Mathematics students’ conceptions and reactions to questions concerning the nature of rational and irrational numbers

Ioannis Rizos; Maria Adam

doi:10.29333/iejme/11977

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Ioannis Rizos ¹ ^* , Maria Adam ²

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¹ Department of Mathematics, University of Thessaly, Lamia, GREECE² Department of Computer Science & Biomedical Informatics, University of Thessaly, Lamia, GREECE^* Corresponding Author

Abstract

In this paper, we present parts of an online qualitative research project which lasted a whole semester about the understanding of real numbers by sixty first-year Greek mathematics undergraduate students during the COVID-19 pandemic. We focus on the distinction between rational and irrational numbers and their location on the number line using straightedge and compass. The results, came of questionnaires, focused interviews and tasks, disclosed some gaps regarding real numbers that the students had from school and revealed confusion between irrational numbers and their decimal approximation. The results also led us to group students’ conceptions of rational and irrational numbers into five categories related to the number and pattern of decimal digits. Teaching practices and perspectives as well as the, negative, impact of the pandemic on teaching and learning mathematics are discussed.

Keywords

real numbers
number line
geometrical constructions
ICT in mathematics education
categories of conceptions

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 17, Issue 3, August 2022, Article No: em0686

https://doi.org/10.29333/iejme/11977

Publication date: 06 Apr 2022

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Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

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APA

Rizos, I., & Adam, M. (2022). Mathematics students’ conceptions and reactions to questions concerning the nature of rational and irrational numbers. International Electronic Journal of Mathematics Education, 17(3), em0686. https://doi.org/10.29333/iejme/11977

Vancouver

Rizos I, Adam M. Mathematics students’ conceptions and reactions to questions concerning the nature of rational and irrational numbers. INT ELECT J MATH ED. 2022;17(3):em0686. https://doi.org/10.29333/iejme/11977

AMA

Rizos I, Adam M. Mathematics students’ conceptions and reactions to questions concerning the nature of rational and irrational numbers. INT ELECT J MATH ED. 2022;17(3), em0686. https://doi.org/10.29333/iejme/11977

Chicago

Rizos, Ioannis, and Maria Adam. "Mathematics students’ conceptions and reactions to questions concerning the nature of rational and irrational numbers". International Electronic Journal of Mathematics Education 2022 17 no. 3 (2022): em0686. https://doi.org/10.29333/iejme/11977

Harvard

Rizos, I., and Adam, M. (2022). Mathematics students’ conceptions and reactions to questions concerning the nature of rational and irrational numbers. International Electronic Journal of Mathematics Education, 17(3), em0686. https://doi.org/10.29333/iejme/11977

MLA

Rizos, Ioannis et al. "Mathematics students’ conceptions and reactions to questions concerning the nature of rational and irrational numbers". International Electronic Journal of Mathematics Education, vol. 17, no. 3, 2022, em0686. https://doi.org/10.29333/iejme/11977