Formation and development of mathematical concepts: Elements for research and teaching

Armando Morales-Carballo; Miguel Díaz Cárdenas; Angie Damián Mojica

doi:10.29333/iejme/14023

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Armando Morales-Carballo ¹ ^* , Miguel Díaz Cárdenas ¹ , Angie Damián Mojica ¹

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¹ Universidad Autónoma de Guerrero, Guerrero, MEXICO^* Corresponding Author

Abstract

This article presents a theoretical-didactic perspective on the formation and development of concepts concerning mathematical objects as a result of research on didactic difficulties in dealing with concepts in school. The theoretical foundation that supports the research is based on the contributions of the materialist approach to the theory of knowledge. Specifically, an interpretation of its application in the teaching of mathematics is under investigation, specifically in the process of formation and development of concepts in the field of Euclidean geometry. However, the elements that are derived are essential for the treatment of concepts in any sub-branch of mathematics. The analysis of this process and the factors that influence the development show some fundamental elements to consider in the research activity in the field of mathematics education.

Keywords

mathematical object
concept
generalization

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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

INT ELECT J MATH ED, 2024, Volume 19, Issue 1, Article No: em0762

https://doi.org/10.29333/iejme/14023

Publication date: 01 Jan 2024

Online publication date: 14 Dec 2023

Article Views: 668

Article Downloads: 319

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References

Angulo, M. L., Arteaga, E., & Carmenates, O. A. (2020). La formación de conceptos matemáticos en el proceso de enseñanza- aprendizaje de la matemática [The formation of mathematical concepts in the teaching-learning process of mathematics]. Revista Conrado [Conrado Magazine], 16(74), 298-305.
Arteaga, E., Díaz, A., García, F., & Del Sol, J. L. (2009). Alternativas metodológicas parala formación y fijación de conceptos geométricos en la geometría plana [Methodological alternatives for the formation and fixation of geometric concepts in plane geometry]. Cuaderns Digitals [Digital Notebooks], 0(60), 1-25.
Ballester, S. (1992). Metodología de la enseñanza de la matemática [Mathematics teaching methodology]. Editorial Pueblo y Educación [People and Education Editorial].
Campistrous, L. A., & Rizo, C. (2003). Sobre la estructura didáctica y metodológica de las clases [About the didactic and methodological structure of the classes]. Instituto Central de ciencias Pedagógicas de Cuba [Central Institute of Pedagogical Sciences of Cuba].
Davýdov, V. (1982). Tipos de generalización en la enseñanza [Types of generalization in teaching]. Pueblo y Educación [People and Education].
Duval, R. (1993). Registres de représentations sémioticiques et funtionnement cognitif de la pensée [Registers of semiotic representations and cognitive functioning of thought]. Annales de Didactique et de Science Cognitives [Annals of Didactics and Cognitive Science], 1(5), 37-65.
Guétmanova, A. (1989). Lógica: Serie biblioteca del estudiante [Logic: Student library series]. Progreso.
Hernández-Gómez, J. C., Locia-Espinoza, E., Morales-Carballo, A., & Sigarreta-Almira, J. M. (2019). El contraejemplo en la elaboración de la definición de función convexa por estudiantes universitarios [The counterexample in the elaboration of the definition of a convex function by university students]. Información Tecnológica [Technological Information], 30(1), 185-202. https://doi.org/10.4067/S0718-07642019000100185
Jungk, W. (1985). Metodología de la enseñanza de la matemática [Mathematics teaching methodology]. Pueblo y Educación [People and Education].
Leontiev, A. N. (1981). Actividad, conciencia, personalidad [Activity, consciousness, personality]. Pueblo y Educación [People and Education].
Locia, E., Mederos, O. B., Sigarreta, J. M., & Villarraga, B. (2018). Aproximación teórico-metodológica a la formación de conceptos matemáticos [Theoretical-methodological approach to the formation of mathematical concepts]. Premisa [Premise], 20(29), 24-38.
Majmutov, M. (1983). La enseñanza problémica [The problematic teaching]. Pueblo y Educación [People and Education].
Morales, A., & Damián, A. (2021a). Errores y dificultades acerca de las rectas notables del triángulo. Etapa preliminar para la elaboración de trayectorias de aprendizaje [Errors and difficulties about the notable lines of the triangle. Preliminary stage for the development of learning trajectories]. UNIÓN: Revista Iberoamericana de Educación Matemática [UNION: Ibero-American Magazine of Mathematics Education], 61, 1-17.
Morales, A., & Damián, A. (2021b). Estrategia didáctica fundamentada en el uso de GeoGebra para mejorar la comprensión del concepto de semejanza de triángulos [Teaching strategy based on the use of GeoGebra to improve understanding of the concept of similarity of triangles]. Innovación Educativa [Educational Innovation], 21(18), 11-34.
Morales-Carballo, A., Damián Mojica, A., & Marmolejo Vega, J. E. (2022). Hypothetical learning trajectory for assimilating the articulated concepts of quadratic function and equation through variational ideas and the use of GeoGebra in pre-university students. International Electronic Journal of Mathematics Education, 17(2), em0678. https://doi.org/10.29333/iejme/11714
Ramos, G., & López, A. (2015). La formación de conceptos: una comparación entre los enfoques cognitivista e histórico-cultural [The formation of concepts: a comparison between cognitivist and historical-cultural approaches]. Educação e Pesquisa [Education and Research], 41(3), 615-628. https://doi.org/10.1590/S1517-9702201507135042
Rizo, C., & Campistrous, L. (2011). Algunas implicaciones de la filosofía Marxista para la enseñanza de la matemática: El caso de Cuba [Some implications of Marxist philosophy for the teaching of mathematics: The case of Cuba]. Revista Iberoamericana de Educación [Ibero-American Journal of Education], 56, 179-199. https://doi.org/10.35362/rie560516
Rubinstein, S. L. (1969). Principios de psicología general [Principles of general psychology]. Edición Revolucionaria [Revolutionary Edition].
Sierpinska, A. (1987). Humanities students and epistemological obstacles related to limits. Educational Studies in Mathematics, 18, 371-397. https://doi.org/10.1007/BF00240986
Tall, D. (1991). The psychology of advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 3-21). Kluwer. https://doi.org/10.1007/0-306-47203-1
Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In D. Tall (Ed.), Advanced mathematical thinking (pp. 65-81). Kluwer. https://doi.org/10.1007/0-306-47203-1_5
Winicki-Landman, G. (2006). Las definiciones en matemáticas y los procesos de su formulación: Algunas reflexiones [Definitions in mathematics and the processes of their formulation: Some reflections]. Acta Latinoamericana de Matemática Educativa [Latin American Educational Mathematics Act], 19, 528-537.

How to cite this article

APA

Morales-Carballo, A., Díaz Cárdenas, M., & Damián Mojica, A. (2024). Formation and development of mathematical concepts: Elements for research and teaching. International Electronic Journal of Mathematics Education, 19(1), em0762. https://doi.org/10.29333/iejme/14023

Vancouver

Morales-Carballo A, Díaz Cárdenas M, Damián Mojica A. Formation and development of mathematical concepts: Elements for research and teaching. INT ELECT J MATH ED. 2024;19(1):em0762. https://doi.org/10.29333/iejme/14023

AMA

Morales-Carballo A, Díaz Cárdenas M, Damián Mojica A. Formation and development of mathematical concepts: Elements for research and teaching. INT ELECT J MATH ED. 2024;19(1), em0762. https://doi.org/10.29333/iejme/14023

Chicago

Morales-Carballo, Armando, Miguel Díaz Cárdenas, and Angie Damián Mojica. "Formation and development of mathematical concepts: Elements for research and teaching". International Electronic Journal of Mathematics Education 2024 19 no. 1 (2024): em0762. https://doi.org/10.29333/iejme/14023

Harvard

Morales-Carballo, A., Díaz Cárdenas, M., and Damián Mojica, A. (2024). Formation and development of mathematical concepts: Elements for research and teaching. International Electronic Journal of Mathematics Education, 19(1), em0762. https://doi.org/10.29333/iejme/14023

MLA

Morales-Carballo, Armando et al. "Formation and development of mathematical concepts: Elements for research and teaching". International Electronic Journal of Mathematics Education, vol. 19, no. 1, 2024, em0762. https://doi.org/10.29333/iejme/14023