Mecanismos cognitivos inconscientes en el aprendizaje de las matemáticas: una mirada desde la Neurociencia
Unconscious cognitive mechanisms in the learning or University Mathematics: a view from Neuroscience
DOI:
https://doi.org/10.30827/retosxxi.9.2025.31195Palabras clave:
matemáticas superiores, neurociencia cognitiva, aprendizaje inconscienteResumen
Esta propuesta está orientada a la identificación de las técnicas experimentales de la neurociencia que son útiles para examinar procesos cognitivos inconscientes relacionados con algunas de las dificultades más comunes que surgen en los procesos de enseñanza y aprendizaje de conceptos matemáticos en la enseñanza superior, lo que constituye un tema de gran interés dentro de la comunidad investigativa en matemática educativa. Para lograr este objetivo, se utiliza una metodología apoyada en una investigación bibliográfica cualitativa y argumentativa, a partir de una muestra aleatoria de 100 documentos originales de las bases de datos WoS, Scopus y SciELO publicados en el período comprendido entre los años 2000 y 2022. Los resultados obtenidos muestran que las técnicas experimentales de la neurociencia examinadas, permiten el estudio de mecanismos cognitivos inconscientes relevantes en la matemática superior, enriqueciendo y contrastando al mismo tiempo, desde una base neurocientífica, los métodos desarrollados por la psicología cognitiva, así como sus aplicaciones a la matemática educativa para el estudio de procesos cognitivos, y generando así, el desarrollo de nuevas metodologías de investigación interdisciplinaria, con una visión más integral de los complejos mecanismos cognitivos que caracterizan a los procesos de aprendizaje de las matemáticas en la educación superior.
Descargas
Citas
Abrahamson, D. y Bakker, A. (2016). Making sense of movement in embodied design for mathematics learning. Cognitive Research: Principles and Implications, 1(33), 1-13. DOI:10.1186/s41235-016-0034-3. DOI: https://doi.org/10.1186/s41235-016-0034-3
Andrà, C., Lindström, P., Arzarello, F., Holmqvist, K., Robutti, O., y Sabena, C. (2015). Reading mathematics representations: An eye tracking study. International Journal of Science and Mathematics Education, 13, 237–259. DOI:10.1007/s10763-013-9484-y DOI: https://doi.org/10.1007/s10763-013-9484-y
Arrigo, G. y D’Amore, B. (2004). Otros hallazgos sobre los obstáculos en la comprensión de algunos teoremas de Georg Cantor. Educación Matemática, 16(2), 5-20. DOI: https://doi.org/10.24844/EM1602.01
Arroyo Hernández, L., Ramos Cisternas, D., Peña Bravo, D., Flores Alberto, S., Choquehuanca Subieta, Y., Campos Venegas, D. y Salgado, O. (2023). Dificultad específica de aprendizaje de las matemáticas: Evidencia disponible en Iberoamérica. Revista Chilena De Educación Matemática, 15(2), 63–74. DOI: https://doi.org/10.46219/rechiem.v15i2.124
Artigue, M. (2000). Teaching and Learning Calculus. What Can be Learned from Education Research and Curricular Changes in France? En E. Dubinsky (Ed.), Research in Collegiate Mathematics Education, IV. American Mathematical Society. DOI:10.1090/cbmath/008/01 DOI: https://doi.org/10.1090/cbmath/008/01
Arzarello, F., Paola, D. Robutti, O., y Sabena, C. (2009). Gestures as semiotic resources in the mathematics classroom. Educational Studies in Mathematics, 70(2), 97–109. DOI: https://doi.org/10.1007/s10649-008-9163-z
Bachelard, G. (2004). La formación del espíritu científico. Siglo XXI.
Bargh, J.A. y Morsella, E. (2008) The unconscious mind. Perspective in Psychological Sciences 3, 73–79. DOI: https://doi.org/10.1111/j.1745-6916.2008.00064.x
Barraza, P., Gómez, D.M., Oyarzún, F., y Dartnell, P. (2014). Long-distance neural synchrony correlates with processing strategies to compare fractions. Neuroscience letters, 567, 40-44. DOI: https://doi.org/10.1016/j.neulet.2014.03.021
Barsalou, L.W. (2007). Grounded cognition. Annual Review of Psychology, 59(1), 617–645. DOI: https://doi.org/10.1146/annurev.psych.59.103006.093639
Beesley, T., Pearson, D. y Le Pelley, M. (2019). Eye tracking as a tool for examining cognitive processes. In Biophysical measurement in experimental social science research, Academic Press, 1-30. DOI: https://doi.org/10.1016/B978-0-12-813092-6.00002-2
Bengtsson, M. (2016). How to plan and perform a qualitative study using content analysis. Nursing Plus Open, 2, 8-14. DOI: https://doi.org/10.1016/j.npls.2016.01.001
Berman, M.G., Jonides, J. y Nee, D.E. (2006). Tools of the Trade: Studying mind and brain with fMRI. SCAN, 1, 158-161. DOI: https://doi.org/10.1093/scan/nsl019
Berntson, G.G. y Cacioppo, J.T. (Eds.). (2009). Handbook of neuroscience for the behavioral sciences (vol. 1). Hoboken. John Wiley & Sons Inc. DOI: https://doi.org/10.1002/9780470478509
Boehm, O. (2014). Kant's Critique of Spinoza. New York: Oxford University Press. DOI: https://doi.org/10.1093/acprof:oso/9780199354801.001.0001
Britten, N., Campbell, R., Pope, C., Donovan, J., Morgan, M., y Pill, R. (2002). Using meta ethnography to synthesise qualitative research: A worked example. Journal of Health Services Research & Policy, 7(4), 209-215. 10.1258/135581902320432732 DOI: https://doi.org/10.1258/135581902320432732
Burgueño, J. (2022). El cerebro que aprende: Padres y Maestros. Journal of Parents and Teachers, 389, 5.
Campbell, S. (2010) Embodied minds and dancing brains: New opportunities for research in mathematics education. En B. Sriraman y L. English (Eds.), Theories of mathematics education: Seeking new frontiers, 309-332. Springer. DOI:10.1007/978-3-642-00742-2_31 DOI: https://doi.org/10.1007/978-3-642-00742-2_31
Chartrand, T.L. y Bargh, J.A. (1996) Automatic activation of impression formation and memorization goals: Nonconscious goal priming reproduces effects of explicit task instructions. Journal of Personal Social Psychology, 71:464–478. 10.1037/0022-3514.71.3.464 DOI: https://doi.org/10.1037//0022-3514.71.3.464
Chiesa, A., Serretti, A., y Jakobsen, J. C. (2013). Mindfulness: top-down or bottom-up emotion regulation strategy? Clinical Psychology Review, 33(1), 82–96. DOI: https://doi.org/10.1016/j.cpr.2012.10.006
Davou, B. (2002). Unconscious processes influencing learning. Psychodynamic Practice, 8(3), 277–294. 10.1080/1353333021000019024 DOI: https://doi.org/10.1080/1353333021000019024
De Smedt, B. y Grabner, R.H. (2016). Potential applications of cognitive neuroscience to mathematics education. ZDM, 48(3), 249-253. Debue, N. y Leemput, C. (2014). What does german load mean? An empirical contribution to the cognitive load theory. Frontier in Psychology, 5, 1099. DOI: https://doi.org/10.3389/fpsyg.2014.01099
Díaz-Barriga, F. y Hernández, G. (2010). Estrategias docentes para un aprendizaje significativo. Una interpretación constructivista (2ª ed.). McGraw-Hill Interamericana.
Díaz-Chang, T., Arredondo, E.H. (2022) La técnica de seguimiento ocular y el estudio de modelos tácitos mediante criterios subjetivos y conductuales. Innovaciones Educativas, 36(24), 37-55. 10.22458/ie.v24i36.3894. DOI: https://doi.org/10.22458/ie.v24i36.3894
Dubinsky, E., Weller, K., Mc Donald, M. y Brown, A. (2005). Some historical issues and paradoxes regarding the concept of infinity: An APOS-based analysis. Educational studies in Mathematics, 58, 335-359. DOI: https://doi.org/10.1007/s10649-005-2531-z
Eisenberger, N.I., Lieberman, M.D. y Williams, K.D. (2003). Does rejection hurt? An fMRI study of social exclusion. Science, 302(5643), 290-292. DOI: https://doi.org/10.1126/science.1089134
Duchowski, A. (2007). Eye movement analysis. In Eye Tracking Methodology (137-153), Springer. DOI: https://doi.org/10.1007/978-1-84628-609-4_12
Edwards, L.D. (2009). Gestures and conceptual integration in mathematical talk. Educational Studies in Mathematics, 70(2), 127-141. DOI: https://doi.org/10.1007/s10649-008-9124-6
Evans, J. (2008). Dual-process accounts of reasoning, judgment, and social cognition. JSBT. Annual Review of Psychology, 255-278. 10.1146/annurev.psych.59.103006.093629 DOI: https://doi.org/10.1146/annurev.psych.59.103006.093629
Finfgeld, D. (2018). A guide to qualitative meta-synthesis. Taylor & Francis Inc.
Fischbein, E. (2001). Tacit models and infinity. Educational studies in Mathematics, 48, 309-329. https://www.jstor.org/stable/3483030 DOI: https://doi.org/10.1023/A:1016088708705
Fukuta, J. y Yamashita, J. (2021). The complex relationship between con-scious/unconscious learning and conscious/unconscious knowledge: The mediating effects of salience in form-meaning connections. Second Language Research. 10.1177/02676583211044950 DOI: https://doi.org/10.1177/02676583211044950
Füstös, J., Gramann, K., Herbert, B.M., y Pollatos, O. (2012). On the embodiment of emotion regulation: interoceptive awareness facilitates reappraisal. Social Cognitive and Affective Neuroscience, 8(8), 911–917. DOI: https://doi.org/10.1093/scan/nss089
Grabner, R.H., Ansari, D., De Smedt, B. et al. (2010). Glossary of technical terms in cognitive neuroscience. ZDM Mathematics Education 42, 661–663. 10.1007/s11858-010-0277-2 DOI: https://doi.org/10.1007/s11858-010-0277-2
Henson, R. (2006). Forward inference using functional neuroimaging: Dissociations versus associations. Trends in cognitive sciences, 10(2), 64-69. DOI: https://doi.org/10.1016/j.tics.2005.12.005
Hernández, O. (2012). Estadística Elemental para Ciencias Sociales. (3ª ed.). Editorial Universidad de Costa Rica.
Hernández-Sampieri, R., Fernández, C. y Baptista, P. (2014). Metodología de la investigación (6ª ed-). McGraw-Hill.
Jonides, J., Nee, D.E., y Berman, M.G. (2006). What has functional neuroimaging told us about the mind? So many examples, so little space. Cortex, 42(3), 414-417. DOI: https://doi.org/10.1016/S0010-9452(08)70372-1
Jung, C.G. (2021). Obra completa de Carl Gustav Jung. Volumen 6. Tipos psicológicos. Editorial Trotta.
Just, M.A. y Carpenter, P.A. (1980). A theory of reading: From eye fixations to comprehension. Psychological Review, 87(4), 329–354. DOI: https://doi.org/10.1037//0033-295X.87.4.329
Kandel, E.R. (2007). In search of memory: The emergence of a new science of mind. WW Norton & Company.
König, P., Ehinger, B.V., Gameiro, R.R., Kaspar, K., Kietzmann, T.C., Ossandón, J.P., Onat, S. y Wilming, N. (2016). Eye movements as a window to cognitive processes. Journal of Eye Movement Research, 9(5), 1-16. DOI: 10.16910/jemr.9.5.3 DOI: https://doi.org/10.16910/jemr.9.5.3
Krippendorff, K. (1980). Content analysis: An introduction to its methodology. SAGE.
Lakoff, G. y Núñez, R. (2000). Where Mathematics comes from. Basic Books.
Leikin, R., Waisman, I. y Leikin, M. (2016). Does solving insight-based problems differ from solving learning-based problems? Some evidence from an ERP study. ZDM- The International Journal on Mathematics Education, 48(3). DOI: https://doi.org/10.1007/s11858-016-0767-y
Lundstrom, B.N., Petersson, K.M., Andersson, J., Johansson, M., Fransson, P., y Ingvar, M. (2003). Isolating the retrieval of imagined pictures during episodic memory: activation of the left precuneus and left prefrontal cortex. Neuroimage, 20(4), 1934-1943. DOI: https://doi.org/10.1016/j.neuroimage.2003.07.017
Maturana, H.R., y Varela, F.J. (1992). The tree of knowledge: The biological roots of human understanding. Shambhala.
Merkley, R., Shimi, A. y Scerif, G. (2016). Electrophysiological markers of newly acquired symbolic numerical representations: the role of magnitude and ordinal information. ZDM-The International Journal on Mathematics Education, 48, 3. DOI: https://doi.org/10.1007/s11858-015-0751-y
Mondéjar, J., Rodríguez, A., & Fierro, B. (2023). El paradigma de apoyos al aprendizaje desde la neurodidáctica: una necesidad en la formación universitaria. Entretextos, 17(33), 90-108. doi:10.5281/zenodo.8218195
Nemirovsky, R. y Borba, M. (2003). Perceptuo-motor activity and imagination in mathematics learning. In N. Pateman, B. Dougherty, y J. Zilliox (Eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education, 1, 103–135. Manoa.
Niedenthal, P.M., Barsalou, L.W., Winkielman, P., Krauth-Gruber, S., y Ric, F. (2005). Embodiment in attitudes, social perception, and emotion. Personality and Social Psychology Review, 9(3), 184–211. DOI: https://doi.org/10.1207/s15327957pspr0903_1
Noblit, H. y Hare, J. (1988). Metha-etnography: synthesizing qualitative studies. Sage Publications. DOI: https://doi.org/10.4135/9781412985000
Parra-Bolaños, N. (2015). Impacto de las técnicas de neuroimagen en las ciencias sociales. Revista Chilena de Neuropsicología, 10(1), 31-37.
Polanyi, M. (1958). Personal Knowledge: Towards a Post-Critical Philosophy. University of Chicago Press.
Poldrack, R.A. (2006). Can cognitive processes be inferred from neuroimaging data? Trends in cognitive sciences, 10(2), 59-63. DOI: https://doi.org/10.1016/j.tics.2005.12.004
Poole A. y Ball, L.J. (2006). Eye Tracking in HCI and Usability Research. Encyclopedia of Human-Computer interaction, 211-219. DOI: https://doi.org/10.4018/978-1-59140-562-7.ch034
Radford, L. (2008). Iconicity and contraction: a semiotic investigation of forms of algebraic generalizations of patterns in different contexts. ZDM-The International Journal on Mathematics Education, 40(1), 83-96. DOI: https://doi.org/10.1007/s11858-007-0061-0
Radford, L. (2017). On inferentialism. Mathematics Education Research Journal, 29(4), 493-508. DOI: https://doi.org/10.1007/s13394-017-0225-3
Radford, L., Arzarello, F., Edwards, L. y Sabena, C. (2017). The multimodal material mind: Embodiment in mathematics education. En J. Cai (Ed.), First compendium for research in mathematics education, 700-721. Publisher.
Radford, L., y D’Amore, B. (2006). Semiotics, culture, and mathematical thinking. Revista latinoamericana de investigación en matemática educativa.
Radford, L., Demers y S. Miranda, I. (2009). Processus d’abstraction en mathématiques. Ottawa, Canada: Centre franco-ontarien de ressources pédagogiques, Imprimeur de la Reine pour l’Ontario.
Recarte, M.Á., Pérez, E., Conchillo, Á., y Nunes, L.M. (2008). Mental workload and visual impairment: Differences between pupil, blink, and subjective rating. The Spanish journal of psychology, 11(2), 374-385. DOI: https://doi.org/10.1017/S1138741600004406
Rodríguez, A., Navarro, A., Carrillo, M.J. e Isla, L. (2023). University coaching experience and academic performance. Education Sciences, 13 (248), 3, 248. https://doi.org/10.3390/educsci13030248 DOI: https://doi.org/10.3390/educsci13030248
Rodríguez, A., Martínez, R., Gallardo, C.P. y Vazquez, D. (2023). Transformar la evaluación para empoderar al estudiante universitario en su aprendizaje y la enseñanza. Revista Iberoamericana de Investigación en Educación. 7, 1-15. https://doi.org/10.58663/riied.vi7.94 DOI: https://doi.org/10.58663/riied.vi7.94
Rodríguez, A. (2024). Pluralidad y potencial de la investigación educativa universitaria. Cuadernos de Pedagogía. 555, sección artículos, 1-6. https://www.cuadernosdepedagogia.com/content/Inicio.aspx?params=H4sIAAAAAAAEAMssdiwoKMovS02xNTIwMjEwNzQyNDIwBQBlRn1kFwAAAA==WKE
Rosch, E., Thompson, E., y Varela, F.J. (1991). The embodied mind: cognitive science and human experience. Cambridge: MIT Press.
Siegel, D J. (2010). The mindful therapist: a clinician’s guide to mindsight and neural integration. New York: W.W. Norton y Co.
Siegel, D.J. (2012). Pocket guide to interpersonal neurobiology: an integrative handbook of the mind. Norton & Company.
Schillinger, L., De Smedt, B. y Grabner, R.H. (2016). When errors count: an EEG study on numerical error monitoring under performance pressure. ZDM-The International Journal on Mathematics Education, 48, 351–363. DOI: https://doi.org/10.1007/s11858-015-0746-8
Schindler, M., y Lilienthal, A.J. (2020). Students’ mathematical creativity process: Insights from eye-tracking stimulated recall interview. International Journal of Science and Mathematics Education, 18, 1565–1586. DOI: https://doi.org/10.1007/s10763-019-10033-0
Soluch, P. y Tarnowski, A. (2013). O metodologii badan eyetrackingowych. Lingwistyka Stosowana, 7, 115-134.
Steinman, R.M. (2004) Gaze control under natural conditions. En L.M. Chalupa y J.S. Werner (Eds.) The Visual Neurosciences (1339-1356), MIT Press. DOI: https://doi.org/10.7551/mitpress/7131.003.0103
Strohmaier, A.R., MacKay, MacKay, K.J., Obersteiner, A. y Reiss, K.M. (2020). Eye-tracking methodology in mathematics education research: A systematic literature review. Educational Studies in Mathematics, 104, 147-200. DOI: https://doi.org/10.1007/s10649-020-09948-1
Susac, A.; Bubic, A.; Kaponja, J.; Planinic, M. y Palmovic, M. (2014). Eye movements reveal students’ strategies in simple equation solving. International Journal of Science and Mathematics Education, 12 (3), 555-577. DOI: https://doi.org/10.1007/s10763-014-9514-4
Sweller, J., van Merriënboer, J.J.G., Paas, F. (2019). Cognitive Architecture and Instructional Design: 20 Years Later. Educational Psychology Review, 31, 261–292. 10.1007/s10648-019-09465-5 DOI: https://doi.org/10.1007/s10648-019-09465-5
Swidan, O. y Arzarello, F. (2022). Adaptive instruction in an inquiry-based mathematics and digitally rich classroom – multiple perspectives. Journal of Mathematical Behavior, 66, 100962. DOI: https://doi.org/10.1016/j.jmathb.2022.100962
Tall, D. (2004). Building theories: The three worlds of mathematics. For the learning of Mathematics, 24, 1, 29-32.
Thompson, E., y Varela, F.J. (2001). Radical embodiment: neural dynamics and consciousness. Trends in Cognitive Sciences, 5(10), 418–425. DOI: https://doi.org/10.1016/S1364-6613(00)01750-2
Valdés-Sosa, P.A., Galan-Garcia, L., Bosch-Bayard, J., Bringas-Vega, M.L., Aubert-Vazquez, E., Rodríguez-Gil, I. y Valdes-Sosa, M.J. (2021). The Cuban Human Brain Mapping Project, a young and middle age population-based EEG, MRI, and cognition dataset. Scientific Data, 8(1), 1-12. DOI: https://doi.org/10.1038/s41597-021-00829-7
Wager, T.D., Jonides, J. y Reading, S. (2004). Neuroimaging studies of shifting attention: a meta-analysis, Neuroimage, 22(4), 1679-1693. DOI: https://doi.org/10.1016/j.neuroimage.2004.03.052
Was, C., Sansosti, F. y Morris, B. (Eds.). (2017). Eye-Tracking Technology Applications in Educational Research. IGI Global. DOI: https://doi.org/10.4018/978-1-5225-1005-5
Weinberger, A.B., y Green, A.E. (2022). Dynamic development of intuitions and explicit knowledge during implicit learning. Cognition, 222, 105008. DOI: https://doi.org/10.1016/j.cognition.2021.105008
Wilson, M. (2002). Six views of embodied cognition. Psychonomic Bulletin & Review, 9(4),625-636. DOI: https://doi.org/10.3758/BF03196322
Publicado
Versiones
- 2025-01-30 (2)
- 2025-01-30 (1)
Cómo citar
Número
Sección
Licencia
Derechos de autor 2024 Revista RETOS XXI
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-CompartirIgual 4.0.
