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University student understanding of the gradient of a function of two variables: an approach from the perspective of the theory of semiotic representation registers

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Abstract

The aim of this research is to study how students recognise the concept of gradient of a function of two variables in its different representations and how they make conversions between these representations. Three groups of university students with different profiles took part in this research, and Duval’s theory of semiotic representations was taken as a framework to analyse the resulting data. The paper describes recognition and conversion difficulties and demonstrates that conversion direction is an important factor when determining students’ success in conversions between representations. We discuss the implications of this study on teaching and learning the concept of gradient at undergraduate level.

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Acknowledgements

We would like to thank Esmeralda Campos and Dorilián López from the Monterrey Institute of Technology for their participation and Manuel Ángel González and Carlos Casanova from the University of Valladolid.

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  1. University of the Basque Country, Donostia-San Sebastián, Spain

    Oihana Moreno-Arotzena, Ion Pombar-Hospitaler & José Ignacio Barragués

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  1. Oihana Moreno-Arotzena
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  2. Ion Pombar-Hospitaler
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  3. José Ignacio Barragués
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Correspondence to José Ignacio Barragués.

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Moreno-Arotzena, O., Pombar-Hospitaler, I. & Barragués, J.I. University student understanding of the gradient of a function of two variables: an approach from the perspective of the theory of semiotic representation registers. Educ Stud Math 106, 65–89 (2021). https://doi.org/10.1007/s10649-020-09994-9

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