Levels of proportional reasoning and microworlds. A study on unitary tele-secondary education
DOI:
https://doi.org/10.15359/ru.38-1.13Keywords:
Education, microworld, unitary tele-secondary education, school mathematics, proportional reasoningAbstract
[Objective] Proportional reasoning is a type of complex thinking that involves recognizing comparisons such as the covariation between magnitudes and multiple comparisons. The aim of this study was to analyze proportional reasoning of students from unitary tele-secondary education using the levels proposed by Karplus (1983) through a microworld like GeoGebra. In the microworld, students can explore and construct meanings about mathematical objects. [Methodology] Four activities were designed in GeoGebra, which were administered to 18 students from a unitary tele-secondary school, an educational modality in Mexico. [Results] It was found that participants are at initial levels that correspond to additive, qualitative, or erroneous structures to justify their procedures. The more complex levels of proportional reasoning, related to the use of ratios and constants of proportionality, were achieved when students interacted with each other and with the microworld. The reasoning levels are not mutually exclusive, as students can reason differently depending on the situation and the software's capabilities. [Conclusions] The use of microworlds in exploring proportional reasoning enables actions that cannot be carried out with pencil and paper, providing opportunities to interact with moving constructions. Additionally, it fosters interactions that reinforce or build collective knowledge.
References
Barros, A. y Stivam E. (2012). O software GeoGebra na Concepção de Micromundo. Revista Do Instituto GeoGebra Internacional De São Paulo, 1(1), 184-194.
Block, D., Ramírez, M. y Reséndiz, L. (2015). Las ayudas personalizadas como recurso de enseñanza de las matemáticas en un aula multigrado. Un estudio de caso. Revista Mexicana de Investigación Educativa, 20(66), 711-735.
Boix, R. (2011). ¿Qué queda de la escuela rural? Algunas reflexiones sobre la realidad pedagógica del aula multigrado. Profesorado. Revista de Currículum y Formación de Profesorado, 15(2), 13-23.
Bustos Jiménez, A. M. (2013). El espacio y el tiempo en la escuela rural: algunas consideraciones sobre la didáctica multigrado. Investigación en la escuela, 79, 31-41.
Butto, C., Fernández, J., Araujo, D. C. y Ramírez, A. I. (2019). El razonamiento proporcional en educación básica. Horizontes Pedagógicos. https://doi.org/10.33881/0123-8264.hop.21204
Corro, E. S. L. y Bolaños, D. J. (2018). La relación tutora entre estudiantes en una clase multigrado de México. Nodos y Nudos, 6(45).
Fernández V. C. y Llinares C. S. (2012). Características del desarrollo del razonamiento proporcional en la educación primaria y secundaria. Enseñanza de las ciencias: revista de investigación y experiencias didácticas, 30(1), 129-142. https://doi.org/10.5565/rev/ec/v30n1.596
Flores, R. C. y Albarrán, A. M. R. (2008). La Telesecundaria, ante la sociedad del conocimiento. Revista Iberoamericana De Educación, 44(7), 1-11. https://doi.org/10.35362/rie4472187
García, E., Santiago, F. y Zepeda, G. (2019). Enseñanza de las matemáticas en escuelas multigrado y telesecundarias. En S. Otten, A.G. Candela, A. de Araujo, C. Haines y C. Munter (Eds.), Proceedings of the forty-first annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. (pp. 1751-1755). St Louis, MO: University of Missouri.
Godino, J. y Batanero, C. (2003). Proporcionalidad y su didáctica para maestros. Departamento de didáctica de las matemáticas. Universidad de Granada. 412-443.
Healy, L. y Kynigos, C. (2010). Charting the microworld territory over time: design and construction in mathematics education. Zdm–Mathematics Education, 42(1), 63-76. https://doi.org/10.1007/s11858-009-0193-5
Heller, P., Ahlgren, A., Post, T., Behr, M. J. y Lesh, R. (1989). Proportional reasoning: The effect of two context variables, rate type, and problem setting. Journal of Research in Science Teaching, 26(3), 205-220. https://doi.org/10.1002/tea.3660260303
Hoyles, C. y Noss, R. (1987). Synthesizing mathematical conceptions and their formalization through the construction of a Logo‐based school mathematics curriculum. International Journal of Mathematical Education in Science and Technology, 18(4), 581-595. https://doi.org/10.1080/0020739870180411
Karplus, R., Pulos, S. y Stage, E. (1983). Proportional reasoning of early adolescents. En R. Lesh y M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 45-90). Nueva York: Academic Press.
Lamon, S. J. (2020). Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers. https://doi.org/10.4324/9781003008057
Lesh, R., Post, T. R. y Behr, M. (1988). Proportional reasoning. En M. Behr y J. Hiebert (Eds.), Number concepts and operations in the middle grades (pp. 93-118). National Council of Teachers of Mathematics, Lawrence Erlbaum Associates.
Mejoredu. Comisión Nacional para la Mejora Continua de la Educación. (2022). Indicadores nacionales de la mejora continua de la educación en México. Cifras del ciclo escolar 2020-2021.
Mochón, S. (2012). Enseñanza del razonamiento proporcional y alternativas para el manejo de la regla de tres. Educación Matemática, 24(1), 133-157.
Modestou, M. y Gagatsis, A. (2010). Cognitive and Metacognitive Aspects of Proportional Reasoning. Mathematical Thinking and Learning, 12(1), 36-53. https://doi.org/10.1080/10986060903465822
Noss, R. y Hoyles, C. (2019). Micromundos, Construccionismo y Matemáticas. Educación Matemática, 31(2), 7-21. https://doi.org/10.24844/em3102.01
Öztürk, M., Demir, Ü. y Akkan, Y. (2021). Investigation of Proportional Reasoning Problem Solving Processes of Seventh Grade Students: A Mixed Method Research. International Journal on Social and Education Sciences, 3(1), 48-67. https://doi.org/10.46328/ijonses.66
Rizo, M. (2006). La interacción y la comunicación desde los enfoques de la psicología social y la sociología fenomenológica: breve exploración teórica. Análisis: Cuadernos de comunicación y cultura. ISSN 0211-2175, 33, 45-62.
Sánchez, E. (2013). Razones, proporciones y proporcionalidad en una situación de reparto: una mirada desde la teoría antropológica de lo didáctico. Revista latinoamericana de Investigación en Matemática Educativa, 16(1), 65-97.
Santos, L. (2006). Atención a la diversidad: Algunas bases teóricas de la didáctica multigrado. Quehacer educativo, 75, 72-79.
SEP (2017). Aprendizajes clave para la educación integral. SEP.
Weir, S. (1987). Cultivating Minds: A Logo Casebook. HarperCollins Publishers.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Shared by Journal and Authors (CC-BY-NC-ND)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors who publish with this journal agree to the following terms:
1. Authors guarantee the journal the right to be the first publication of the work as licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
2. Authors can set separate additional agreements for non-exclusive distribution of the version of the work published in the journal (eg, place it in an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
3. The authors have declared to hold all permissions to use the resources they provided in the paper (images, tables, among others) and assume full responsibility for damages to third parties.
4. The opinions expressed in the paper are the exclusive responsibility of the authors and do not necessarily represent the opinion of the editors or the Universidad Nacional.
Uniciencia Journal and all its productions are under Creative Commons Atribución-NoComercial-SinDerivadas 4.0 Unported.
There is neither fee for access nor Article Processing Charge (APC)