Conocimiento didáctico-matemático de futuros profesores al crear problemas de probabilidad basados en noticias

Rocío Álvarez-Arroyo; Carmen Batanero; María Magdalena Gea

doi:10.35763/aiem28.7429

Authors

Rocío Álvarez-Arroyo Universidad de Granada https://orcid.org/0000-0002-3201-8542
Carmen Batanero Universidad de Granada https://orcid.org/0000-0002-4189-7139
María Magdalena Gea Universidad de Granada https://orcid.org/0000-0002-5229-0121

DOI:

https://doi.org/10.35763/aiem28.7429

Keywords:

Secondary school teacher trainees, Probability problem solving, Didactic analysis competence, Media

Abstract

Using the didactic-mathematical knowledge model of the ontosemiotic approach, we assessed the knowledge of 70 prospective secondary school teachers during their training when creating probabilistic problems from news reports. Participants were asked to choose issue news, create and solve probabilistic questions about the issue, indicate the educational level at which the problem was aimed, and identify possible difficulties. The identified problems were appropriate, addressed topics of interest to students, used news from various sources and covered PISA contexts. Most questions were solved correctly, and, in addition to probabilistic calculations, some included reasoning and decision-making. However, the participants demonstrated lower competence in predicting potential student difficulties. The results provide new information about the knowledge of teachers by creating probabilistic problems in the context and identifying areas for teacher training improvement.

Downloads

Download data is not yet available.

References

Alonso-Castaño, M., Alonso, P., Mellone, M., & Rodríguez-Muñiz, L. (2021). What mathematical knowledge do prospective teachers reveal when creating and solving a probability problem? Mathematics, 9(24), 3300. https://doi.org/10.3390/math9243300

Álvarez-Arroyo, R., Batanero, C., & Gea, M. M. (2024a). Probabilistic literacy and reasoning of prospective secondary school teachers when interpreting media news. ZDM Mathematics Education, 56, 1045–1058 https://doi.org/10.1007/s11858-024-01586-8

Álvarez-Arroyo, R., Gea, M. M., & Batanero, C. (2024b). Conocimiento probabilístico común y especializado de futuros profesores de secundaria al interpretar un informe sobre la COVID-19. Aula Abierta, 53(3), 211–220. https://doi.org/10.17811/rifie.20627

Batanero, C., Gea, M. M., & Álvarez-Arroyo, R. (2023). La educación del razonamiento probabilístico. Educação Matemática Pesquisa, 25(2), 127–144. https://doi.org/10.23925/1983-3156.2023v25i2p127-144

Baumanns, L., & Rott, B. (2022). The process of problem posing: Development of a descriptive phase model of problem posing. Educational Studies in Mathematics, 110(2), 251–269. https://doi.org/10.1007/s10649-021-10136-y

Benjamin, D. J. (2019). Errors in probabilistic reasoning and judgment biases. En B. D. Bernheim, S. DellaVigna, & D. Laibson (Eds.), Handbook of behavioral economics: Applications and foundations (Vol. 2, pp. 69–186). Elsevier. https://doi.org/10.1016/bs.hesbe.2018.11.002

Borovcnik, M. (2016). Probabilistic thinking and probability literacy in the context of risk. Educação Matemática Pesquisa, 18(3), 1491–1516.

Brückler, F. M., & Milin Šipuš, Ž. (2023). Pre-service mathematics teachers’ understanding of conditional probability in the context of the COVID-19 pandemic. European Journal of Science and Mathematics Education, 11(1), 89–104. https://doi.org/10.30935/scimath/12436

Burgos, M., López-Martín, M. del M., Aguayo-Arriagada, C. G., & Albanese, V. (2022). Análisis cognitivo de tareas de comparación de probabilidades por futuro profesorado de Educación Primaria. Uniciencia, 36(1), 1–24. https://doi.org/10.15359/ru.36-1.38

Burgos, M., Tizón-Escamilla, N., & Chaverri, J. (2024). A model for problem creation: Implications for teacher training. Mathematics Education Research Journal, 37, 55–84. https://doi.org/10.1007/s13394-023-00482-w

Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem posing research in mathematics education: Some answered and unanswered questions. En F. Singer, F. N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 3–34). Springer.

Cai, J., Koichu, B., Rott, B., & Jiang, C. (2024). Advances in research on mathematical problem posing: Focus on task variables. The Journal of Mathematical Behavior, 76, 101186. https://doi.org/10.1016/j.jmathb.2024.101186

Cai, J., & Leikin, R. (2020). Affect in mathematical problem posing: Conceptualization, advances, and future directions for research. Educational Studies in Mathematics, 105(3), 287–301. https://doi.org/10.1007/s10649-020-10008-x

Cho, H., Cannon, J., Lopez, R., & Li, W. (2024). Social media literacy: A conceptual framework. New Media & Society, 26(2), 941–960. https://doi.org/10.1177/1461444821106853

D’Amelio, A. (2004). Eventos mutuamente excluyentes y eventos independientes: Concepciones y dificultades. En L. Díaz (Ed.), Acta Latinoamericana de Matemática Educativa (pp. 138–144). Comité Latinoamericano de Matemática Educativa.

Díaz, C., Contreras, J. M., Batanero, C., & Roa, R. (2012). Evaluación de sesgos en el razonamiento sobre probabilidad condicional en futuros profesores de Educación Secundaria. Bolema: Boletim de Educação Matemática, 26, 1207–1226. https://doi.org/10.1590/S0103-636X2012000400006

Díaz, C., & de la Fuente, I. (2007). Assessing students’ difficulties with conditional probability and Bayesian reasoning. International Electronic Journal of Mathematics Education, 2(3), 128–148. https://doi.org/10.29333/iejme/180

Falk, R. (1986). Conditional probabilities: Insights and difficulties. En R. Davidson & J. Swift (Eds.), Proceedings of the Second International Conference on Teaching Statistics (pp. 292–297). International Statistical Institute.

Fernández, C., Ivars, P., & Llinares, S. (2023). El desarrollo de la competencia mirar profesionalmente el pensamiento matemático de los estudiantes durante los períodos de práctica. Revista Interuniversitaria de Formación del Profesorado, 98(37.2), 127–146. https://doi.org/10.47553/rifop.v98i37.2.99296

Gal, I. (2005). Towards “probability literacy” for all citizens: Building blocks and instructional dilemmas. En G. A. Jones (Ed.), Exploring probability in school (pp. 39–63). Springer.

Gea, M. M., & Fernández, J. A. (2018). Conocimiento de futuros profesores de los primeros años escolares para enseñar probabilidad. Avances de Investigación en Educación Matemática, 14, 15–30. https://doi.org/10.35763/aiem.v0i14.21

Godino, J. D. (2009). Categorías de análisis de los conocimientos del profesor de matemáticas. UNIÓN – Revista Iberoamericana de Educación Matemática, 20, 13–31. http://revistaunion.org/index.php/UNION/article/view/1063

Godino, J. D. (2024). Enfoque ontosemiótico en educación matemática. Fundamentos, herramientas y aplicaciones. Aula Magna.

Godino, J. D., Giacomone, B., Batanero, C., & Font, V. (2017). Enfoque ontosemiótico de los conocimientos y competencias del profesor de matemáticas. Bolema: Boletim de Educação Matemática, 31(57), 90–113.

https://doi.org/10.1590/1980-4415v31n57a05

Gómez, E., Batanero, C., & Contreras, J. M. (2014). Conocimiento matemático de futuros profesores para la enseñanza de la probabilidad desde el enfoque frecuencial. Bolema: Boletim de Educação Matemática, 28, 209–229. https://doi.org/10.1590/1980-4415v28n48a11

Liljedahl, P., & Cai, J. (2021). Empirical research on problem solving and problem posing: A look at the state of the art. ZDM Mathematics Education, 53, 723–735. https://doi.org/10.1007/s11858-021-01291-w

Malaspina, U., Torres, C., & Rubio, N. (2019). How to stimulate in-service teachers’ didactic analysis competence by means of problem posing. En P. Liljedahl & L. Santos-Trigo (Eds.), Mathematical problem solving (pp. 133–151). Springer. https://doi.org/10.1007/978-3-030-10472-6_7

Ministerio de Educación y Formación Profesional (MEFP). (2022a). Real Decreto 217/2022, de 29 de marzo, por el que se establece la ordenación y las enseñanzas mínimas de la Educación Secundaria Obligatoria. MEFP. https://www.boe.es/eli/es/rd/2022/03/29/217/con

Ministerio de Educación y Formación Profesional (MEFP). (2022b). Real Decreto 243/2022, de 5 de abril, por el que se establecen la ordenación y las enseñanzas mínimas del Bachillerato. MEFP. https://www.boe.es/eli/es/rd/2022/04/05/243/con

Montes, M., Chico, J., Martín-Díaz, J. P., & Badillo, E. (2024). Mathematics teachers’ specialized knowledge mobilized through problem transformation. The Journal of Mathematical Behavior, 73, 101132. https://doi.org/10.1016/j.jmathb.2024.101132

Muñiz-Rodríguez, L., Velázquez, P. A., Rodríguez-Muñiz, L. J., & Valcke, M. (2016). Is there a gap in initial secondary mathematics teacher education in Spain compared to other countries? Revista de Educación, 372, 106–132. https://doi.org/10.4438/1988-592X-RE-2015-372-317

Neuendorf, K. A. (2018). Content analysis and thematic analysis. En P. Brough (Ed.), Advanced research methods for applied psychology: Design, analysis and reporting (1st ed., pp. 211–223). Routledge. https://doi.org/10.4324/9781315517971

OECD. (2022). PISA 2022 assessment and analytical framework. OECD.

Pfannkuch, M., Ben-Zvi, D., & Budgett, S. (2018). Innovations in statistical modeling to connect data, chance and context. ZDM Mathematics Education, 50(7), 1113–1123. https://doi.org/10.1007/s11858-018-0989-2

Pino-Fan, L. R., Assis, A., & Castro, W. F. (2015). Towards a methodology for the characterization of teachers’ didactic-mathematical knowledge. EURASIA Journal of Mathematics, Science and Technology Education, 11(6), 1429–1456. https://doi.org/10.12973/eurasia.2015.1403a

Silber, S., & Cai, J. (2021). Exploring underprepared undergraduate students’ mathematical problem posing. ZDM Mathematics Education, 53(4), 877–889. https://doi.org/10.1007/s11858-021-01272-z

Silver, E. A. (2013). Problem-posing research in mathematics education: Looking back, looking around, and looking ahead. Educational Studies in Mathematics, 83, 157–162. https://doi.org/10.1007/s10649-013-9477-3

Sosa-Martín, D., Perdomo-Díaz, J., Bruno, A., Almeida, R., & García-Alonso, I. (2024). The influence of problem-posing task situation: Prospective primary teachers working with fractions. The Journal of Mathematical Behavior, 73, 101139. https://doi.org/10.1016/j.jmathb.2024.101139

Tizón-Escamilla, N., & Burgos, M. (2023). Creation of problems by prospective teachers to develop proportional and algebraic reasonings in a probabilistic context. Education Sciences, 13(12), 1186. https://doi.org/10.3390/educsci13121186

Valenzuela-Ruiz, S. M., Batanero, C., Begué, N., & Garzón-Guerrero, J. A. (2023). Conocimiento didáctico-matemático sobre la distribución de la media muestral de profesorado de Bachillerato en formación. Uniciencia, 37(1), 44–64. https://doi.org/10.15359/ru.37-1.3

Vásquez, C., & Alsina, Á. (2015). El conocimiento del profesorado para enseñar probabilidad: Un análisis global desde el modelo del conocimiento didáctico-matemático. Avances de Investigación en Educación Matemática, 7, 27–48. https://doi.org/10.35763/aiem.v1i7.104