“How is this possible?” - Secondary PSTs’ conceptions of variability in the context of probabilistic thinking
DOI:
https://doi.org/10.52041/iase25.149Abstract
Abstract: In the past, the consideration of (data) variability has been repeatedly characterized as a fundamental element of statistical thinking. However, motivated by recent curricular changes in Austrian secondary schools, this study situates the concept within the context of individual ideas about probabilities in random experiments. A thematic analysis of pre-service teachers’ answers to a pen-and- paper study in October 2024 gives insights into how variability is conceptualized within the interplay of patterns and deviations in the context of the empirical law of large numbers at the beginning of their tertiary stochastics training.References
Biehler, R. (1994). Probabilistic thinking, statistical reasoning, and the search for causes—Do we need a probabilistic revolution after we have taught data analysis? In J. Garfield (Ed.), Research papers from the Fourth International Conference on Teaching Statistics (ICOTS 4) (pp. 20–37). Minneapolis, MN: University of Minnesota.
Biehler, R. (2007). Denken in Verteilungen - Vergleichen von Verteilungen. Der Mathematikunterricht, 53, 3–11.
Biehler, R., & Prömmel, A. (2013). Von ersten stochastischen Erfahrungen mit großen Zahlen bis zum 1/√n – Gesetz – ein didaktisch orientiertes Stufenkonzept. Stochastik in der Schule, 33(2), 14–25.
Biehler, R., & Steinbring, H. (1982). Bernoullis Theorem: Eine „Erklärung“ für das empirische Gesetz der großen Zahlen? In H.-G. Steiner (Ed.), Mathematik-Philosophie-Bildung (pp. 296–334). Aulis- Verlag Deubner.
Biehler, R., Engel, J., & Frischemeier, D. (2023). Stochastik: Leitidee Daten und Zufall. In R. Bruder, A. Büchter, H. Gasteiger, B. Schmidt-Thieme, & H.-G. Weigand (Eds.). Handbuch der Mathematikdidaktik (pp. 243–278). Springer. https://doi.org/10.1007/978-3-662-66604-3_8
BMBWF (2025). Curriculum for the secondary level (AHS) in Austria. https://www.ris.bka.gv.at/GeltendeFassung.wxe?Abfrage=Bundesnormen&Gesetzesnummer=100 08568
Braun, V. & Clarke, V. (2022). Thematic analysis: A practical guide (1st ed.). SAGE.
Díaz, S. (2022). Methodological strategies for using stimulated recall in interpreting research. Onomázein, 55, 55–71. https://revistachilenadederecho.uc.cl/index.php/onom/article/view/51645
Eichler, A., & Vogel, M. (2013). Leitidee Daten und Zufall : Von konkreten Beispielen zur Didaktik der Stochastik (2nd ed.). Springer Spektrum. https://doi.org/10.1007/978-3-658-00118-6
Ericsson, K. A., & Simon, H. A. (1993). Protocol analysis: Verbal reports as data (2nd ed.). MIT Press. https://doi.org/10.7551/mitpress/5657.001.0001
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.
Garfield, J., & Ben-Zvi, D. (2005). A framework for teaching and assessing reasoning about variability. Statistics Education Research Journal, 4(1), 92–99. https://doi.org/10.52041/serj.v4i1.527
Konold, C., & Pollatsek, A. (2002). Data Analysis as the Search for Signals in Noisy Processes. Journal for Research in Mathematics Education, 33(4), 259–289. https://doi.org/10.2307/749741
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
Moore, D. S. (1990). Uncertainty. In L. A. Steen (Ed.), On the shoulders of giants: New approaches to numeracy (pp. 95–137). National Academies Press.
Prömmel, A. (2013). Das GESIM-Konzept. Springer Spektrum. https://doi.org/10.1007/978-3-658- 00594-8_2
Reading, C., & Reid, J. (2010). Reasoning about variation: Rethinking theoretical frameworks to inform practice. In C. Reading (Ed.), Data and context in statistics education: Towards an evidence-based society. Proceedings of the Eighth International Conference on Teaching Statistics (ICOTS-8), Ljubljana, Slovenia. Voorburg, The Netherlands: International Statistics Institute.
Reading, C., & Shaughnessy, J. M. (2004). Reasoning about variation. In D. Ben-Zvi & J. B. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 201–226). Springer. https://doi.org/10.1007/1-4020-2278-6
Riemer, W. (2023). Statistik unterrichten: eine handlungsorientierte Didaktik der Stochastik. Klett- Kallmeyer.
Schnell, S. (2014). Muster und Variabilität erkunden: Konstruktionsprozesse kontextspezifischer Vorstellungen zum Phänomen Zufall. Springer Spektrum. https://doi.org/10.1007/978-3-658- 03805-2
Schupp, H. (1982). Zum Verhältnis statistischer und wahrscheinlichkeitstheoretischer Komponenten im Stochastik-Unterricht der Sekundarstufe I. Journal für Mathematik-Didaktik, 3, 207–226.
Shaughnessy, M. (2007). Research on statistics learning and reasoning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 957–1009). Information Age Publishing.
Sommerhoff, D., Weixler, S., & Hamedinger, C. (2023). Sensitivity to sample size in the context of the empirical law of large numbers: Comparing the effectiveness of three approaches to support early secondary school students. Journal für Mathematik-Didaktik, 44(1), 233–267. https://doi.org/10.1007/s13138-022-00213-x
Torok, R., & Watson, J. (2000). Development of the Concept of Statistical Variation: An Exploratory Study. Mathematics Education Research Journal, 12, 147–169. https://doi.org/10.1007/BF03217081
Watson, J. M., Callingham, R. A., & Kelly, B. A. (2007). Students’ appreciation of expectation and variation as a foundation for statistical understanding. Mathematical Thinking and Learning, 9(2), 83–130. https://doi.org/10.1080/10986060709336812
Watson, J. M., & Kelly, B. A. (2004). Expectation versus variation: Students’ decision making in a chance environment. Canadian Journal of Math, Science & Technology Education, 4(3), 371–396. https://doi.org/10.1080/14926150409556620
Watson, Kelly, B. A., Callingham, R. A., & Shaughnessy, J. M. (2003). The measurement of school students' understanding of statistical variation. International Journal of Mathematical Education in Science and Technology, 34(1), 1–29. https://doi.org/10.1080/0020739021000018791
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
