Abstract
Curriculum change and the ready access to school level appropriate statistical software has seen the focus of statistical practice for novice statisticians move from primarily constructing graphs and calculating statistics to describing and reasoning from distributions. Many multi-faceted concepts and statistical ideas underpin distributions, which students find difficult to navigate and cognitively coordinate. Limited research, however, exists on how to enhance students’ communication when describing distributions. This paper explores the actions of a teacher as she supported 14–15-year-old students to develop notions of distribution and to describe distributions. The findings indicated that the teacher, through knowing, modelling, and listening, supported the development of student statistical language and communication. Students, through engaging in specifically designed instructional activities to engineer learning around the concept of distribution, seem to be able to transition from using their own language to using statistical language to describe distributions that communicated the concepts and features that were identified in the distribution description framework.
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References
Arnold, P. (2013). Statistical investigative questions: An enquiry into posing and answering investigative questions from existing data. (Doctoral thesis.) The University of Auckland, New Zealand.
Arnold, P., Pfannkuch, M., Wild, C., Regan, M., & Budgett, S. (2011). Enhancing students’ inferential reasoning: From hands-on to “movies”. Journal of Statistics Education, 19(2), 1–32. https://doi.org/10.1080/10691898.2011.11889609
Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools. Freudenthal Institute.
Bakker, A., & Gravemeijer, K. P. E. (2004). Learning to reason about distribution. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 147–168). Kluwer Academic Publishers.
Ben-Zvi, D., & Arcavi, A. (2001). Junior high school students’ construction of global views of data and data representations. Educational Studies in Mathematics, 45, 35–65. https://doi.org/10.1023/A:1013809201228
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 statistical inference: Innovative ways of connecting chance and data. Proceedings of the Fifth International Research Forum on Statistical Reasoning, Thinking and Literacy (SRTL-5, August 2007), University of Warwick, England (pp. 1–26). The University of Warwick.
Biehler, R. (1997). Students’ difficulties in practicing computer-supported data analysis: Some hypothetical generalizations from results of two exploratory studies. In J. Garfield & G. Burrill (Eds.), Research on the role of technology in teaching and learning statistics. Proceedings of the International Association for Statistical Education Round Table Conference (July 1996), Granada, Spain (pp. 169–190). International Statistical Institute.
Biehler, R., Frischemeier, D., Reading, C., & Shaughnessy, J.M. (2018). Reasoning about data. In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education (pp. 139–192). Springer. https://doi.org/10.1007/978-3-319-66195-7_5
Clarke, V., Braun, V., & Hayfield, N. (2015). Thematic analysis. In J. A. Smith (Ed.), Qualitative psychology: A practical guide to research methods (pp. 222–248). SAGE Publications.
Cobb, P., & McClain, K. (2004). 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.
Dunn, P. K., Carey, M. D., Richardson, A. M., & McDonald, C. (2016). Learning the language of statistics: Challenges and teaching approaches. Statistical Education Research Journal, 15(1), 8–27. https://doi.org/10.52041/serj.v15i1.255
Kaplan, J. J., Rogness, N. T., & Fisher, D. G. (2014). Exploiting lexical ambiguity to help students understand the meaning of random. Statistical Education Research Journal, 13(1), 9–24.
Makar, K., & Confrey, J. (2005). “Variation-talk”: Articulating meaning in statistics. Statistics Education Research Journal, 4(1), 27–54.
Ministry of Education. (2007). The New Zealand Curriculum. Learning Media.
Pfannkuch, M. (2006). Comparing box plot distributions: A teacher’s reasoning. Statistics Education Research Journal, 5(2), 27–45.
Pfannkuch, M. (2007). Year 11 students' informal inferential reasoning: A case study about the interpretation of box plots. International Electronic Journal of Mathematics Education, 2(3), 149–167. https://doi.org/10.29333/iejme/181
Pfannkuch, M., Arnold, P., & Wild, C. J. (2011). Statistics: It’s reasoning not calculating. (Summary research report on Building students’ inferential reasoning: Levels 5 and 6).http://www.tlri.org.nz/tlri-research/research-completed/school-sector/building-students-inferential-reasoning-statistics
Pfannkuch, M., Regan, M., Wild, C. J., & Horton, N. (2010). Telling data stories: Essential dialogues for comparative reasoning. Journal of Statistics Education, 18(1), 1–38. https://doi.org/10.1080/10691898.2010.11889479
Pfannkuch, M., Wild, C., Horton, N., & Regan, M. (2009). A teacher’s guide to informal comparative reasoning. http://www.censusatschool.org.nz/2008/informal-inference/nzteachersguide-2009-08-04.pdf
Prediger, S., Gravemeijer, K., & Confrey, J. (2015). Design research with a focus on learning processes: An overview on achievements and challenges. ZDM, 47(6), 877–891. https://doi.org/10.1007/s11858-015-0722-3
Terry, G., Hayfield, N., Clarke, V., & Braun, V. (2017). Thematic analysis. In C. Willig & W. Stainton Rogers (Eds.), The SAGE handbook of qualitative research in psychology (2nd edition) (pp. 17–37). SAGE Publications.
Wild, C. J. (2006). The concept of distribution. Statistics Education Research Journal, 5(2), 10–26.
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Arnold, P., Pfannkuch, M. Engaging novice statisticians in statistical communications. Math Ed Res J 36 (Suppl 1), 147–173 (2024). https://doi.org/10.1007/s13394-022-00442-w
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DOI: https://doi.org/10.1007/s13394-022-00442-w