The Use of Logical Implication as an Indicator of Understanding the Concept of Number Sequences

José Mariano Bajo-Benito; Gloria Sánchez-Matamoros García; José María Gavilán-Izquierdo

doi:10.29333/ejmste/11429

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José Mariano Bajo-Benito ¹ ^* , Gloria Sánchez-Matamoros García ¹ , José María Gavilán-Izquierdo ¹

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¹ Universidad de Sevilla, SPAIN^* Corresponding Author

Abstract

This paper aims to characterise an indicator of the development of the number sequence scheme among students at the level of Compulsory Secondary Education (14-16 years old students). To do so, we use a scheme development proposed by the APOS theory to characterise students’ use of relations between mathematical elements when solving a mathematical task. We use a qualitative methodology and the data collection instruments are a written questionnaire and a semi-structured interview. In this work we show the questionnaire task that provides analytical expressions and ask students to determine which of them numbers sequences are. We find that students’ use of logical implication when solving tasks related to number sequences is an indicator of the development of the scheme. This indicator helps to locate the transition mechanisms between the levels of development of the number sequence scheme. Moreover, our research shows that arithmetic and geometric progressions play a key role as an indicator of the development of the number sequence scheme.

Keywords

number sequences
arithmetic and geometric progressions
APOS theory
scheme
compulsory secondary education

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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

EURASIA J Math Sci Tech Ed, Volume 17, Issue 12, December 2021, Article No: em2058

https://doi.org/10.29333/ejmste/11429

Publication date: 17 Dec 2021

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Article Downloads: 1003

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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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How to cite this article

APA

Bajo-Benito, J. M., Sánchez-Matamoros García, G., & Gavilán-Izquierdo, J. M. (2021). The Use of Logical Implication as an Indicator of Understanding the Concept of Number Sequences. Eurasia Journal of Mathematics, Science and Technology Education, 17(12), em2058. https://doi.org/10.29333/ejmste/11429

Vancouver

Bajo-Benito JM, Sánchez-Matamoros García G, Gavilán-Izquierdo JM. The Use of Logical Implication as an Indicator of Understanding the Concept of Number Sequences. EURASIA J Math Sci Tech Ed. 2021;17(12):em2058. https://doi.org/10.29333/ejmste/11429

AMA

Bajo-Benito JM, Sánchez-Matamoros García G, Gavilán-Izquierdo JM. The Use of Logical Implication as an Indicator of Understanding the Concept of Number Sequences. EURASIA J Math Sci Tech Ed. 2021;17(12), em2058. https://doi.org/10.29333/ejmste/11429

Chicago

Bajo-Benito, José Mariano, Gloria Sánchez-Matamoros García, and José María Gavilán-Izquierdo. "The Use of Logical Implication as an Indicator of Understanding the Concept of Number Sequences". Eurasia Journal of Mathematics, Science and Technology Education 2021 17 no. 12 (2021): em2058. https://doi.org/10.29333/ejmste/11429

Harvard

Bajo-Benito, J. M., Sánchez-Matamoros García, G., and Gavilán-Izquierdo, J. M. (2021). The Use of Logical Implication as an Indicator of Understanding the Concept of Number Sequences. Eurasia Journal of Mathematics, Science and Technology Education, 17(12), em2058. https://doi.org/10.29333/ejmste/11429

MLA

Bajo-Benito, José Mariano et al. "The Use of Logical Implication as an Indicator of Understanding the Concept of Number Sequences". Eurasia Journal of Mathematics, Science and Technology Education, vol. 17, no. 12, 2021, em2058. https://doi.org/10.29333/ejmste/11429