a functional context. Math Ed Res J (2023). https://doi.org/10.1007/s13394-023-00458-w

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