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Word problems associated with the use of functional strategies among grade 4 students

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Abstract

This article discusses the characteristics of word problems that are associated with students’ use of functional strategies and their ability to represent the generalization of functions. In the context of a broader research project designed to explore and foster functional thinking among elementary school students, twenty-five grade 4 (9- to 10-year-old) students were asked to identify functional relationships in five problems involving specific or indeterminate quantities. Their responses to a number of questions involving the generalization of the relationships in the problems were analyzed and associated to the characteristics of the problems. The type of representation of generalization used (verbal, generic, or symbolic) was also identified. Our findings indicate that grade 4 students showed potential for functional thinking prior to receiving instruction on variables and their notation. Such thinking was most effectively prompted when they worked with word problems that explicitly involved an additive function. When students generalized functional relationships, they represented them verbally or with generic examples. None of the students used symbolic representation. The originality of this study lies in the description of the specific characteristics of word problems that are associated with functional thinking; this information will prove useful to both teachers and curriculum designers. Identifying these characteristics could help build and propose tasks that encourage students to use more than one and more sophisticated strategies.

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Notes

  1. The word for “20” in Spanish is “veinte” and for “15,” “quince.”

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Funding

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) and the grant “Jose Castillejo” funded by the Spanish Ministry of Economy and Competitiveness; the third author benefited from a CONICYT grant awarded by the Chilean Government.

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  1. University of Granada, Campus de Cartuja s/n, 18071, Granada, Spain

    Rafael Ramírez & Cristina Ayala-Altamirano

  2. Department of Education, Tufts University, 12 Upper Campus Rd., Paige Hall, Medford, MA, 02155, USA

    Bárbara M. Brizuela

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  1. Rafael Ramírez
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Ramírez, R., Brizuela, B.M. & Ayala-Altamirano, C. Word problems associated with the use of functional strategies among grade 4 students. Math Ed Res J 34, 317–341 (2022). https://doi.org/10.1007/s13394-020-00346-7

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