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Fourth-graders’ justifications in early algebra tasks involving a functional relationship

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Abstract

In the context of early algebra research and as part of a classroom teaching experiment (CTE), we investigated fourth grade (9- to 10-year-old) students’ justifications of how they performed tasks involving the functional relationship y = 2x. We related their written justifications (part of the task) to the task characteristics, which included various semiotic systems (verbal, numerical and alphanumeric, among others) and the demand of different type of justifications. The role of classroom discussion in helping express the functional relationship orally in more sophisticated terms was also investigated. The findings showed that students’ written justifications changed with the semiotic system involved in the task. Oral discussion helped students generalize in more sophisticated terms than in their written justifications, in which they omitted information or used less precise language.

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Notes

  1. Students’ identities are coded as Si where i=1 … 25. T-R refers to the teacher-researcher.

  2. The Spanish word for fifteen is ‘quince’, hence the ‘Q’.

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Acknowledgement(s)

This work has been developed within the project with reference EDU2016-75771-P, financed by the State Research Agency (SRA) from Spain and European Regional Development Fund (ERDF); the corresponding author benefited from a CONICYT grant awarded by the Chilean Government.

The authors wish to thank the editor and the reviewers for their help in improving the article.

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  1. Universidad de Granada, Granada, Spain

    Cristina Ayala-Altamirano

  2. Universidad de Salamanca, Travesía Madrigal de las Altas Torres, 3, 05003, Ávila, España

    Marta Molina

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  1. Cristina Ayala-Altamirano
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Correspondence to Cristina Ayala-Altamirano.

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Ayala-Altamirano, C., Molina, M. Fourth-graders’ justifications in early algebra tasks involving a functional relationship. Educ Stud Math 107, 359–382 (2021). https://doi.org/10.1007/s10649-021-10036-1

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