Didactic-Mathematical Knowledge of Prospective Primary School Teachers to Teach Probability

Authors

DOI:

https://doi.org/10.21814/rpe.39849

Keywords:

Probability, Didactic-Mathematical Knowledge, Prospective teachers, Primary Education, Assessment

Abstract

The training of primary school teachers in probability is essential to develop an early understanding of probabilistic concepts in their students. The aim of this paper is to assess the didactic-mathematical knowledge to teach probability of Spanish prospective primary school teachers. To achieve this, 156 prospective teachers were asked to complete a questionnaire with three tasks, each with four sections. The first one involves solving and justifying the task and assesses common knowledge of probability; the second section requires identifying the mathematical objects involved in the solution and assesses the epistemic facet of didactic knowledge; the third requires discriminating the correct and incorrect answers to the task by fictitious students, thus analysing the cognitive facet; and the fourth consists of suggesting actions to overcome the students' errors, thus assessing the mediational and interactional facets. Participants demonstrated good common content knowledge and correctly identified the correct and incorrect answers of the fictitious students. Performance in identifying mathematical objects, explaining students' errors and suggesting didactic actions was lower. These results suggest areas that need to be strengthened in the training of primary school teachers to teach probability.

Downloads

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), e3300. https://doi.org/10.3390/math9243300

Alsina, A., & Bosch, E. (2023). Estadística y probabilidad en infantil y primaria: Diez materiales manipulativos esenciales para desarrollar el sentido estocástico. TANGRAM: Revista de Educação Matemática, 6(3), 23-59. https://doi.org/10.30612/tangram.v6i3.17587

Álvarez-Arroyo, R., Batanero, C., & Gea, M. M. (2024). Probabilistic literacy and reasoning of prospective secondary school teachers when interpreting media news. ZDM Mathematics Education, 56(6), 1045-1058. https://doi.org/10.1007/s11858-024-01586-8

Bargagliotti, A., Franklin, C., Arnold, P., Gould, R., Johnson, S., Perez, L., & Spangler, D. A. (2020). Pre-K-12 Guidelines for Assessment and Instruction in Statistics Education II (GAISE II): A framework for statistics and data science education. American Statistical Association.

Batanero, C., Hernández-Solís, L. A., & Gea, M. M. (2023). Analysing Costa Rican and Spanish students’ comparisons of probabilities and ratios. Statistics Education Research Journal, 22(3), e7. https://doi.org/10.52041/serj.v22i3.659

Burgos, M., López-Martín, M. M., Tizón, N., & Aguayo C. G. (2024). ¿Cómo resuelven futuros maestros tareas de proporcionalidad en el contexto probabilístico? Mirada desde los niveles de razonamiento algebraico. Aula Abierta, 53(2), 199-207. https://doi.org/10.17811/rifie.19972

Cañizares, M. J. (1997). Influencia del razonamiento proporcional y combinatorio y de creencias subjetivas en las intuiciones probabilísticas primarias [Tesis de doctorado publicada]. Universidad de Granada.

Chernoff, E. J., Vashchyshyn, I., & Neufeld, H. (2018). Comparing the relative probabilities of events. In C. Batanero & E. J. Chernoff (Eds.), Teaching and learning stochastics. Advances in probability education research (pp. 277-291). Springer. https://doi.org/10.1007/978-3-319-72871-1_16

Fernandes, J. A., Gea, M. M., & Diniz, L. N. (2019a). Tarefas propostas por futuros professores dos primeiros anos para ensinar probabilidades. Revista Brasileira de Educação, 24, e240039. http://dx.doi.org/10.1590/S1413-24782019240039

Fernandes, J. A., Gea, M. M., & Ferreira, P. (2019b). Conhecimento de estatística bivariada de futuros professores portugueses dos primeiros anos. Revista Portuguesa de Educação, 32(2), 40-56. https://doi.org/10.21814/rpe.16121

Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. Reidel.

Gal, I. (2005). Towards ‘probability literacy’ for all citizens: Building blocks and instructional dilemmas. In G. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 43-71). Springer. https://doi.org/10.1007/0-387-24530-8_3

Godino, J. D. (2009). Categorías de análisis de los conocimientos del profesor de matemáticas. Unión: Revista Iberoamericana de Educación Matemática, 5(20), 13-31. https://union.fespm.es/index.php/UNION/article/view/106320

Godino, J. D, (2024). Enfoque ontosemiótico en educación matemática. Fundamentos, herramientas y aplicaciones. Aula Magna. https://blog.ciaem-redumate.org/wp-content/uploads/2024/08/jdgodino2024_enfoque-ontosemiotico.pdf

Godino, J. D., Batanero, C., & Cañizares, M.J. (1988). Azar y probabilidad. Fundamentos didácticos y propuestas curriculares. Síntesis.

Gómez-Torres, E. (2014). Evaluación y desarrollo del conocimiento matemático para la enseñanza de la probabilidad en futuros profesores de educación primaria [Tesis de doctorado publicada]. Universidad de Granada. http://hdl.handle.net/10481/34020

Green, D. R. (1982). Probability concepts in school pupils aged 11-16 years [Published doctoral thesis]. Loughborough University. https://hdl.handle.net/2134/7409

Hourigan, M., & Leavy, A. M. (2020). Pre-service teachers’ understanding of probabilistic fairness: Analysis of decisions around task design. International Journal of Mathematical Education in Science and Technology, 51(7), 997-1019. https://doi.org/10.1080/0020739X.2019.1648891

Ingram, J. (2022). Randomness and probability: Exploring student teachers’ conceptions. Mathematical Thinking and Learning, 26(1), 1-19. https://doi.org/10.1080/10986065.2021.2016029

Konold, C. (1989). Informal conceptions of probability. Cognition and Instruction, 6(1), 59-98. https://doi.org/10.1207/s1532690xci0601_3

Krippendorff, K. (2018). Content analysis: An introduction to its methodology (4th Ed.). Sage.

Lecoutre, M.-P. (1992). Cognitive models and problem spaces in “purely random” situations. Educational Studies in Mathematics, 23(6), 557-568. https://doi.org/10.1007/BF00540060

Llinares, S., & Chapman, O. (Eds.). (2019). International handbook of mathematics teacher education: Tools and processes in mathematics teacher education (2nd Ed., Vol. 2). Brill.

Lo, J.-J., Leatham, K. R., & Van Zoest, L. R. (2014). Research trends in mathematics teacher education. Springer. https://doi.org/10.1007/978-3-319-02562-9

Pino-Fan, L. R., & Godino, J. (2015). Perspectiva ampliada del conocimiento didáctico-matemático del profesor. Paradigma, 36(1), p. 87-109. https://revistaparadigma.com.br/index.php/paradigma/article/view/552

Real Decreto 157/2022, de 1 de marzo, por el que se establecen la ordenación y las enseñanzas mínimas de la educación primaria. Ministerio de Educación y Formación Profesional, N.º 52.

Roldán, A.F., Batanero, C., & Beltrán-Pellicer, P. (2018). El diagrama de árbol: Un recurso intuitivo en probabilidad y combinatoria. Épsilon: Revista de Educación Matemática, (100), 49-63. https://tierradenumeros.com/publication/201812-epsilon-diagrama-arbol/

Sharma, S. (2015). Teaching probability: A socio-constructivist perspective. Teaching Statistics, 37(3), 78-84. https://doi.org/10.1111/test.12075

Tversky, A., & Kahneman, D. (1974). Judgement under uncertainty: Heuristics and biases. Science, 185(4157), 1124-1131. https://doi.org/10.1126/science.185.4157.1124

Van Dooren, W. (2014). Probabilistic thinking: Analyses from a psychological perspective. In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic thinking (pp. 123-126). Springer. https://doi.org/10.1007/978-94-007-7155-0_7

Vásquez, C., & Alsina, A. (2015a). Conocimiento didáctico-matemático del profesorado de educación primaria sobre probabilidad: Diseño, construcción y validación de un instrumento de evaluación. Bolema, 29(52), 681-703. https://doi.org/10.1590/1980-4415v29n52a13

Vásquez, C., & Alsina, A. (2015b). 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

Published

2025-05-13

How to Cite

Batanero, C., D. Vera , O. ., D. Pallauta , J. ., & Valenzuela-Ruiz , S. M. . (2025). Didactic-Mathematical Knowledge of Prospective Primary School Teachers to Teach Probability. Portuguese Journal of Education, 38(1), e25013. https://doi.org/10.21814/rpe.39849