Mathematical Connections Activated in High School Students’ Practice Solving Tasks on the Exponential and Logarithmic Functions

Karen Gisel Campo-Meneses; Vicenç Font; Javier García-García; Alicia Sánchez

doi:10.29333/ejmste/11126

Full Text (PDF)

Karen Gisel Campo-Meneses ¹, Vicenç Font ² ^* , Javier García-García ¹, Alicia Sánchez ²

More Detail

¹ Universidad Autónoma de Guerrero, MEXICO
² Universitat de Barcelona, SPAIN
^* Corresponding Author

Abstract

The current paper aims to identify the mathematical connections activated by 10 Mexican high school students while solving mathematical tasks that involve the exponential and logarithmic function. We used the Expanded Mathematical Connections Model (EMCM) and the Onto-Semiotic Approach of Cognition and Mathematical Instruction (OSA) as theoretical frameworks. Task-based interviews were used to collect data that was analyzed using thematic and onto-semiotic analyses. It was found that the connection of reversibility is essential for achieving students’ full understanding of the existent relationship between the exponential and logarithmic function; however, this requires a network of connections.

Keywords

exponential function
logarithmic function
mathematical connections
mathematical practice

License

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

https://doi.org/10.29333/ejmste/11126

EURASIA J Math Sci Tech Ed, 2021 - Volume 17 Issue 9, Article No: em1998

Publication date: 06 Aug 2021

Article Views: 1397

Article Downloads: 566

Open Access References How to cite this article

References

Bingölbali, E., & Coşkun, M. (2016). A proposed conceptual framework for enhancing the use of making connections skill in mathematics teaching. Education and Science, 41(183), 233-249. https://doi.org/10.15390/EB.2016.4764
Borji V., Font, V., Alamolhodaei, H., & Sánchez, A. (2018). Application of the complementarities of two theories, APOS and OSA, for the analysis of the university students’ understanding on the graph of the function and its derivative. Eurasia Journal of Mathematics Science and Technology Education, 14(6), 2301-2315. https://doi.org/10.29333/ejmste/89514
Braun, V., & Clarke, V. (2012). Thematic analysis. In H. Cooper (Ed.), Handbook of research methods in psychology (pp. 57-71). American Psychological Association. https://doi.org/10.1037/13620-004
Breda, A., Hummes, V., da Silva, R. S., & Sánchez, A. (2021). El papel de la fase de observación de la implementación en la metodología estudio de clases [The role of the observation phase of implementation in the lesson study methodology]. Bolema, 35(69), 263-288. https://doi.org/10.1590/1980-4415v35n69a13
Breda, A., Pino-Fan, L., & Font, V. (2017). Meta didactic-mathematical knowledge of teachers: criteria for the reflection and assessment on teaching practice. Eurasia Journal of Mathematics Science and Technology Education, 13(6), 1893-1918. https://doi.org/10.12973/eurasia.2017.01207a
Businskas, A. M. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections (Unpublished dissertation), Faculty of Education, Simon Fraser University, Canada.
Campo-Meneses, K., & García-García, J. (2020). Explorando las conexiones matemáticas asociadas a la función exponencial y logarítmica en estudiantes universitarios colombianos [Exploring the mathematical connections associated with the exponential and logarithmic function in Colombian university students]. Educación Matemática 32(3), 209-240. http://doi.org/10.24844/EM3203.08
Eli, J. A., Mohr-Schroeder, M. J., & Lee, C. W. (2011). Exploring mathematical connections of prospective middle-grades teachers through card-sorting tasks. Mathematics Education Research Journal, 23(3), 297-319. https://doi.org/10.1007/s13394-011-0017-0
Eli, J. A., Mohr-Schroeder, M. J., & Lee, C. W. (2013). Mathematical connection and their relationship to mathematics knowledge for teaching geometry. School Science and Mathematics, 113(3), 120-134. https://doi.org/10.1111/ssm.12009
Escobar, N. V. (2014). Elementos históricos para la enseñanza de la función logarítmica en la educación básica [Historical elements for the teaching of the logarithmic function in basic education]. Revista Brasileira de História da Matemática, 14(29), 83-115.
Ferrari-Escolá, M., Martínez, G., & Méndez-Guevara, M. (2016). “Multiply by adding”: Development of logarithmic-exponential covariational reasoning in high school students. Journal of Mathematical Behavior, 42(2016), 92-108. https://doi.org/10.1016/j.jmathb.2016.03.003
Font, V., Godino, J. D., & Gallardo, J. (2013). The emergence of objects from mathematical practices. Educational Studies in Mathematics, 82, 97-124. https://doi.org/10.1007/s10649-012-9411-0
García, J. (2018). Conexiones matemáticas y concepciones alternativas asociadas a la derivada y a la integral en estudiantes del preuniversitario [Mathematical connections and alternative conceptions associated with the derivative and the integral in pre-university students] (Unpublished doctoral dissertation), Autonomous University of Guerrero, México.
García-García, J., & Dolores-Flores, C. (2018). Intra-mathematical connections made by high school students in performing Calculus tasks. International Journal of Mathematical Education in Science and Technology, 49(2), 227-252. https://doi.org/10.1080/0020739X.2017.1355994
García-García, J., & Dolores-Flores, C. (2021). Pre-university students’ mathematical connections when sketching the graph of derivative and antiderivative functions. Mathematics Education Research Journal, 33(1), 1–22. https://doi.org/10.1007/s13394-019-00286-x
García-García, J., & Dolores-Flores, C. (2020). Exploring pre-university students´ mathematical connections when solving Calculus application problems. International Journal of Mathematical Education in Science and Technology, 1-25. http://doi.org/10.1080/0020739X.2020.1729429.
Generalitat de Catalunya. Currículum Ensenyament Secundària Obligatòria. Àmbit de Matemàtiques [Compulsory Secondary Education Curriculum. Field of Mathematics.]. Decret 187/2015 DOGC núm. 6945 – 28.8.2015.
Godino, J. D. Batanero, C. & Font, V. (2019). The onto-semiotic approach: Implications for the prescriptive character of didactics. For the Learning of Mathematics, 39 (1), 37-42.
Goldin, G. A. (2000). A scientific perspective on structured, task-based interviews in mathematics education research. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 517-545). Lawrence Erlbaum Associates.
Gruver, J. (2018). A trajectory for developing conceptual understanding of logarithmic relationships. Journal of Mathematical Behavior, 50, 1-22. https://doi.org/10.1016/j.jmathb.2017.12.003
Jaijan, W., & Loipha, S. (2012). Making mathematical connections with transformations using open approach. HRD Journal, 3(1), 91-100.
Koestler, C., Felton, M., Bieda, K., & Otten, S., (2013). Connecting the NCTM process standards and the CCSSM practices. National Council of Teacher of Mathematics United States of America.
Kuper, E., & Carlson, M. (2020). Foundational ways of thinking for understanding the idea of logarithm. Journal of Mathematical Behavior, 57, 100740, https://doi.org/10.1016/j.jmathb.2019.100740
Mhlolo, M. K. (2012). Mathematical connections of a higher cognitive Level: A tool we may use to identify these in practice. African Journal of Research in Mathematics, Science and Technology Education, 16(2), 176-191. https://doi.org/10.1080/10288457.2012.10740738
Moreno, N., Angulo, R., & Reducindo, I. (2018). Mapas conceptuales híbridos para la enseñanza de la física y matemática en el aula [Hybrid concept maps for teaching physics and mathematics in the classroom]. Innovación e Investigación en Matemática Educativa, 3(1), 113-130.
MEN. (1998). Lineamientos Curriculares de Matemáticas [Mathematics Curriculum Guidelines]. Ministerio de Educación Nacional.
NCTM. (2000). Principles and standards for school mathematics.
NCTM. (2013). Connecting the NCTM process standards and the CCSSM practices.
Rodríguez-Nieto, C., Rodríguez-Vásquez, F. M., & Font, V. (2020). A new view about connections. The mathematical connections established by a teacher when teaching the derivative. International Journal of Mathematical Education in Science and Technology, 1-26. https://doi.org/10.1080/0020739X.2020.1799254
Rodríguez-Nieto, C., Font, V., Borji, V., & Rodríguez-Vasquez, F. (2021). Mathematical connections from a networking theory between extended theory of Mathematical Connections and Onto-semiotic approach. International Journal of Mathematical Education in Science and Technology, 1-27. https://doi.org/10.1080/0020739X.2021.1875071
Rondero, C., & Font, V. (2015) Articulación de la complejidad matemática de la media aritmética [Articulation of the mathematical complexity of the arithmetic mean]. Enseñanza de las Ciencias, 33(2), 29-49. https://doi.org/10.5565/rev/ensciencias.1386
SEP. (2017). Programa de estudios del componente básico del marco curricular común de la educación media superior. Asignatura: Cálculo diferencial [Study program of the basic component of the common curricular framework of upper secondary education. Subject: Differential Calculus]. http://www.sems.gob.mx/work/models/sems/Resource/12615/5/images/BT_Calculo_Diferencial.pdf
Sureda, P., & Otero, M. (2013). Estudio sobre el proceso de conceptualización de la función exponencial [Study on the process of conceptualization of the exponential function]. Educación Matemática, 25(2), 89-118.
Weber, K. (2002). Students’ understanding of exponential and logarithmic functions. In D. Quinney (Ed.), Proceedings of the 2nd international Conference on the Teaching of Mathematics (pp. 1-7). John Wiley & Sons.

How to cite this article

APA

Campo-Meneses, K. G., Font, V., García-García, J., & Sánchez, A. (2021). Mathematical Connections Activated in High School Students’ Practice Solving Tasks on the Exponential and Logarithmic Functions. Eurasia Journal of Mathematics, Science and Technology Education, 17(9), em1998. https://doi.org/10.29333/ejmste/11126

Vancouver

Campo-Meneses KG, Font V, García-García J, Sánchez A. Mathematical Connections Activated in High School Students’ Practice Solving Tasks on the Exponential and Logarithmic Functions. EURASIA J Math Sci Tech Ed. 2021;17(9):em1998. https://doi.org/10.29333/ejmste/11126

AMA

Campo-Meneses KG, Font V, García-García J, Sánchez A. Mathematical Connections Activated in High School Students’ Practice Solving Tasks on the Exponential and Logarithmic Functions. EURASIA J Math Sci Tech Ed. 2021;17(9), em1998. https://doi.org/10.29333/ejmste/11126

Chicago

Campo-Meneses, Karen Gisel, Vicenç Font, Javier García-García, and Alicia Sánchez. "Mathematical Connections Activated in High School Students’ Practice Solving Tasks on the Exponential and Logarithmic Functions". Eurasia Journal of Mathematics, Science and Technology Education 2021 17 no. 9 (2021): em1998. https://doi.org/10.29333/ejmste/11126

Harvard

Campo-Meneses, K. G., Font, V., García-García, J., and Sánchez, A. (2021). Mathematical Connections Activated in High School Students’ Practice Solving Tasks on the Exponential and Logarithmic Functions. Eurasia Journal of Mathematics, Science and Technology Education, 17(9), em1998. https://doi.org/10.29333/ejmste/11126

MLA

Campo-Meneses, Karen Gisel et al. "Mathematical Connections Activated in High School Students’ Practice Solving Tasks on the Exponential and Logarithmic Functions". Eurasia Journal of Mathematics, Science and Technology Education, vol. 17, no. 9, 2021, em1998. https://doi.org/10.29333/ejmste/11126