Detección, provocación y superación de bloqueos de resolución de problemas matemáticos en magisterio

Albert Mallart-Solaz

doi:10.30827/pna.v17i3.24615

Authors

Albert Mallart-Solaz University of Barcelona https://orcid.org/0000-0003-3442-1551

DOI:

https://doi.org/10.30827/pna.v17i3.24615

Keywords:

Blockages, Creativity, Mathematical Competence, Mathematics Education, Problem solving, Teacher training

Abstract

This study explores Problem-Solving blockages, their provocation and overcoming with 53 Primary Education Geometry Didactics students. Questionnaires and tasks are designed, and expert readings, group discussions and problem solving and problem posing are proposed. Three origins of blockages are considered: affective, cognitive, cultural and environmental. In conclusion: identifying own Problem-Solving blockages does not imply knowing how to provoke them, being Problem-Posing competent and having a blockages’ list does not assure knowing how to provoke them, studying blockages overcoming is not enough to help overcoming them, and detecting blockages and overcoming them does not imply a correct resolution.

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Author Biography

Albert Mallart-Solaz, University of Barcelona

PhD in Mathematics Education, Autonomous University of Barcelona (UAB) and Mathematics degree at University of Barcelona (UB). Associate Professor of the Dept. of Signal at the Faculty of Telecommunications Engineering at the Ramon Llull University (URL), Associate Professor of the Dept. of Statistics at the UB, Associate Professor of the Dept. of Mathematics Education at UB since 2010 and mathematics teacher of high school since 2001.

References

Arora, R., Arora, P. y Chadha, B. (2020). Problem Solving and Reasoning ability in Mathematics of Senior Secondary School Students in Relation to Emotional intelligence. A Journal of Composition Theory, 13(2), 938-948.

Attami, D., Budiyono, B. y Indriati, D. (2020). The mathematical problem-solving ability of junior high school students based on their mathematical resilience. Journal of Physics: Conference Series, 1469. https://doi.org/10.1088/1742-6596/1469/1/012152 DOI: https://doi.org/10.1088/1742-6596/1469/1/012152

Beltrán, C., Guerrero, F. y Ramírez, O. (2009). La superación del ¡atascado! desde la heurística: un estudio en una comunidad de estudiantes para profesor de matemáticas. En García, O. (Ed), Memorias del 10 Encuentro Colombiano de Matemática Educativa. Hilbert Blanco. http://asocolme.org/index.php/eventos/anteriores/ecme-13/conferencistas-y-cursillistas/43-publicaciones-asocolme/memorias-ecme

Cai, J. y Hwang, S. (2020). Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research, 102, 101391. https://doi.org/10.1016/j.ijer.2019.01.001 DOI: https://doi.org/10.1016/j.ijer.2019.01.001

Cai, J., Chen, T., Li, X., Xu, R., Zhang, S., Hu, Y. y Song, N. (2020). Exploring the impact of a problem-posing workshop on elementary school mathematics teachers’ conceptions on problem posing and lesson design. International Journal of Educational Research, 102, 1-12. https://doi.org/10.1016/j.ijer.2019.02.004 DOI: https://doi.org/10.1016/j.ijer.2019.02.004

Chávez, C. F. y Rojas, O. (2021). Algunas consideraciones sobre el pensamiento divergente y la creatividad a partir de la resolución de un problema geométrico con múltiples vías de solución. Números. Revista de Didáctica de las Matemáticas, 107, 91-108.

Díaz, J.A. y Díaz, R. (2018). Los métodos de resolución de problemas y el desarrollo del pensamiento matemático. Bolema, 32(60), 57-74. https://doi.org/10.1590/1980-4415v32n60a03 DOI: https://doi.org/10.1590/1980-4415v32n60a03

Gómez-Chacón, I. M. (2002). Afecto y aprendizaje matemático: causas y consecuencias de la interacción emocional. En J. Carrillo (Ed.), Reflexiones sobre el pasado, presente y futuro de las Matemáticas (pp. 197-227). Universidad de Huelva.

Guzmán, M. (1991). Para pensar mejor. Labor.

Haavold, P., Hwa Lee, K. y Sriraman, B. (2018). Creativity in Mathematics Education. En S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 1-10). Springer. https://doi.org/10.1007/978-3-319-77487-9_33-7 DOI: https://doi.org/10.1007/978-3-319-77487-9_33-7

Liljedahl, P. (2013). Illumination: An affective experience? The International Journal on Mathematics Education, 45(2), 253-265. https://doi.org/10.1007/s11858-012-0473-3 DOI: https://doi.org/10.1007/s11858-012-0473-3

Mallart, A., Font, V. y Malaspina, U. (2016). Reflexión sobre el significado de qué es un buen problema en la formación inicial de maestros. Perfiles Educativos, 38(152), 14-30. https://doi.org/10.22201/iisue.24486167e.2016.152.57585 DOI: https://doi.org/10.22201/iisue.24486167e.2016.152.57585

Mason, J., Burton, L. y Stacey, K. (1989). Pensar Matemáticamente. Labor.

Mehta, R. y Dahl, D. W. (2019). Creativity: Past, present, and future. Consumer Psychol Review, 2(1), 30-49. https://doi.org/10.1002/arcp.1044 DOI: https://doi.org/10.1002/arcp.1044

Niss, M. y Højgaard, T. (2019). Mathematical competencies revisited. Educational Studies in Mathematics, 102(1), 9-28. https://doi.org/10.1007/s10649-019-09903-9 DOI: https://doi.org/10.1007/s10649-019-09903-9

Özdemir, D. A. y Işiksal, M. (2019). Mathematically gifted students’ differentiated needs: what kind of support do they need? International Journal of Mathematical Education in Science and Technology, 1-19. https://doi.org/10.1080/0020739X.2019.1658817 DOI: https://doi.org/10.1080/0020739X.2019.1658817

Polya, G. (1945). How to solve it. Princeton University Press. DOI: https://doi.org/10.1515/9781400828678

Loría, J.R. y Lupiáñez, J.L. (2019). Estudio del conocimiento de profesores de secundaria sobre procesos matemáticos. PNA, 13(4), 247-269. https://doi.org/10.30827/pna.v13i4.8892 DOI: https://doi.org/10.30827/pna.v13i4.8892

Sánchez, F. y Fiol, M. (2016). Creatividad matemática: Momentos de insight en estudiantes de 4º de ESO. Journal of Research in Mathematics Education, 5(1), 28-55. https://doi.org/10.17583/redimat.2016.1809 DOI: https://doi.org/10.17583/redimat.2016.1809

Sengül, S. y Katranci, Y. (2015). Free problem posing cases of prospective mathematics teachers: Difficulties and solutions. Procedia-Social and Behavioral Sciences, 174, 1983-1990. https://doi.org/10.1016/j.sbspro.2015.01.864 DOI: https://doi.org/10.1016/j.sbspro.2015.01.864

Villalonga, J. y Deulofeu, J. (2017). La base de orientación en la resolución de problemas: “Cuando me bloqueo o me equivoco.” REDIMAT, 6(3), 256-282. https://doi.org/10.17583/redimat.2017.2262 DOI: https://doi.org/10.17583/redimat.2017.2262

Wertheimer, M. (1959). Productive thinking. Harper and Brothers.