Mathematical Connections Related to Exponential and Logarithmic Functions: A Literature Review
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Published:
Jul 31, 2023
Keywords:
Exponential function, Logarithmic function, Mathematical Connections, Literature review
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Abstract
This paper reports a review of the Mathematics Education literature related to exponential and logarithmic functions and mathematical connections. Mainly, it seeks to answer the question: What is the current state of research related to exponential and logarithmic functions and mathematical connections in the field of Mathematics Education? To answer it, the systematic review was used as a method, through which a search for research focused on the preselected theme was carried out and analyzed taking into account, mainly, the objective, theoretical approach, contribution, and the reported results. This allowed, among other things, to identify what had been done to date and what would be viable studies to carry out. The results indicate that there is still much to explore in the line of mathematical connections, in addition to the need to carry out designs close to the teacher's practice, which promotes the understanding of exponential and logarithmic functions in students, based on the making of mathematical connections.
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RANGE: Jurnal Pendidikan Matematika
References
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Campo-Meneses, K. G., & Cruz, G. (2020). Caracterización de la práctica de una profesora al implementar un diseño sobre la función exponencial que integra GeoGebra [Characterization of the practice of a teacher when implementing a design on the exponential function that integrates GeoGebra]. Paradigma, XLI(Extra 2), 125–146. https://orcid.org/0000-0001-7483-3134https://orcid.org/0000-0001-7391-9462
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), 1–14. https://doi.org/10.29333/ejmste/11126
Campo-Meneses, K. G., & 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. https://doi.org/10.24844/EM3203.08
Campo-Meneses, K. G., & García-García, J. (2021). La comprensión de las funciones exponencial y logarítmica: una mirada desde las Conexiones Matemáticas y el Enfoque Ontosemiótico [The understanding of exponential and logarithmic functions: a look from the Mathematical Connections and the Ontosemiotic Approach]. PNA, 16(1), 25–56. https://doi.org/10.30827/pna.v16i1.15817
Dans-moreno, E., Monserrat-Vásquez, F., & García-García, J. (2022). Conexiones Matemáticas asociadas a las ecuaciones diferenciales ordinarias de primer orden [Mathematical connections associated with first order ordinary differential equations.]. PNA. Revista de Investigación en Didáctica de la Matemática, 17(1), 25–50. https://doi.org/https://doi.org/10.30827/pna.v17i1.23748
De Gamboa, G., Caviedes, S., & Badillo, E. (2022). Mathematical Connections and the Mathematics Teacher’s Specialised Knowledge. Mathematics, 10, 2–24. https://doi.org/10.3390/math10214010
de la Fuente, A., & Deulofeu, J. (2022). Uso de las conexiones entre representaciones por parte del profesor en la construcción del lenguaje algebraico [Use of connections between representations by the teacher in the construction of algebraic language]. Bolema - Mathematics Education Bulletin, 36(72), 389–410. https://doi.org/10.1590/1980-4415v36n72a17
Diana, N., Suryadi, D., & Dahlan, J. A. (2020). Analysis of students’ mathematical connection abilities in solving problem of circle material: Transposition study. Journal for the Education of Gifted Young Scientists, 8(2), 829–842. https://doi.org/10.17478/JEGYS.689673
Dolores-Flores, C., Rivera-López, M. I., & García-García, J. (2019). Exploring mathematical connections of pre-university students through tasks involving rates of change. International Journal of Mathematical Education in Science and Technology, 50(3), 369–389. https://doi.org/10.1080/0020739X.2018.1507050
Foster, J., & Lee, H. (2021). Prospective Teachers’ Pedagogical Considerations of Mathematical Connections: A Framework to Motivate Attention to and Awareness of Connections. Mathematics Teacher Education and Development, 23.4, 95–118.
Frketic, M. A., Berk, D., & Rossi, T. (2019). An Investigation into College Students’ Learning about Logarithmic Functions: A Thorny problem. Psychology and Behavioral Science International Journal, 10(4). https://doi.org/10.19080/pbsij.2019.10.555792
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. (2021a). 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. (2021b). Exploring pre-university students’ mathematical connections when solving Calculus application problems. International Journal of Mathematical Education in Science and Technology, 52(6), 912–936. https://doi.org/10.1080/0020739x.2020.1729429
García-García, J., Hernández-Yañez, M., & Rivera-López, M. (2022). Conexiones matemáticas promovidas en los planes y programas de estudio mexicanos de nivel secundaria y media superior sobre el concepto de ecuación cuadrática [Mathematical connections promoted in the Mexican plans and study programs of secondary and upper secondary level on the concept of quadratic equation]. IE Revista de Investigación Educativa de la REDIECH, 13, 1–20. https://doi.org/10.33010/ie_rie_rediech.v13i0.1485
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
Hatisaru, V. (2022). Mathematical connections established in the teaching of functions. Teaching Mathematics and its Applications: An International Journal ofthe IMA (2022), 1–21. https://doi.org/https://doi.org/10.1093/teamat/hrac013 Advance
Hernández-Yañez, M. E., García-García, J., & Campo-Meneses, K. G. (2023). Conexiones matemáticas asociadas al concepto de ecuación cuadrática que establecen futuros profesores mexicanos de matemáticas [Mathematical connections associated with the concept of quadratic equation established by future Mexican mathematics teachers.]. Uniciencia, 37(1), 1–26. https://doi.org/http://dx.doi.org/10.15359/ru.37-1.13
Jesson, J. K., Matheson, L., & Lacey, F. M. (2011). Doing your Literature Review (1a ed.). SAGE. https://doi.org/10.4135/9781473921856.n6
Kenedi, A. K., Helsa, Y., Ariani, Y., Ainil, M., & Hendri, S. (2019). Mathematical connection of elementary school students to solve mathematical problems. Journal on Mathematics Education, 10(1), 69–79. https://doi.org/10.22342/jme.10.1.5416.69- 80
Kleden, M. A., Sugi, Y., & Samo, D. D. (2021). Analysis of Mathematical Connections Ability on Junior High School Students. International Journal of Educational Management and Innovation, 2(3), 261. https://doi.org/10.12928/ijemi.v2i3.3785
Kuper, E., & Carlson, M. (2020). Foundational ways of thinking for understanding the idea of logarithm. Journal of Mathematical Behavior, 57. https://doi.org/10.1016/j.jmathb.2019.100740
Lagos, J. (2020). Validation of module on exponential and logarithmic functions using the understanding by design lesson plan for grade 11 mathematics students. African Educational Research Journal, 8(2), 262–271. https://doi.org/10.30918/AERJ.82.20.006
Ministerio de Educación Nacional (MEN). (1998). Lineamientos curriculares [Curricular guidelines]. MEN.
Ministerio de Educación Nacional [MEN]. (2006). Estándares Básicos de Competencias en Matemáticas [Basic Competence Standards in Mathematics]. MEN.
Ministry of National Education. (2013). Secondary level mathematics curriculum: Grades 9–12. Directorate of State Books.
Mpofu, S., & Mudaly. (2020). Grade 11 Rural Learners Understanding of Functions: A Commognition Perspective. African Journal of Research in Mathematics, Science and Technology Education, 24(2), 156–168. https://doi.org/https://doi.org/10.1080/18117295.2020.1798670
National Council of Teacher of Mathematics [NCTM]. (2013). Connecting the NCTM process standards and the CCSSM practices. NCTM.
Navarro, C., & Ramirez, M. (2018). Mapeo sistemático de la literatura sobre evaluación docente [Systematic mapping of the literature on teacher evaluation] (2013-2017). Educação e Pesquisa, 44, 1–22. https://doi.org/https://doi.org/10.1590/S1678-4634201844185677
Oviedo, A. F., & Lizárraga, A. (2022). Revisión de la literatura sobre evaluación de la formación continua de docentes en Matemáticas [Review of the literature on assessment of the continuous training of teachers in Mathematics]. Educacion Matematica, 34(1). https://doi.org/https://doi.org/10.24844/EM3401.05
Payton, S. (2019). Fostering mathematical connections in introductory linear algebra through adapted inquiry. ZDM - Mathematics Education, 51(7), 1239–1252. https://doi.org/10.1007/s11858-019-01029-9
Petticrew, M., & Roberts, H. (2006). Systematic Reviews in the Social Sciences. Blackwell Publishing. https://doi.org/10.1002/9780470754887
Qohar, A., & Rozak, A. (2021). Implementation of Think Pair Share (TPS) Cooperative Learning Model to Improve Mathematical Connection Ability. Journal of Education Research and Evaluation, 5(1), 87. https://doi.org/10.23887/jere.v5i1.24930
Quilang, L. J. L., & Lazaro, L. L. (2022). Mathematical connections made during investigative tasks in statistics and probability. International Journal of Evaluation and Research in Education, 11(1), 239–249. https://doi.org/10.11591/ijere.v11i1.21730
Rahmawati, D., Budiyono, & Saputro, D. R. S. (2019). Analysis of student’s mathematical connection ability in linear equation system with two variables. Journal of Physics: Conference Series, 1211(1). https://doi.org/10.1088/1742-6596/1211/1/012107
Rodríguez-Nieto, C. A., Cervantes-Barraza, J. A., & Font, V. (2023). Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories. Eurasia Journal of Mathematics, Science and Technology Education, 19(5). https://doi.org/10.29333/ejmste/13157
Rodríguez-Nieto, C. A., & Alsina, Á. (2022). Networking Between Ethnomathematics, STEAM Education, and the Globalized Approach to Analyze Mathematical Connections in Daily Practices. Eurasia Journal of Mathematics, Science and Technology Education, 18(3), 1–22. https://doi.org/10.29333/ejmste/11710
Rodríguez-Nieto, C. A., Font, V., Borji, V., & Rodríguez-Vásquez, F. M. (2021). Mathematical connections from a networking of theories 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
Rodríguez-Nieto, C. A., 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. A., Rodríguez-Vásquez, F. M., Font, V., & Morales-Carballo, A. (2021). Una visión desde la red de teorías TAC-EOS sobre el papel de las conexiones matemáticas en la comprensión de la derivada [A vision from the TAC-EOS networking between theories on the role of mathematical connections in understanding the derivative]. Revemop, 3, 1–32. https://doi.org/10.33532/revemop.e202115
Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., & García-García, J. (2021). Pre-service math teachers’ mathematical connections in the context of problem-solving about the derivative. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 12(1), 202–220. https://doi.org/10.16949/turkbilmat.797182
Saleh, S., Purwanto, P., Sudirman, S., Hidayanto, E., & Susiswo, S. (2018). Elementary School Teachers’ Mathematical Connections in Solving Trigonometry Problem. Research in Social Sciences and Technology, 3(3), 32–41. https://doi.org/https://doi.org/10.46303/ressat.03.03.3
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