Actividad matemática creativa y desarrollo del talento matemático a través del modelo praxeológico

Autores

DOI:

https://doi.org/10.24320/redie.2022.24.e01.4167

Palabras clave:

creatividad, talento, generalización, matemáticas

Resumen

Se presenta un modelo teórico para el estudio del talento matemático, fundamentado en la Teoría Antropológica de lo Didáctico y la noción de creatividad. En dicho modelo se proponen dos componentes de la actividad matemática creativa: la Componente Matemática, que sustenta las técnicas matemáticas; y la Componente Creativa, definida por cuatro funciones: producir técnicas nuevas, optimizar técnicas, considerar tareas desde diversos ángulos y adaptar una técnica. Con base en los modelos Teórico y Epistemológico de Referencia sobre sucesiones infinitas, se genera un diseño didáctico conformado por seis situaciones problemáticas y se implementa en una institución creada para potenciar el talento matemático. El análisis de dos tareas realizadas por una pareja de niños constituye un estudio de caso, que permite ilustrar que enfrentar tareas retadoras de un mismo tipo, bajo condiciones institucionales propicias, posibilita el desarrollo del talento matemático.

Descargas

Los datos de descargas todavía no están disponibles.

Biografía del autor

Zeidy Margarita Barraza-García, Instituto Politécnico Nacional, México

Zeidy M. Barraza-García is finishing her Ph. D. in Educational Mathematics at CICATA-IPN (México). She has worked as a professor at in several universities and as a instructor in nurturing talent programs.She has extensive experience in the design and implementation of continuing education programs aimed at teachers of mathematics at the basic level and is the author of book chapter publications, extensive publications, and has presented papers at national and international academic events.

Avenilde Romo Vázquez, Cinvestav, Instituto Politécnico Nacional, México

Avenilde Romo Vázquez obtained her PhD in mathematics education research at Paris 7 University in Paris, France. In 2011, she joined the Mathematics Education Program at the National Polytechnic Institute of Mexico where is a full professor. In 2018, she became an Editor-in-Chief of journal Educación Matemática. Her research interests include the modelling mathematical activities and professional development of mathematics teachers. She has led more than 20 masters’ thesis and doctoral dissertations. She published different articles and book chapters about the teaching and learning of modelling mathematical activities.

Solange Roa-Fuentes, Universidad Industrial de Santander, España

Solange Roa-Fuentes received her PhD in Educational Mathematics at the Centro de Investigaciones y de Estudios Avanzados de IPN (Mexico). Currently, Solange is tenured professor in the Mathematics department at Universidad Industrial de Santander (Bucaramanga, Colombia). Solange Roa-Fuentes is particularly interested in the research of the Development of potential mathematical talent, Advance mathematical thinking and Algebraic thinking. She has supervised twenty-four master thesis and two doctoral thesis. Dr. Solange Roa-Fuentes has published several scientific papers, book chapters and books about the construction of mathematical concepts and the mathematical talent.

Referencias

Artigue, M. (2008). Didactical design in mathematics education. En C. Winslow (Ed.), Nordic research in mathematics education. Proceedings from NORMA08 (pp. 7-16). Copenhague.

Assmus, D. y Frizlar, T. (2018). Mathematical giftedness and creativity in primary grades. En F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness (pp. 55-81). Springer.

Barquero, B. y Bosch, M. (2015). Didactic engineering as a research methodology: From fundamental situations to study and research paths. En A. Watson y M. Ohtani (Eds.), Task design in mathematics education. New ICMI study series (pp. 249-272). Springer.

Barraza-García, Z. M., Romo-Vázquez, A. y Roa-Fuentes, S. (2020). A theoretical model for the development of mathematical talent through mathematical creativity. Education Sciences, 10(4), 118. https://doi.org/10.3390/educsci10040118

Boaler, J. (2016). Mathematical mindsets. Jossey-Bass.

Bosch, M., Chevallard, Y., García, F. J. y Monaghan, J. (Eds.) (2019). Working with the anthropological theory of the didactic in mathematics. Routledge.

Brody, L. (2005). The study of exceptional talent. High Ability Studies, 16(1), 87-96. https://doi.org/10.1080/13598130500115304

Bustamante, E. (2017). Un modelo epistemológico de referencia asociado a las sucesiones en la educación básica regular del Perú [Tesis de maestría no publicada]. Pontificia Universidad Católica del Perú.

Castela, C. y Romo-Vázquez, A. (2011). Des mathématiques a l’automatique: étude des effets de transposition sur la transformée de Laplace dans la formation des ingénieurs [De las matemáticas a la automática: estudio de los efectos de la transposición sobre la transformación de Laplace en la formación de ingenieros]. Recherches en Didactique des Mathématiques, 31(1), 79-130. https://dialnet.unirioja.es/servlet/articulo?codigo=3635944

Chaachoua, H., Bessot, A., Romo-Vázquez, A. y Castela, C. (2019). Developments and functionalities in the praxeological model. En M. Bosch, Y. Chevallard, F. J. García y J. Monaghan (Eds.), Working with the anthropological theory of the didactic (pp. 41-60). Routledge.

Chevallard, Y. (2002). Organiser l’étude [Organiza el estudio]. En J. L. Dorier (Ed.), Actes de la 11éme École d´éte de didactique des mathématiques (pp. 3-22). La pensée Sauvage.

Chevallard, Y. (2019). Introducing the anthropological theory of the didactic: an attempt at a principled approach. Hiroshima Journal of Mathematics Education, 12, 71-114. https://www.jasme.jp/hjme/download/05_Yves%20Chevallard.pdf

Clark, B. (2011). No child is just born gifted: Creating and developing unlimited potential. En J. L. Jolly, D. J. Treffinger, T. F. Inman y J. F. Smutny (Eds.), Parenting for high potential (pp. 4-11). Prufrock Press.

Dickman, B. (2018). Creativity in question and answer digital spaces for mathematics education: A case study of the water triangle for proportional reasoning. En V. Freiman y J. L. Tassell (Eds.), Creativity and Technology in Mathematics Education (pp. 233-248). Springer.

Dimitriadis, C. (2011). Developing mathematical ability in primary school through a ‘pull-out’ program: A case study. Education 3-13. International Journal of Primary, Elementary and Early Years Education, 39(5), 467-482. https://doi.org/10.1080/03004271003769939

Greenes, C. (1981). Identifying the gifted student in mathematics. The Arithmetic Teacher, 28(6), 14-17. https://www.jstor.org/stable/41191796

House, P. A. (1987). Providing opportunities for the mathematically gifted, K-12. Reston.

Karwowski, M., Jankowska, D. M. y Szwajkowski, W. (2017). Creativity, imagination, and early mathematics education. En R. Leikin y B. Sriraman (Eds.), Creativity and giftedness (pp. 183-199). Springer.

Kattou, M., Kontoyianni, K., Pitta-Pantazi, D. y Christou, C. (2015). Connecting mathematical creativity to mathematical ability. ZDM Mathematics Education, 45(2), 167-181. https://doi.org/10.1007/s11858-012-0467-1

Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. University of Chicago Press.

Leikin, R. (2011). The education of mathematically gifted students: Some complexities and questions. The Mathematics Enthusiast, 8(1), 167-188. https://scholarworks.umt.edu/tme/vol8/iss1/9

Mann, E. L., Chamberlin, S. A. y Graefe, A. K. (2017). The prominence of affect in creativity: Expanding the conception of creativity in mathematical problem solving. En R. Leikin y B. Sriraman (Eds.), Creativity and giftedness (pp. 57-73). Springer.

Mhlolo, M. K. (2017). Regular classroom teachers’ recognition and support of the creative potential of mildly gifted mathematics learners. ZDM Mathematics Education, 49(1), 81-94. https://doi.org/10.1007/s11858-016-0824-6

National Council of Teachers of Mathematics. (2000). Principles and standars for school mathematics. Autor.

Oktaç, A., Roa-Fuentes, S. y Rodríguez, M. (2011). Equity issues concerning gifted children in mathematics: a perspective from México. En B. Atweh, M. Graven, W. Secada y P. Valero (Eds.), Mapping equity and quality in mathematics education (pp. 351-364). Springer.

Radford, L (2010). Layers of generality and types of generalization in pattern activities. PNA, 4(2), 37-62. http://funes.uniandes.edu.co/609/

Rivera, F. D. (2013). Teaching and learning patterns in school mathematics: Psychological and pedagogical. Springer.

Sala, G., Barquero, B., Monreal, N., Font, V. y Barajas, M. (2016). Evaluación del potencial de creatividad matemática en el diseño de una c-unidad. En J. A. Macías, A. Jiménez, J. L. González, M. T. Sánchez, P. Hernández, C. Fernández, F. J. Ruiz, T. Fernández y A. Berciano (Eds.), Investigación en Educación Matemática XX (pp. 469-478). SEIEM.

Schindler, M., Joklitschke, J. y Rott, B. (2018). Mathematical creativity and its subdomain-specificity. Investigating the appropriateness of solutions in multiple solution tasks. En F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness (pp. 115-142). Springer.

Sheffield, L. J. (2016). Dangerous myths about “gifted” mathematics students. ZDM Mathematics Education 49(1), 13-23. https://doi.org/10.1007/s11858-016-0814-8

Shriki, A. (2010). Working like real mathematicians: Developing prospective teachers’ awareness of mathematical creativity through generating new concepts. Educational Studies in Mathematics, 73, 159-179. https://doi.org/10.1007/s10649-009-9212-2

Sierra, T. A. (2006). Lo matemático en el diseño y análisis de organizaciones didácticas. Los sistemas de numeración y la medida de magnitudes continuas [Tesis doctoral no publicada]. Universidad Complutense de Madrid.

Singer, F. M., Sheffield, L. J., Freiman, V. y Brandl, M. (Eds.) (2016). Research on and activities for mathematically gifted students. Springer Open.

Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? Journal of Secondary Gifted Education, 17(1), 20-36. https://doi.org/10.4219/jsge-2005-389

Thomas, G. (2015). How to do your case study. Sage.

Tourón, J. (2019). Las altas capacidades en el sistema educativo español: reflexiones sobre el concepto y la identificación. Revista de Investigación Educativa, 38(1), 15-32. https://doi.org/10.6018/rie.396781

Vale, I. y Pimentel, T. (2011). Mathematical challenging tasks in elementary grades. En M. Pytlak, T. Rowland y E. Swoboda (Eds.), Proceedings of the seventh congress of the European Society for Research in Mathematics Education (pp. 1154-1164). ERME.

Vergel, R. (2015). Generalización de patrones y formas de pensamiento algebraico temprano. PNA, 9(3), 193-215. http://funes.uniandes.edu.co/6440/

Villarraga, M., Martínez, P. y Benavides, M. (2004). Hacia la definición del término talento. En M. Benavides, A. Maz, E. Castro y R. Blanco (Eds.), La educación de niños con talento en Iberoamérica (pp. 25-35). Trineo.

Publicado

2022-02-08

Número

Sección

Artículos

Metricas