Establishing sociomathematical norms in statistics teaching in lower-secondary classrooms
DOI:
https://doi.org/10.52041/serj.860Keywords:
Statistics education, Statistical literacy, Sociomathematical norms, Classroom researchAbstract
Because digital technologies and collection of data about our lives are omnipresent in our society, statistics has become an increasingly important school subject. In this article, we investigate the development of statistical literacy in a class of middle school students over the course of a one-year case study. Previously, the students tended to work procedurally with statistics, but during the study, they increasingly engaged in questioning statistical information, justifying statistical interpretations, and communicating data-based claims about issues within and beyond their school context. We take a social constructivist perspective and analyse which sociomathematical norms related to statistical literacy emerged during the classroom interactions. We identified two such norms—what counts as a valuable description of a data set and what counts as a valuable answer to a statistical investigation—that connected classroom interactions with the aim of supporting students’ development of statistical literacy, especially its dispositional elements. The study contributes a rare empirical exploration of how to support students’ development of statistical literacy at the classroom level.
References
Bargagliotti, A. E., 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). American Statistical Association and National Council of Teachers of Mathematics. https://www.amstat.org/asa/files/pdfs/GAISE/GAISEIIPreK-12_Full.pdf
Ben-Zvi, D., & Garfield, J. (2004). Statistical literacy, reasoning, and thinking: Goals, definitions, and challenges. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 3–15). Kluwer Academic Publishers. https://doi.org/10.1007/1-4020-2278-6_1
Ben-Zvi, D., Gil, E., & Apel, N. (2007). What is hidden beyond the data? Helping young students to reason and argue about some wider universe. In D. Pratt & J. Ainley (Eds.), Reasoning about informal inferential statistical reasoning: A collection of current research studies (pp. 29–35). University of Warwick.
Büscher, C. (2018). Mathematical literacy on statistical measures: A design research study. Springer. https://doi.org/10.1007/978-3-658-23069-2
Büscher, C. (2022). Design principles for developing statistical literacy in middle schools. Statistics Education Research Journal, 21(1), Article 8. https://doi.org/10.52041/serj.v21i1.80
Büscher, C. (2024). Adapting Habermas’ construct of communicative rationality into a framework for analyzing students’ statistical literacy. Educational Studies in Mathematics, 117(1), 121–141. https://doi.org/10.1007/s10649-024-10325-5
Callingham, R., & Watson, J. (2017). The development of statistical literacy at school. Statistics Education Research Journal, 16(1), 181–201. https://doi.org/10.52041/serj.v16i1.223
Caspersen, S. (2021, April 3). I det rigeste lokalområde tjener de fem gange mere end bunden [In the wealthiest local area, they earn five times more than those at the bottom]. Arbejderbev ægelsens Erhvervsråd. https://www.ae.dk/analyse/2021-04-i-det-rigeste-lokalomraade-tjener-de-fem-gange-mere-end-bunden
Charmaz, K. (2014). Constructing grounded theory. SAGE.
Clark, P. G., Moore, K. C., & Carlson, M. P. (2008). Documenting the emergence of “speaking with meaning” as a sociomathematical norm in professional learning community discourse. Journal of Mathematical Behavior, 27(4), 297–310. https://doi.org/10.1016/j.jmathb.2009.01.001
Cobb, P. (1999). Individual and collective mathematical development: The case of statistical data analysis. Mathematical Thinking and Learning, 1(1), 5–43. https://doi.org/10.1207/s15327833mtl0101_1
Cobb, P., & McClain, K. (2005). Principles of instructional design for supporting the development of students’ statistical reasoning. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 375–395). Kluwer Academic Publishers. https://doi.org/10.1007/1-4020-2278-6_16
Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. Journal of the Learning Sciences, 10(1–2), 113–163. https://doi.org/10.1207/S15327809JLS10-1-2_6
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. (2021). Promoting statistical literacy: Challenges and reflections with a Brazilian perspective. In C. Monterio & L. Carvalho (Eds.), Temas emergentes em letramento estatistico (pp. 37–59). UFPE Press.
Gal, I. (2022). Critical understanding of civic statistics: Engaging with important contexts, texts, and opinion questions. In J. Ridgway (Ed.), Statistics for empowerment and social engagement: Teaching civic statistics to develop informed citizens (pp. 323–343). Springer. https://doi.org/10.1007/978-3-031-20748-8_13
Konold, C., & Miller, C. D. (2022). TinkerPlots (Version 2022) [Computer software]. Learn Troop.
Lopez, L. M., & Allal, L. (2007). Sociomathematical norms and the regulation of problem solving in classroom microcultures. International Journal of Educational Research, 46(5), 252–265. https://doi.org/10.1016/j.ijer.2007.10.005
Ministry of Children and Education. (2019). Matematik: Fælles mål [Mathematics: Common objectives]. https://emu.dk/sites/default/files/2020-09/GSK_F%C3%A6llesM%C3%A5l_Matematik.pdf
Neupert, S. (2021, April 6). Danskernes indtægt opgjort for hvert sogn - det tjener de rigeste og de fattigste [Danes’ income broken down by parish – what the richest and poorest earn]. TV 2 Nyheder. https://nyheder.tv2.dk/business/2021-04-06-danskernes-indtaegt-opgjort-for-hvert-sogn-det-tjener-de-rigeste-og-de-fattigste
Phadke, S., Beckman, M., & Morgan, K. L. (2024). Examining the role of context in statistical literacy outcomes using an isomorphic assessment instrument. Statistics Education Research Journal, 23(1), Article 4. https://doi.org/10.52041/serj.v23i1.529
Ridgway, J. (Ed.). (2022). Statistics for empowerment and social engagement: Teaching civic statistics to develop informed citizens. Springer. https://doi.org/10.1007/978-3-031-20748-8
Sabbag, A., Garfield, J., & Zieffler, A. (2018). Assessing statistical literacy and statistical reasoning: The REALI instrument. Statistics Education Research Journal, 17(2), 141–160. https://doi.org/10.52041/serj.v17i2.163
Skott, C. K., & Østergaard, C. H. (2018). En matematiklærers professionelle udvikling [A mathematics teacher’s professional development]. In J. Bundsgaard, M. Georgsen, S. T. Graf, T. I. Hansen, & C. K. Skott (Eds.), Innovativ undervisning med it. Forskning i tre demonstrationsskoleforsøg II (pp. 157–178). Aarhus Universitetsforlag.
Skott, J. (2008). Introduktion til Paul Cobbs matematikdidaktiske arbejde [Introduction to Paul Cobb’s work in mathematics education]. MONA, 4, 42–58. https://doi.org/10.7146/mona.v0i4.36629
Thomas, G. (2011). A typology for the case study in social science following a review of definition, discourse, and structure. Qualitative Inquiry, 17(6), 511–521. https://doi.org/10.1177/1077800411409884
van Zoest, L. R., Stockero, S. L., & Taylor, C. E. (2012). The durability of professional and sociomathematical norms intentionally fostered in an early pedagogy course. Journal of Mathematics Teacher Education, 15(4), 293–315. https://doi.org/10.1007/s10857-011-9183-y
Visnovska, J., & Cobb, P. (2019). Supporting shifts in teachers’ views of a classroom statistical activity: Problem context in teaching statistics. Mathematical Thinking and Learning, 21(4), 285–305. https://doi.org/10.1080/10986065.2019.1576003
Voigt, J. (1998). The culture of the mathematics classroom: Negotiating the mathematical meaning of empirical phenomena. In F. Seeger, J. Voigt, & U. Waschescio (Eds.), The culture of the mathematics classroom (pp. 191–202). Cambridge University Press.
Weiland, T. (2017). Problematizing statistical literacy: An intersection of critical and statistical literacies. Educational Studies in Mathematics, 96(1), 33–47. https://doi.org/10.1007/s10649-017-9764-5
Weiland, T. (2019). Critical mathematics education and statistics education: Possibilities for transforming the school mathematics curriculum. In G. Burrill & D. Ben-Zvi (Eds.), Topics and trends in current statistics education research (pp. 391–411). Springer. https://doi.org/10.1007/978-3-030-03472-6_18
Widjaja, W. (2012). Exercising sociomathematical norms in classroom discourse about data representation: Insights from one case study of a grade 6 lesson in Indonesia. The Mathematics Educator, 13(2), 21–38. http://hdl.handle.net/10536/DRO/DU:30048395
Yackel, E. (2002). What we can learn from analyzing the teacher’s role in collective argumentation. Journal of Mathematical Behavior 21(4), 423–440. https://doi.org/10.1016/S0732-3123(02)00143-8
Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477. https://doi.org/10.5951/jresematheduc.27.4.0458
Ziegler, L., & Garfield, J. (2018). Developing a statistical literacy assessment for the modern introductory statistics course. Statistics Education Research Journal, 17(2), 161–178. https://doi.org/10.52041/serj.v17i2.164