Decision-making in contexts of risk and uncertainty: An instrument for secondary education

Andrea Stephanie Vergara-Gómez; Carolina Andrea Henríquez-Rivas

doi:10.29333/ejmste/17175

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Andrea Stephanie Vergara-Gómez ¹ ^* , Carolina Andrea Henríquez-Rivas ¹

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¹ Faculty of Basic Sciences, Center for Research in Mathematics and Statistics Education (CIEMAE), Universidad Católica del Maule, Talca, CHILE^* Corresponding Author

Abstract

Probability and statistics help us make well-informed decisions in context of risk and uncertainty. These contexts, which are inherent to daily life, range from games of chance to 21^st century current events. However, in the field of mathematics education, research focused specifically on how young people make decisions is nascent. Through an exploratory and descriptive design in six stages, we present the formulation and content validation process of forced-response questionnaire that aims to explore how students in secondary education make decisions in contexts of risk and uncertainty, considering six everyday situations. The process of validation included the participation of six experts in this area, who assessed the content of the instrument in question. The results of the content validity coefficient show an adequate level of agreement among the expert judges, allowing for a validated instrument whose use in the secondary school classroom can contribute to the recognition and characterization of patterns of reasoning for decision-making.

Keywords

probability and statistics
secondary education
questionnaire
daily life
content validation
exploratory design

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 21, Issue 10, 2025, Article No: em2717

https://doi.org/10.29333/ejmste/17175

Publication date: 01 Oct 2025

Online publication date: 30 Sep 2025

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References

Amaya-Gómez, R., Dumar, V., Sánchez-Silva, M., Torres-Cuello, M. A., Avila, A., & Muñoz, F. (2023). An analysis of engineering students’ risk perception to support process safety learning process. Education for Chemical Engineers, 42, 7-19. https://doi.org/10.1016/j.ece.2022.10.003
Arend, R. J. (2024). Uncertainty in strategic decision making. Springer. https://doi.org/10.1007/978-3-031-48553-4_3
Arkes, H. R., Gigerenzer, G., & Hertwig, R. (2016). How bad is incoherence? Decision, 3(1), 20-39. https://doi.org/10.1037/dec0000043
Aven, T., & van Kessenich, A. M. (2020). Teaching children and youths about risk and risk analysis: What are the goals and the risk analytical foundation? Journal of Risk Research, 23(5), 557-570. https://doi.org/10.1080/13669877.2018.1547785
Bartram, D. (2007). Increasing validity with forced-choice criterion measurement formats. International Journal of Selection and Assessment, 15(3), 263-272. https://doi.org/10.1111/j.1468-2389.2007.00386.x
Batanero C. (2020). Probability teaching and learning. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 682-686). Springer. https://doi.org/10.1007/978-3-030-15789-0_128
Batanero, C., Ortiz, J. J., Serrano, L., & Albanese, V. (2016). Razonamiento sobre probabilidad condicional en situaciones de riesgo [Reasoning about conditional probability in risk situations]. Suma, 83, 73-80.
Borovcnik M (2011). Strengthening the role of probability within statistics curricula. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics–Challenges for teaching and teacher education. A joint ICMI/IASE study (pp. 71-83). Springer. https://doi.org/10.1007/978-94-007-1131-0_11
Borovcnik, M. (2015). Risk and decision making: The “logic” of probability. The Mathematics Enthusiast, 12(1), 113-139. https://doi.org/10.54870/1551-3440.1339
Borovcnik, M. (2016). Probabilistic thinking and probability literacy in the context of risk. Educação Matemática Pesquisa Revista do Programa de Estudos Pós-Graduados em Educação Matemática, 18(3), 1491-1516.
Borovcnik, M. (2020). Risk and decision making: Fundamental aspects. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 728-740). https://doi.org/10.1007/978-3-030-15789-0_100006
Borovcnik, M., & Kapadia, R. (2018). Reasoning with risk: Teaching probability and risk as twin concepts. In C. Batanero, & E. J. Chernoff (Eds.), Teaching and learning stochastics (pp. 3-22). Springer. https://doi.org/10.1007/978-3-319-72871-1_1
Boyatzis, R. (1998). Transforming qualitative information: Thematic analysis and code development. SAGE.
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
Cadena, J. E., Osorio, A. F., Torero, J. L., Reniers, G., & Lange, D. (2020). Uncertainty-based decision-making in fire safety: Analyzing the alternatives. Journal of Loss Prevention in the Process Industries, 68, Article 104288. https://doi.org/10.1016/j.jlp.2020.104288
Cebesoy, U. B. (2021). Pre-service science teachers’ informal reasoning patterns and risk perceptions in SSI: Case of gene therapy. European Journal of Science and Mathematics Education, 9(4), 211-229. https://doi.org/10.30935/scimath/11237
Choi, Y. B. (1993). Paradigms and conventions: Uncertainty, decision making, and entrepreneurship. University of Michigan Press. https://doi.org/10.3998/mpub.13334
Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. American Mathematical Monthly, 104(9), 801-823. https://doi.org/10.1080/00029890.1997.11990723
Costa, D., Arantes, J., & Keating, J. (2022). A dual-process approach to cooperative decision-making under uncertainty. PLoS ONE, 17(3), Article e0265759. https://doi.org/10.1371/journal.pone.0265759
Cournot, A. A. (1843). Exposition de la théorie des chances et des probabilités [Exposition of the theory of chances and probabilities]. Hachette.
Creswell, J. W., & Creswell. J. D. (2018). Research design: Qualitative, quantitative, and mixed method approaches (5th ed.). SAGE.
Eichler, A., & Vogel, M. (2016). Young students’ mental modelling of statistical situations. In D. Ben-Zvi, & K. Makar (Eds.), The teaching and learning of statistics (pp. 13-23). Springer. https://doi.org/10.1007/978-3-319-23470-0_2
Elbehary, S. G. A. (2021). Reasoning under uncertainty within the context of probability education: A case study of preservice mathematics teachers. Pythagoras, 42(1). https://doi.org/10.4102/pythagoras.v42i1.630
Engel, J., Erickson, T., & Martignon, L. (2019). Teaching about decision trees for classification problems. In S. Budgett (Ed.), Proceedings of the IASE 2019 Satellite Conference. https://doi.org/10.52041/srap.19303
Escobar-Pérez, J., & Cuervo-Martínez, Á. (2008). Validez de contenido y juicio de expertos: Una aproximación a su utilización [Content validity and expert judgment: An approach to its use]. Avances en Medición, 6(1), 27-36.
Gal, I. (2002). Adults’ statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1), 1-25. https://doi.org/10.1111/j.1751-5823.2002.tb00336.x
Gal, I. (2005). Towards” probability literacy” for all citizens: Building blocks and instructional dilemmas. In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 39-63). Springer. https://doi.org/10.1007/0-387-24530-8_3
Galicia Alarcón, L. A., Balderrama Trápaga, J. A., & Edel Navarro, R. (2017). Validez de contenido por juicio de expertos: Propuesta de una herramienta virtual [Content validity by expert judgment: Proposal for a virtual tool]. Apertura, 9(2), 42-53. https://doi.org/10.32870/Ap.v9n2.993
Gaona, J., & Arévalo-Meneses, F. (2024). Thematic bibliometric analysis of 37 specialized journals in mathematical education research indexed in Scopus or Web of Science. Eurasia Journal of Mathematics, Science and Technology Education, 20(5), Article em2446. https://doi.org/10.29333/ejmste/14577
Garcia-Retamero, R., Sobkow, A., Petrova, D., Garrido, D., & Traczyk, J. (2019). Numeracy and risk literacy: What have we learned so far? The Spanish Journal of Psychology, 22, Article e10. https://doi.org/10.1017/sjp.2019.16
Gigerenzer, G., & Gaissmaier, W. (2011). Heuristic decision making. Annual Review of Psychology, 62(1), 451-482. https://doi.org/10.1146/annurev-psych-120709-145346
Greer, B., & Mukhopadhyay, S. (2005). Teaching and learning the mathematization of uncertainty: Historical, cultural, social and political contexts. In G. A. Jones (Ed.), Exploring probability in school. Mathematics education library, vol. 40 (pp. 297-324). Springer. https://doi.org/10.1007/0-387-24530-8_13
Hernández-Nieto, R. A. (2002). Contributions to statistical analysis. Universidad de Los Andes.
Knight, F. H. (1921). Risk, uncertainty and profit. Hart, Schaffner and Marx.
Kruglanski, A. W., & Gigerenzer, G. (2018). Intuitive and deliberate judgments are based on common principles. In Kruglanski, A. W (Ed.), The motivated mind: Selected work of Arie W. Kruglanski (pp. 104-128). Routledge. https://doi.org/10.4324/9781315175867-4
Lappas, D., Georgios, K., & Karampelas, P. (2023). Using game-based learning in order to enhance decision making under uncertainty. International Journal of Film and Media Arts, 8(1), 36-51. https://doi.org/10.24140/ijfma.v8.n1.02
Larson, K., White, D., Gober, P., & Wutich, A. (2015). Decision-making under uncertainty for water sustainability and urban climate change adaptation. Sustainability, 7(11), 14761-14784. https://doi.org/10.3390/su71114761
Lavín, C., García, R., & Fuentes, M. (2024). Navigating uncertainty: The role of mood and confidence in decision-making flexibility and performance. Behavioral Sciences, 14(12), Article 1144. https://doi.org/10.3390/bs14121144
Leuker, C., Pachur, T., Hertwig, R., & Pleskac, T. J. (2018). Exploiting risk-reward structures in decision making under uncertainty. Cognition, 175, 186-200. https://doi.org/10.1016/j.cognition.2018.02.019
Levy, H. (2006). Studies in risk and uncertainty. Springer. https://doi.org/10.1007/0-387-29311-6
Lucarelli, C., Maggi, M., & Uberti, P. (2021). Risk seeking or risk averse? Phenomenology and perception. In Viale, R., Filotto, U., Alemanni, B., & Mousavi, S. (Eds.), Financial education and risk literacy (pp. 220-235). Elgar Online. https://doi.org/10.4337/9781789908855.00021
Makar, K., & Ben-Zvi, D. (2011). The role of context in developing reasoning about informal statistical inference. Mathematical Thinking and Learning, 13(1-2), 1-4. https://doi.org/10.1080/10986065.2011.538291
Makar, K., & Confrey, J. (2005). “Variation-talk”: Articulating meaning in statistics. Statistics Education Research Journal, 4(1), 27-54. https://doi.org/10.52041/serj.v4i1.524
Makar, K., & Rubin, A. (2018). Learning about statistical inference. In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education (pp. 261-294). Springer. https://doi.org/10.1007/978-3-319-66195-7_8
Malaspina, M., & Malaspina, U. (2020). Game invention as means to stimulate probabilistic thinking. Statistics Education Research Journal, 19(1), 57-72. https://doi.org/10.52041/serj.v19i1.119
Martignon, L. (2019). How to foster risk literacy in children and youngsters. In J. M. Contreras, M. M. Gea, M. M. López-Martín, & E. Molina-Portillo (Eds.), Proceedings of the Third International Virtual Congress on Statistical Education (pp. 1-13).
Martignon, L., & Laskey, K. (2019). Statistical literacy for classification under risk: An educational perspective. AStA Wirtschafts-Und Sozialstatistisches Archiv, 13(3-4), 269-278. https://doi.org/10.1007/s11943-019-00259-3
Martignon, L., Erickson, T., & Viale, R. (2022). Transparent, simple and robust fast-and-frugal trees and their construction. Frontiers in Human Dynamics, 4. https://doi.org/10.3389/fhumd.2022.790033
McNicholas, C., & Marcella, R. (2022). Information behaviour in high risk decision making: Study of international postgraduates. Journal of Information Science, 50(6), 1525-1540. https://doi.org/10.1177/01655515221124080
Mian, P., Conte, T., Natali, A., Biolchini, J., Mendes, E., & Travassos, G. (2005). Lessons learned on applying systematic reviews to software engineering. In Proceedings of the 3^rd International Workshop ‘Guidelines For Empirical Work’ in the Workshop Series on Empirical Software Engineering.
Moallemi, E. A., Zare, F., Hebinck, A., Szetey, K., Molina-Perez, E., Zyngier, R. L., Hadjikakou, M., Kwakkel, J., Haasnoot, M., Miller, K. K., Groves, D. G., Leith, P., & Bryan, B. A. (2023). Knowledge co-production for decision-making in human-natural systems under uncertainty. Global Environmental Change, 82, Article 102727. https://doi.org/10.1016/j.gloenvcha.2023.102727
Moore, D. S. (1991). Uncertainty. In L. A. Steen (Ed.), On the shoulders of giants: New approaches to numeracy (pp. 95-137). National Academies Press.
Mousavi, S., & Gigerenzer, G. (2014). Risk, uncertainty, and heuristics. Journal of Business Research, 67(8), 1671-1678. https://doi.org/10.1016/j.jbusres.2014.02.013
OECD. (2010). Learning mathematics for life: A perspective from PISA. OECD Publishing. https://doi.org/10.1787/9789264075009-en
OECD. (2019). Governing board: PISA 2021 mathematics framework (second draft). OECD. https://www.oecd.org/pisa/sitedocument/PISA-2021-mathematics-framework.pdf
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
Pleskac, T. J. (2008). Decision making and learning while taking sequential risks. Journal of Experimental Psychology: Learning, Memory, and Cognition, 34(1), 167-185. https://doi.org/10.1037/0278-7393.34.1.167
Ramírez-Contreras, A., Zúñiga-Silva, L., & Ojeda-Gómez, E. (2023). Un estudio sobre la intuición probabilística de los estudiantes de matemáticas para la toma de decisiones en la escuela secundaria [A study on mathematics students’ probabilistic intuition for decision-making in secondary school]. Revista Electrónica Internacional de Educación Matemática, 18(4), Article em0749. https://doi.org/10.29333/iejme/13586
Rodríguez-Muñiz, L. J., Muñiz-Rodríguez, L., García-Alonso, I., López-Serentill, P., Vásquez, C., & Alsina, À. (2022). Navigating between abstraction and context in secondary school statistics education (Nadando entre dos orillas: Abstracción y contexto en educación estadística en secundaria). Culture and Education, 34(3), 689-725. https://doi.org/10.1080/11356405.2022.2058794
Samuel, G., Lucivero, F., Knowles, B., & Wright, K. (2024). Carbon accounting in the digital industry: The need to move towards decision making in uncertainty. Sustainability, 16(5), Article 2017. https://doi.org/10.3390/su16052017
Shaughnessy, J. M. (2019). Recommendations about the big ideas in statistics education: A retrospective from curriculum and research. Cuadernos de Investigación y Formación en Educación Matemática, 18, 44-58. https://doi.org/10.22533/at.ed.2952206043
Turra, Y., Villagra, C. P., Mellado, M. E., & Aravena, O. A. (2022). Diseño y validación de una escala de percepción de los estudiantes sobre la cultura de evaluación como aprendizaje [Design and validation of a scale of student perceptions of the culture of assessment as learning]. RELIEVE, 28(2), Article art. 9. https://doi.org/10.30827/relieve.v28i2.25195
Ubilla, F. M., & Gorgorió, N. (2023). Using Eurostat data to teach statistics to prospective primary teachers: On how the context of the task may promote their social awareness. Journal of Mathematics Teacher Education, 28(3), 655-680. https://doi.org/10.1007/s10857-023-09611-5
van Der Bles, A. M., Van Der Linden, S., Freeman, A. L., Mitchell, J., Galvao, A. B., Zaval, L., & Spiegelhalter, D. J. (2019). Communicating uncertainty about facts, numbers and science. Royal Society Open Science, 6(5), Article 181870. https://doi.org/10.1098/rsos.181870
Vasilachis de Galdino, I. (2006). Estrategias de investigación cualitativa [Qualitative research strategies]. Gedisa.
Vergara-Gómez, A. (2024). Decision-making in situations of uncertainty as school mathematical knowledge. Acta Scientiae, 26(1), 125-156. http://www.periodicos.ulbra.br/index.php/acta/article/view/7705
Wald, A. (1939). Contributions to the theory of statistical estimation and testing hypotheses. The Annals of Mathematical Statistics, 10(4), 299-326. https://doi.org/10.1214/aoms/1177732144
Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223-248. https://doi.org/10.1111/j.1751-5823.1999.tb00442.x
Wroughton, J. R., McGowan, H. M., Weiss, L. V., & Cope, T. M. (2013). Exploring the role of context in students’ understanding of sampling. Statistics Education Research Journal, 12(2), 32-58. https://doi.org/10.52041/serj.v12i2.303
Yilmaz, Z., Ergül, K., & Aşik, G. (2023). Role of context in statistics: Interpreting social and historical events. Statistics Education Research Journal, 22(1), Article 6. https://doi.org/10.52041/serj.v22i1.72
Yoe, C. (2019). Principles of risk analysis (2nd ed.). CRC Press. https://doi.org/10.1201/9780429021121

How to cite this article

APA

Vergara-Gómez, A. S., & Henríquez-Rivas, C. A. (2025). Decision-making in contexts of risk and uncertainty: An instrument for secondary education. Eurasia Journal of Mathematics, Science and Technology Education, 21(10), em2717. https://doi.org/10.29333/ejmste/17175

Vancouver

Vergara-Gómez AS, Henríquez-Rivas CA. Decision-making in contexts of risk and uncertainty: An instrument for secondary education. EURASIA J Math Sci Tech Ed. 2025;21(10):em2717. https://doi.org/10.29333/ejmste/17175

AMA

Vergara-Gómez AS, Henríquez-Rivas CA. Decision-making in contexts of risk and uncertainty: An instrument for secondary education. EURASIA J Math Sci Tech Ed. 2025;21(10), em2717. https://doi.org/10.29333/ejmste/17175

Chicago

Vergara-Gómez, Andrea Stephanie, and Carolina Andrea Henríquez-Rivas. "Decision-making in contexts of risk and uncertainty: An instrument for secondary education". Eurasia Journal of Mathematics, Science and Technology Education 2025 21 no. 10 (2025): em2717. https://doi.org/10.29333/ejmste/17175

Harvard

Vergara-Gómez, A. S., and Henríquez-Rivas, C. A. (2025). Decision-making in contexts of risk and uncertainty: An instrument for secondary education. Eurasia Journal of Mathematics, Science and Technology Education, 21(10), em2717. https://doi.org/10.29333/ejmste/17175

MLA

Vergara-Gómez, Andrea Stephanie et al. "Decision-making in contexts of risk and uncertainty: An instrument for secondary education". Eurasia Journal of Mathematics, Science and Technology Education, vol. 21, no. 10, 2025, em2717. https://doi.org/10.29333/ejmste/17175