Teaching linear algebra from a qualitative look at systems of linear equations
Article Sidebar
Main Article Content
A reflection on Leonhard Euler's article "On an apparent contradiction in the theory of curved lines" is presented, showing the proximity of this work with some of the main concepts of linear algebra. A non-exhaustive documentary approach is applied, to point out, both in the historical context of mathematics and in the classroom, how the appearance of new solution methods (algorithms) can have a retarding effect on the construction of new knowledge, we finally characterize and present the epistemological obstacle that we call “The paradigm of the solution”.
Artigue, M. (2018). Epistemología y didáctica. El Cálculo y Su Enseñanza, 11, 1–31. https://recacym.org/index.php/recacym/article/view/26
Bourbaki, N. (2007). Elements d’histoire des matehmatique. Springer. https://doi.org/10.1007/978-3-540-33981-6
Boyer, C. B. (2001). Historia de la matemática. Alianza Editorial. S. A.
Brousseau, G. (2002). Theory of Didactical Situations in Mathematics. Mathematics Education Library. https://doi.org/10.1007/0-306-47211-2
Chavarría Bueno, S. L. (2019). Historia del concepto de espacio vectorial, con consideraciones sobre la enseñanza del álgebra lineal en la Licenciatura en Matemáticas de la Universidad del Valle [tesis de maestría, Universidad del Valle]. Repositorio institucional. https://bibliotecadigital.univalle.edu.co/handle/10893/14091
Bix, R. (2006). Conics and Cubics. A Concrete Introduction to Algebraic Curves. Springer. https://doi.org/10.1007/0-387-39273-4_3
Dogan, H. (2019). Some aspects of linear independence schemas. ZDM, 51, 1169–1181. https://doi.org/10.1007/s11858-019-01082-4
Dorier, J.-L. (2000). Epistemological Analysis of the Genesis of the Theory of Vector Spaces. In J.-L. Dorier (Ed.), On the Teaching of Linear Algebra (pp. 3–81). https://doi.org/10.1007/0-306-47224-4_1
Dorier, J.-L. (2002). On the Teaching of Linear Algebra. Mathematics Education Library. https://doi.org/10.1007/0-306-47224-4
Euler, L. (1750). Sur une contradiction apparente dans la doctrine des lignes courbes. Mémories de l’académie Des Sciences de Berlin, 4, 219–233.
Grossman, S. I., y Flores Godoy, J. J. (2012). Álgebra Lineal (7° ed).The McGraw-Hill. https://www.academia.edu/39168811/%C3%81lgebra_lineal_Stanley_I_Grossman_S_and_Jos%C3%A9_Job_Flores_Godoy_7ED
Howson, A. G. (1974). Review of Mathematical Thought from Ancient to Modern Times. The Mathematical Gazette, 58(403), 58–59. https://doi.org/10.2307/3615488.
Kazunga, C. y Bansilal, S. (2020). An APOS analysis of solving systems of equations using the inverse matrix method. Educational Studies in Mathematics, 103, 339-358. https://doi.org/10.1007/s10649-020-09935-6
Kolman, B., y Hill, D. R. (2006). Álgebra Lineal (8° ed.). Pearson Education, Inc. https://www.academia.edu/42188978/Algebra_Lineal_Bernard_Kolman_y_David_R_Hill_Octava_Edici%C3%B3n
Martínez, H. J., y Sanabria, A. M. (2014). Álgebra Lineal (Primera). Programa Editorial Universidad del Valle. https://programaeditorial.univalle.edu.co/gpd-algebra-lineal-9789587650945-633217fc97763.html
Monroy Guzmán, L. A. (2011). El Álgebra Lineal en el contexto histórico de las Matemáticas [tesis de maestría, Universidad del Valle]. Retrieved from https://tinyurl.com/wqubabm
Oktaç, A. (2018). Conceptions About System of Linear Equations and Solution. In S. Stewart, C. Andrews-Larson, A. Berman, & M. Zandieh (Eds.), Challenges and Strategies in Teaching Linear Algebra (pp. 71–101). https://doi.org/10.1007/978-3-319-66811-6_4
Parraguez, M. (2009). Evolución Cognitiva del Concepto de Espacio Vectorial. [tesis doctoral, Instituto Politécnico Nacional]. Repositorio Dspace https://tesis.ipn.mx/handle/123456789/11764
Sierpińska, A. (1988). Epistemological obstacles in teaching mathematics. Didactica Mathematicae, 8(1). https://eudml.org/doc/295203
Simon, M. A. (2017). Explicating mathematical concept and mathematicalconception as theoretical constructs for mathematics education research. Educational Studies in Mathematics, 94(2), 117–137. https://doi.org/10.1007/s10649-016-9728-1
Stewart, S., y Thomas, M. O. J. (2019). Student perspectives on proof in linear algebra. ZDM, 51(7), 1069–1082. https://doi.org/10.1007/s11858-019-01087-z
Turgut, M. (2021). Reinventing Geometric Linear Transformations in a Dynamic Geometry Environment: Multimodal Analysis of Student Reasoning. International Journal of Science and Mathematics Education, 20. https://doi.org/10.1007/s10763-021-10185-y
Downloads
Accepted 2022-12-12
Published 2023-02-15
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.