Preservice teachers interpreting and acting on students’ responses to a probability problem
DOI:
https://doi.org/10.52041/serj.v24i2.819Keywords:
Probability, Teacher training, Ontosemiotic appoach, Didactic analysisAbstract
To ensure the learning of mathematics, teachers must be able to analyse their students’ mathematical practices when solving tasks, interpret the difficulties that students encounter, and decide how to manage students’ difficulties. This competence in didactic analysis and intervention allows teachers to adapt their teaching to meet individual student needs. In this paper, we analyse how preservice teachers interpreted students’ responses to a task involving the proportional determination of probabilities and understanding the sample space. We propose didactic strategies that help students overcome difficulties. The results revealed the difficulties some preservice teachers experienced in adequately interpreting student responses and making informed decisions to improve learning.
References
Australian Curriculum, Assessment and Reporting Authority. (2014). Foundation to year 10 curriculum: Statistics and probability (ACMSPO24).
Batanero, C., & Álvarez-Arroyo, R. (2024). Teaching and learning of probability. ZDM - Mathematics Education, 56(1), 5–17. https://doi.org/10.1007/s11858-023-01511-5
Batanero, C., Gómez, E., Contreras, J. M., & Díaz, C. (2015). Mathematical knowledge of primary school teachers in training for the teaching of probability: An exploratory study. Práxis Educativa, 10(1), 11–34. https://doi.org/10.5212/PraxEduc.v.10i1.0001
Batanero, C., Hernández-Solís, L. A., & Gea, M. M. (2023). Analysing Costa Rican and Spanish students’ proportional reasoning and comparison of probabilities. Statistics Education Research Journal, 22(3), Article 7. https://doi.org/10.52041/serj.v22i3.659
Begolli, K. N., Dai, T., McGinn, K. M., & Booth, J. L. (2021). Could probability be out of proportion? Self-explanation and example-based practice help students with lower proportional reasoning skills learn probability. Instructional Science, 49, 441–473. https://doi.org/10.1007/s11251-021-09550-9
Bryant, P., & Nunes, T. (2012). Children’s understanding of probability: A literature review. The Nuffield Foundation.
Buforn, A., Llinares, S., Fernández, C., Coles, A., & Brown, L. (2020). Pre-service teachers’ knowledge of the unitizing process in recognizing students’ reasoning to propose teaching decisions. International Journal of Mathematics Education in Science and Technology, 53(2), 425–443. https://doi.org/10.1080/0020739X.2020.1777333
Burgos, M., López-Martín, M. M., Aguayo, C. G., & Albanese, V. (2022). Cognitive analysis of probability comparison tasks by prospective primary school teachers. Uniciencia, 36(1), 1–24. https://doi.org/10.15359/ru.36-1.38
Burgos, M., López-Martín, M. M., Albanese, V., & Aguayo-Arriagada, C. G. (2023). Analysis of primary school students’ answers to fair game tasks: An experience with preservice teachers. BEIO, Bulletin of Statistics and Operations Research, 39(3), 48–69.
Cohen, L., Manion, L., & Morrison, K. (2000). Research methods in education. Routledge. https://doi.org/10.4324/9780203224342
Dröse, J., Griese, B., & Wessel, L. (2022). Prospective teachers’ diagnostic judgments on students’ understanding of conditional probabilities. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.), Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 3080–3088). Free University of Bozen-Bolzano and European Research in Mathematics Education.
Franco, J., & Alsina, Á. (2022). El conocimiento del profesorado de Educación Primaria para enseñar estadística y probabilidad: Una revisión sistemática. [Primary school teachers’ knowledge to teach statistics and probability: A systematic review]. Aula Abierta, 51(1), 7–16. https://doi.org/10.17811/rifie.51.1.2022.7-16
Godino, J. D., Giacomone, B., Batanero, C., & Font, V. (2017). Enfoque Ontosemiótcio de los conocimientos y competencias del profesor de matemáticas [Ontosemiotic approach to mathematics teacher's knowledge and competences]. Bolema: Boletim de Educação Matemática, 31(57), 90–113. https://doi.org/10.1590/1980-4415v31n57a05
Hernández-Solís, L. A., Batanero, C., & Gea, M. M. (2024). Relación entre la construcción de espacios muestrales y el razonamiento proporcional de estudiantes costarricenses [Relating the construction of sample spaces and proportional reasoning in Costa Rican students]. Revista de Educación Estadística, 3, 1–28. https://doi.org/10.29035/redes.3.1.1
Hernández-Solís, L. A., Batanero, C., Gea, M. M., & Álvarez-Arroyo, R. (2021). Construcción de espacios muestrales asociados a distintos tipos de sucesos: Un estudio exploratorio con estudiantes de Educación Primaria [Construction of sample spaces associated with different types of events: An exploratory study with primary education students]. Educación Matemática, 33(1), 181–207. https://doi.org/10.24844/em3301.07
Ivars, P., Fernández, C., Llinares, S., & Choy, B. H. (2018). Enhancing noticing: Using a hypothetical learning trajectory to improve pre-service primary teachers’ professional discourse. Eurasia Journal of Mathematics, Science and Technology Education, 14(11), Article em1599. https://doi.org/10.29333/ejmste/93421
Jakobsen, A., Ribeiro, C. M., & Mellone, M. (2014). Norwegian prospective teachers’ MKT when interpreting pupils’ productions on a fraction task. Nordic Studies in Mathematics Education, 19(3–4), 135–150.
Leavy, P. (2022). Research design: Quantitative, qualitative, mixed methods, arts-based, and community-based participatory research approaches. Guilford Publications.
Ministerio de Educación y Formación Profesional (2022). Real Decreto 157/2022, de 1 de marzo, por el que se establecen la ordenación y las enseñanzas mínimas de la Educación Primaria [Royal Decree 157/2022, of March 1, Establishing the organization and minimum curricular standards for primary education]. Boletín Oficial del Estado, 52(I), 24386–24504.
Mohamed, N. (2012). Evaluación del conocimiento de los futuros profesores de primaria sobre probabilidad [Assessment of prospective primary school teachers' knowledge of probability] [Unpublished doctoral dissertation]. University of Granada.
Montes, M. (2021). Introducción al Seminario: Investigación cualitativa en educación matemática [Introduction to the seminar: Qualitative research in mathematics education]. In P. D. Diago, D. F. Yáñez, M. T. González-Astudillo, & D. Carrillo (Eds.), Investigación en Educación Matemática XXIV (pp. 53–63). Servicios Educativos Integrados al Estado de México.
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics.
Ortiz, J. J., & Mohamed, N. (2014). Prospective teachers’ knowledge of sample space. Quadrante, 23(2), 5–22.
Sánchez, E., & Valdez, J. (2017). Las ideas fundamentales de probabilidad en el razonamiento de estudiantes de bachillerato [Fundamental ideas of probability in the reasoning of high school students]. Avances de Investigación en Educación Matemática, 11, 127–143. https://doi.org/10.35763/aiem.v1i11.180
Simpson, A., & Haltiwanger, L. (2017). This is the first time I’ve done this: Exploring secondary prospective mathematics teachers’ noticing of students’ mathematical thinking. Journal of Mathematics Teacher Education, 20(4), 335–355. https://doi.org/10.1007/s10857-016-9352-0
Supply, A. S., Van Dooren, W., & Onghena, P. (2020). Can we count on early numerical abilities for early probabilistic reasoning abilities? Mathematical Thinking and Learning, 24(1), 19–37. https://doi.org/10.1080/10986065.2020.1805551
Supply, A. S., Vanluydt, E., Van Dooren, W., & Onghena, P. (2023). Out of proportion or out of context? Comparing 8- to 9-year-olds’ proportional reasoning abilities across fair-sharing, mixtures, and probability contexts. Educational Studies in Mathematics, 113(3), 371–388. https://doi.org/10.1007/s10649-023-10212-5
Van Dooren, W. (2014). Probabilistic thinking: Analyses from a psychological perspective. In E. Chernoff & B. Sriraman, (Eds.), Probabilistic thinking: Advances in mathematics education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7155-0_7
Vásquez, C., & Alsina, Á. (2015a). Conocimiento didáctico-matemático del profesorado de Educación Primaria sobre probabilidad: Diseño, construcción y validación de un instrumento de evaluación. [Didactic-Mathematical knowledge of primary education teachers about probability: Design, construction and validation of an assessment instrument]. Bolema: Boletim de Educação Matemática, 29(52), 681–703. https://doi.org/10.1590/1980-4415v29n52a13
Vásquez, C., & Alsina, Á. (2015b). El conocimiento del profesorado para enseñar probabilidad: Un análisis global desde el modelo del Conocimiento Didáctico-matemático [Teachers’ knowledge to teach probability: A global analysis from the didactic-mathematical knowledge model]. Avances de Investigación en Educación Matemática, 7, 27–48. https://doi.org/10.35763/aiem.v1i7.104
Vásquez, C., & Alsina, Á. (2017). Aproximación al conocimiento común del contenido para enseñar probabilidad desde el modelo del Conocimiento Didáctico-matemático [Approaching common content knowledge to teach probability from the didactic-mathematical knowledge model]. Educación Matemática, 29(3), 79–108. https://doi.org/10.24844/EM2903.03
Wasserstein, R. L., Schirm, A. L., & Lazar, N. A. (2019). Moving to a world beyond “p< 0.05.” The American Statistician, 73(s1), 1–19. https://doi.org/10.1080/00031305.2019.1583913
