The integration of probability-based arguments in risk-related contexts
DOI:
https://doi.org/10.52041/iase25.125Abstract
Probabilistic reasoning is key for decision making, especially in risk-related contexts. For example, erroneous HIV self-test results pose risks that must be evaluated when considering public approval. This requires incorporating probabilities (e.g., for not being infected even though a positive test result is given) into the decision-making process. We examine how upper secondary school students use such probability-based arguments in risk-related contexts before and after an intervention on conditional probabilities. A qualitative content analysis classifies their arguments as (i) mathematical, (ii) context- related, (iii) transitional (between mathematical and context-related), (iv) affective, or (v) based on anticipated personal experience. A central result of the analysis is that after the intervention, students used mathematical arguments more frequently than prior to the intervention on conditional probabilities.References
Aven, T., & Renn, O. (2009). On risk defined as an event where the outcome is uncertain. Journal of Risk Research, 12(1), 1–11. https://doi.org/10.1080/13669870802488883.
Aven, T. (2023). Risk literacy: Foundational issues and its connection to risk science. Risk Analysis: An Official Publication of the Society for Risk Analysis. Advance online publication. https://doi.org/10.1111/risa.14223.
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.
Binder, K., Krauss, S., & Bruckmaier, G. (2015). Effects of visualizing statistical information–an empirical study on tree diagrams and 2×2 tables. Frontiers in Psychology, 6, 1186. https://doi.org/10.3389/fpsyg.2015.01186.
Binder, K., Krauss, S., & Wiesner, P. (2020). A New Visualization for Probabilistic Situations Containing Two Binary Events: The Frequency Net. Frontiers in Psychology, 11, 750. https://doi.org/10.3389/fpsyg.2020.00750.
Böcherer-Linder, K., & Eichler, A. (2019). How to improve performance in Bayesian inference tasks: a comparison of five visualizations. Frontiers in Psychology, 10, 267. https://doi.org/10.3389/fpsyg.2019.00267.
Büchter, T., Eichler, A., Steib, N., Binder, K., Böcherer-Linder, K., Krauss, S., & Vogel, M. (2022). How to train novices in Bayesian reasoning. Mathematics, 10(9), 1558. https://doi.org/10.3390/math10091558.
Budgett, S., & Pfannkuch, M. (2019). Visualizing chance: tackling conditional probability misconceptions. Topics and trends in current statistics education research: International perspectives, 3-25. https://doi.org/10.1007/978-3-030-03472-6_1.
Christenson, N., Chang Rundgren, S. N., & Höglund, H. O. (2012). Using the SEE-SEP model to analyze upper secondary students’ use of supporting reasons in arguing socioscientific issues. Journal of Science Education and Technology, 21, 342-352. https://doi.org/10.1007/s10956-011- 9328-x.
Díaz, C., & Batanero, C. (2009). University students’ knowledge and biases in conditional probability reasoning. International Electronic Journal of Mathematics Education, 4(3), 131-162. https://doi.org/10.29333/iejme/234.
Engel, J., & Martignon, L. (2015). Dynamisch-interaktive Visualisierung elementarer Konzepte zu Daten und Wahrscheinlichkeiten. Lernen und Lernstörungen, 4, 139–145. https://doi.org/10.1024/2235-0977/a000101.
Feufel, M. A., Keller, N., Kendel, F., & Spies, C. D. (2023). Boosting for insight and/or boosting for agency? How to maximize accurate test interpretation with natural frequencies. BMC Medical Education, 23(1), 75. https://doi.org/10.1186/s12909-023-04025-6.
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.
Gigerenzer, G., Gaissmaier, W., Kurz-Milcke, E., Schwartz, L. M., & Woloshin, S. (2007). Helping doctors and patients make sense of health statistics. Psychological science in the public interest, 8(2), 53-96. https://doi.org/10.1111/j.1539-6053.2008.00033.x.
Hansen, J., & Hammann, M. (2017). Risk in Science Instruction. Science & Education, 26(7-9), 749– 775. https://doi.org/10.1007/s11191-017-9923-1.
Harman, J. L., Weinhardt, J. M., Beck, J. W., & Mai, I. (2021). Interpreting time-series COVID data: Reasoning biases, risk perception, and support for public health measures. Scientific Reports, 11(1), 15585. https://doi.org/10.1038/s41598-021-95134-z.
Kim, S., Kim, S., Choi, Y.-J., & Do, Y. K. (2024). Natural frequency tree- versus conditional probability formula-based training for medical students’ estimation of screening test predictive values: A
randomized controlled trial. BMC Medical Education, 24(1), 1207. https://doi.org/10.1186/s12909- 024-06209-0.
Kolstø, S. D. (2006). Patterns in students’ argumentation confronted with a risk‐focused socio‐scientific issue. International Journal of Science Education, 28(14), 1689-1716. https://doi.org/10.1080/09500690600560878.
Martignon, L., & Hoffrage, U. (2019). Wer wagt, gewinnt? Wie Sie die Risikokompetenz von Kindern und Jugendlichen fördern können (1. Auflage). Hogrefe.
Martignon, L., & Monti, M. (2010). Conditions for risk assessment as a topic for probabilistic education. In Proceedings of the Eighth International Conference on Teaching Statistics. Lublijana, Slovenia: International Statistical Institute and International Association for Statistical Education.
McCrum-Gardner, E. (2008). Which is the correct statistical test to use? British Journal of Oral and Maxillofacial Surgery, 46(1), 38–41. https://doi.org/10.1016/j.bjoms.2007.09.002.
McDowell, M., & Jacobs, P. (2017). Meta-analysis of the effect of natural frequencies on Bayesian reasoning. Psychological Bulletin, 143(12), 1273. https://doi.org/10.1037/bul0000126.
Operskalski, J. T., & Barbey, A. K. (2016). Risk literacy in medical decision-making. Science, 352(6284), 413–414. https://doi.org/10.1126/science.aaf7966.
Pratt, D., Ainley, J., Kent, P., Levinson, R., Yogui, C., & Kapadia, R. (2011). Role of context in risk- based reasoning. Mathematical Thinking and Learning, 13(4), 322-345. https://doi.org/10.1080/10986065.2011.608346.
Prodromou, T. (2015). Adults’ perceptions of risk in the Big Data Era. The Mathematics Enthusiast, 12(1), 364-377. https://doi.org/10.54870/1551-3440.1353.
Radakovic, N. (2015). Pedagogy of risk: Why and how should we teach risk in high school math classes? The Mathematics Enthusiast. 12(1), 307–329. https://doi.org/10.54870/1551- 3440.1350.
Renkl, A. (2014). The Worked Examples Principle in Multimedia Learning. In R. E. Mayer (Ed.) The Cambridge Handbook of Multimedia Learning, Cambridge University Press: Cambridge, UK, 391–412. https://psycnet.apa.org/doi/10.1017/CBO9781139547369.020.
Schenk, L., Hamza, K. M., Enghag, M., Lundegård, I., Arvanitis, L., Haglund, K., & Wojcik, A. (2019). Teaching and discussing about risk: seven elements of potential significance for science education. International Journal of Science Education, 41(9), 1271–1286. https://doi.org/10.1080/09500693.2019.1606961.
Schulze, C., & Hertwig, R. (2022). Experiencing statistical information improves children’s and adults’ inferences. Psychonomic Bulletin & Review, 29(6), 2302–2313. https://doi.org/10.3758/s13423- 022-02075-3.
Sedlmeier, P., & Gigerenzer, G. (2001). Teaching Bayesian reasoning in less than two hours. Journal of Experimental Psychology: General, 130(3), 380–400. https://doi.org/10.1037//0096- 3445.130.3.380.
Steib, N., Büchter, T., Eichler, A., Binder, K., Krauss, S., Böcherer-Linder, K., Vogel, M., & Hilbert, S. (2025). How to teach Bayesian reasoning: An empirical study comparing four different probability training courses. Learning and Instruction, 95, 102032. https://doi.org/10.1016/j.learninstruc.2024.102032.
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.
Zhu, L., & Gigerenzer, G. (2006). Children can solve Bayesian problems: The role of representation in mental computation. Cognition, 98(3), 287–308. https://doi.org/10.1016/j.cognition.2004.12.003.
