Archives
Current issue
About
About us
Aims and Scope
Abstracting and Indexing
Editorial Office
Open Access Policy
Publication Ethics
Journal History
Publisher
Follow us: Twitter
Contact
For Authors
Editorial Policy
Peer Review Policy
Manuscript Preparation Guidelines
Copyright & Licencing
Publication Fees
Fee Waiver Policy for Doctoral Students
EJMSTE Language Editing Service
More
Statistics
Special Issues
Special Issue Announcements
Published Special Issues
RESEARCH PAPER
The Use of Logical Implication as an Indicator of Understanding the Concept of Number Sequences
1
Universidad de Sevilla, SPAIN
Publication date: 2021-12-17
EURASIA J. Math., Sci Tech. Ed 2021;17(12):em2058
KEYWORDS
number sequencesarithmetic and geometric progressionsAPOS theoryschemecompulsory secondary education
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.
REFERENCES (29)
1.
Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Fuentes, S. R., Trigueros, M., & Weller, K. (2014). APOS theory: A framework for research and curriculum development in mathematics education. Springer. https://doi.org/10.1007/978-1-....
2.
Asiala, M., Brown, A., DeVries, D. J., Dubinsky, E., Mathews, D., & Thomas, K. (1996). A framework for research and curriculum development in undergraduate mathematics education. Research in Collegiate Mathematics Education II, 6, 1-32. https://doi.org/10.1090/cbmath....
3.
Bagni, G. T. (2005). Infinite series from history to mathematics education. International Journal for Mathematics Teaching and Learning https://www.cimt.org.uk/journa....
4.
Bajo Benito, J. M., Gavilán-Izquierdo, J. M., & Sánchez-Matamoros García, G. (2019). Caracterización del esquema de sucesión numérica en estudiantes de Educación Secundaria Obligatoria [Characterization of the numeric sequence schema among Compulsory Secondary Education students]. Enseñanza de las Ciencias, 37(3), 149-167. https://doi.org/10.5565/rev/en....
5.
Baker, B., Cooley, L., & Trigueros, M. (2000). A calculus graphing schema. Journal for Research in Mathematics Education, 31(5), 557-578. https://doi.org/10.2307/749887.
6.
BOE (Boletín Oficial del Estado) (2007). Real Decreto 1631/2006, de 29 de diciembre, por el que se establecen las enseñanzas mínimas correspondientes a la Educación Secundaria Obligatoria [Royal Decree 1631/2006, of December 29, which establishes the minimum education corresponding to Compulsory Secondary Education]. Official State Gazette, 5, 677-773. https://www.boe.es/eli/es/rd/2....
7.
Cañadas, M. (2007). Descripción y caracterización del razonamiento inductivo utilizado por estudiantes de educación secundaria al resolver tareas relacionadas con sucesiones lineales y cuadráticas [Description and characterization of inductive reasoning used by high school students when solving tasks related to linear and quadratic sequences] (Unpublished doctoral thesis) Universidad de Granada.
8.
Codes Valcarce, M., & González-Martín, A. S. (2017). Sucesión de sumas parciales como proceso iterativo infinito: un paso hacia la comprensión de las series numéricas desde el modelo APOS [Sequence of partial sums as an infinite iterative process: A step towards the understanding of numerical series from an APOS perspective]. Enseñanza de las Ciencias, 35(1), 89-110. https://doi.org/10.5565/rev/en....
9.
Codes, M., González Astudillo, M. T., Delgado Martín, M. L., & Monterrubio Pérez, M. C. (2013). Growth in the understanding of infinite numerical series: A glance through the Pirie and Kieren theory. International Journal of Mathematical Education in Science and Technology, 44(5), 652-662. https://doi.org/10.1080/002073....
10.
Djasuli, M., Sa’dijah, C., Parta, I. N., & Daniel, T. (2017). Students’ reflective abstraction in solving number sequence problems. International Electronic Journal of Mathematics Education, 12(3), 621-632. https://doi.org/10.29333/iejme....
11.
Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 95-126). Kluwer. https://doi.org/10.1007/0-306-....
12.
Duval, R. (2006). Un tema crucial en la Educación Matemática: La habilidad para cambiar el registro de representación [A crucial issue in mathematics education: The ability to change the register of representation]. La Gaceta de la Real Sociedad Matemática Española, 9(1), 143-168.
13.
Fuentealba, C, Badillo, E., Sánchez-Matamoros, G., & Trigueros M. (2017). Thematization of derivative schema in university students: nuances in constructing relations between a function's successive derivatives. International Journal of Mathematical Education in Science and Technology, 48(3), 374-392. https://doi.org/10.1080/002073....
14.
Fuentealba, C., Badillo, E., & Sánchez-Matamoros, G. (2019a). Identificación y caracterización de los subniveles de desarrollo del esquema de derivada [Identification and characterization of the development sub-levels of the derivative schema]. Enseñanza de las Ciencias, 37(2), 63-84. https://doi.org/10.5565/rev/en....
15.
Fuentealba, C., Badillo, E., Sánchez-Matamoros, G., & Cárcamo, A. (2019b). The understanding of the derivative concept in higher education. Eurasia Journal of Mathematics, Science and Technology Education, 15(2), em1662. https://doi.org/10.29333/ejmst....
16.
Gonzalez, J., Medina, P., Vilanova, S., & Astiz, M. (2011). Un aporte para trabajar sucesiones numéricas con Geogebra [A contribution to work numerical sequences with Geogebra]. Revista de Educación Matemática, 26, 1-19.
17.
Mamona-Downs, J. (2001). Letting the intuitive bear on the formal: A didactical approach for the understanding of the limit of a sequence. Educational Studies in Mathematics, 48, 259-288. https://doi.org/10.1023/A:1016....
18.
McDonald, M. A., Mathews, D. M., & Strobel, K. H. (2000). Understanding sequences: A tale of two objects. Research in Collegiate Mathematics Education IV, American Mathematical Society, Providence, Rhode Island, 8, 77-102. https://doi.org/10.1090/cbmath....
19.
Mor, Y., Noss, R., Hoyles, C., Kahn, K., & Simpson, G. (2006). Designing to see and share structure in number sequences. The International Journal for Technology in Mathematics Education, 13(2), 65-78.
20.
Piaget, J. & García, R. (1983). Psicogénesis e historia de la ciencia [Psychogenesis and history of science]. Siglo XXI Editores.
21.
Przenioslo, M. (2006). Conceptions of a sequence formed in secondary schools. International Journal of Mathematical Education in Science and Technology, 37(7), 805-823. https://doi.org/10.1080/002073....
22.
Roa-Fuentes, S. & Oktac, A. (2010). Construcción de una descomposición genética: Análisis teórico del concepto transformación lineal [Constructing a genetic decomposition: Theoretical analysis of the linear transformation concept]. Revista Latinoamericana de Investigación en Matemática Educativa, 13(1), 89-112.
23.
Roh, K.H. (2008). Students’ images and their understanding of definitions of the limit of a sequence. Educational Studies in Mathematics, 69, 217-233. https://doi.org/10.1007/s10649....
24.
Sánchez-Matamoros, G. (2004). Análisis de la comprensión en los alumnos de bachillerato y primer año de universidad sobre la noción matemática de derivada (desarrollo del concepto) [Analysis of the understanding in high school and first year university students about the mathematical notion of derivative (concept development)] (Doctoral thesis). Universidad de Sevilla.
25.
Sánchez-Matamoros, G., García, M., & Llinares, S. (2008). La comprensión de la derivada como objeto de investigación en didáctica de la matemática [The understanding of derivative as the object of investigation in mathematics education]. Revista latinoamericana de investigación en matemática educativa, 11(2), 267-296.
26.
Sánchez-Matamoros, G., García, M., & Llinares, S. (2013). Algunos indicadores del desarrollo del esquema de derivada de una función [Some Indicators of the Development of Derivative Schema]. Bolema, 27(45) 281-302.
27.
Stewart, J., Hernández, R., & Sanmiguel, C. (2007). Introducción al cálculo [Introduction to calculus]. S.A. Ediciones Thomson.
28.
Valls, J., Pons, J., & Llinares, S. (2011). Coordinación de los procesos de aproximación en la comprensión del límite de una función [Coordination of approximations in secondary school students’ understanding of the concept of limit of a function]. Enseñanza de las Ciencias, 29(3), 325-338. https://doi.org/10.5565/rev/ec....
29.
Weigand, H.-G. (2015). Discrete or continuous?– A model for a technology supporteddiscrete approach to calculus. In K. Krainer & N. Vondrová (Eds.), Proceedings of the Ninth Conference of the European Society for Research in Mathematics Education (pp. 2580-2586). ERME.
Share
RELATED ARTICLE
| eISSN: | 1305-8223 |
| ISSN: | 1305-8215 |
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
