La comprensión de las demostraciones matemáticas. Un estudio de revisión

The comprehension of mathematical proof. A review study

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Cesar Augusto Hernández-Suárez
Raúl Prada-Núñez
David Andree Parada-Carrillo
Laura Daniela Pumarejo-García
Resumen

En este artículo se realizó una revisión de la literatura relacionada con la comprensión de las demostraciones matemáticas en el ámbito de la educación superior. Para esto, se parte del concepto de comprensión, y posteriormente se vincula al de las demostraciones matemáticas mediante exploración de investigaciones que la hayan estudiado. Estos artículos han sido agrupados en cuatro categorías: investigaciones centradas en el cambio de presentación del contenido, investigaciones centradas en el cambio del modelo de evaluación, modelos cognitivos que trabajan la comprensión de las demostraciones y estudios que han aplicado el modelo de evaluación en educación superior. En este análisis se manifiesta la necesidad de crear líneas de investigación que se enfoquen en la comprensión de manera similar a las demás actividades demostrativas. 

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Ainsworth, S., & Burcham, S. (2007). The impact of text coherence on learning by self-explanation. Learning and Instruction, 17(3), 286–303. doi: 10.1016/j.learninstruc.2007.02.004 DOI: https://doi.org/10.1016/j.learninstruc.2007.02.004

Alcock, L. (2009). e-Proofs: Student experience of online resources to aid understanding of mathematical proofs. In Proceedings of the 12th Conference on Research in Undergraduate Mathematics Education. Raleigh, NC: Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education DOI: https://doi.org/10.11120/msor.2009.09040007

Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Roa Fuentes, S., Trigueros, M., & Weller, K. (2014). APOS Theory. doi:10.1007/978-1-4614-7966-6 DOI: https://doi.org/10.1007/978-1-4614-7966-6

Balacheff, N. (1987). Processus de preuve et situations de validation (Proving Processes and Situations for Validation). Educational Studies in Mathematics, 18(2), 147-176. Retrieved January 18, 2021, from http://www.jstor.org/stable/3482413 DOI: https://doi.org/10.1007/BF00314724

Belin, M., & Akar, G. K. (2020). The effect of quantitative reasoning on prospective mathematics teachers’ proof comprehension: The case of real numbers. The Journal of Mathematical Behavior, 57, 100757. doi: 10.1016/j.jmathb.2020.100757 DOI: https://doi.org/10.1016/j.jmathb.2020.100757

Ben-Zvi, D. & Sfard, A. (2007). Ariadne's thread, Daedalus' wings, and the learner's autonomy. Education & Didactique, 1(3), 117-134. Recuperado de: https://journals.openedition.org/educationdidactique/241?lang=es# DOI: https://doi.org/10.4000/educationdidactique.241

Conradie, J., & Frith, J. (2000). Comprehension tests in mathematics. Educational Studies in Mathematics, 42(3), 225-235. Doi: https://doi.org/10.1023/A:1017502919000 DOI: https://doi.org/10.1023/A:1017502919000

Guirao-Goris,J.A; Olmedo Salas,A; Ferrer Ferrandis, E.(2008) El artículo de revisión. Revista Iberoamericana de Enfermería Comunitaria, 1, 1, 6. Disponible en http://revista.enfermeriacomunitaria.org/articuloCompleto.php?ID=7. Consultado el 23/07/2008

Harel, G. & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. American Mathematical Society, 7, 234-283. Recuperado de: https://math.ucsd.edu/~harel/Students%27%20Proof%20Schemes.pdf DOI: https://doi.org/10.1090/cbmath/007/07

Harel, G. & Sowder, L. (2007) Toward Comprehensive Perspectives on the Learning and Teaching of Proof. In: Lester, F., Ed., Second Handbook of Research on Mathematics Education. Recuperado de: https://math.ucsd.edu/~harel/TowardComprehensivePerspective.pdf

Hersh, R. (1993). Proving is convincing and explaining. Educational Studies in Mathematics, 24(4), 389-399 DOI: https://doi.org/10.1007/BF01273372

Hodds, Alcock, & Inglis. (2014). Self-Explanation Training Improves Proof Comprehension. Journal for Research in Mathematics Education, 45(1), 62-101. doi:10.5951/jresematheduc.45.1.0062 DOI: https://doi.org/10.5951/jresematheduc.45.1.0062

Kolahdouz, F., Radmehr, F., & Alamolhodaei, H. (2019). Exploring students’ proof comprehension of the Cauchy Generalized Mean Value Theorem. Teaching Mathematics and Its Applications: An International Journal of the IMA, 1-20. doi:10.1093/teamat/hrz016 DOI: https://doi.org/10.1093/teamat/hrz016

Leron, U. (1983). Structuring mathematical proofs. American Mathematical Monthly, 90(3), 174-184 DOI: https://doi.org/10.2307/2975544

Mejia-Ramos, J. P., Fuller, E., Weber, K., Rhoads, K., & Samkoff, A. (2012). An assessment model for proof comprehension in undergraduate mathematics. Educational Studies in Mathematics, 79(1), 3–18. doi:10.1007/s10649-011-9349-7 DOI: https://doi.org/10.1007/s10649-011-9349-7

Mejia-Ramos, J. P., & Inglis, M. (2009). Argumentative and proving activities in mathematics education research. In F.-L. Lin, F.-J. Hsieh, G. Hanna, & M. Recuperado de: http://140.122.140.1/~icmi19/files/Volume_2.pdf

Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in Mathematics, 27(3), 249–266. doi:10.1007/bf01273731 DOI: https://doi.org/10.1007/BF01273731

Neuhaus, S., & Rach, S. (2019). Proof comprehension of undergraduate students and the relation to individual characteristics. In Eleventh Congress of the European Society for Research in Mathematics Education (No. 31). Freudenthal Group; Freudenthal Institute; ERME

Pfeiffer, K. (2011). Features and purposes of mathematical proofs in the view of novice students: observations from proof validation and evaluation performances (Doctoral dissertation, National University of Ireland, Galway)

Rach, S., & Heinze, A. (2017). The transition from school to university in mathematics: Which influence do school-related variables have. International Journal of Science and Mathematics Education, 15(7), 1343-1363. https://doi.org/10.1007/s10763-016-9744-8 DOI: https://doi.org/10.1007/s10763-016-9744-8

Real Academia Española. (s.f.). Comprensión. En Diccionario de la lengua española Recuperado en 01 de abril 2021, de https://dle.rae.es/comprensi%C3%B3n

Rowland, T. (2001). Generic proofs in number theory. In S. Campbell and R. Zazkis (Eds.), Learning and teaching number theory: Research in cognition and instruction. (pp. 157-184). Westport, CT: Ablex Publishing

Sánchez Upegui, A. A. (2011). Manual de redacción académica e investigativa: cómo escribir, evaluar y publicar artículos. Fundación Universitaria Católica de Norte

Selden, A., & Selden, J. (2017). A comparison of proof comprehension, proof construction, proof validation and proof evaluation. In Proceedings of the Conference on Didactics of Mathematics in Higher Education as a Scientific Discipline (pp. 339-345)

Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of well-taught mathematics courses. Educational psychologist, 23(2), 145-166 DOI: https://doi.org/10.1207/s15326985ep2302_5

Sparks, J. R. (2012). Language/Discourse Comprehension and Understanding. In Encyclopedia of the Sciences of Learning (pp. 1713-1717). Norbert M. Seel. https://doi.org/10.1007/978-1-4419-1428-6_100 DOI: https://doi.org/10.1007/978-1-4419-1428-6_1005

Strauss, A., & Corbin, J. M. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Sage Publications, Inc

Thompson, P. W. (1994). The development of the concept of speed and its relationship to concepts of rate. In G. Vergnaud, G. Harel, & J. Coufrey (Eds.). The development of multiplicative reasoning in the learning of mathematics (pp. 179–234). SUNY Press.

Weber, K., & Mejia-Ramos, J. P. (2011). Why and how mathematicians read proofs: an exploratory study. Educational Studies in Mathematics, 76(3), 329–344. doi:10.1007/s10649-010-9292-z DOI: https://doi.org/10.1007/s10649-010-9292-z

Weber, K. (2015). Effective Proof-Reading Strategies for Comprehending Mathematical Proofs. International Journal of Research in Undergraduate Mathematics Education, 1(3), 289–314. doi:10.1007/s40753-015-0011-0 DOI: https://doi.org/10.1007/s40753-015-0011-0

Yang, K.-L., & Lin, F.-L. (2007). A model of reading comprehension of geometry proof. Educational Studies in Mathematics, 67(1), 59–76. doi:10.1007/s10649-007-9080-6 DOI: https://doi.org/10.1007/s10649-007-9080-6

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