DESIGN PRINCIPLES FOR DEVELOPING STATISTICAL LITERACY IN MIDDLE SCHOOLS
DOI:
https://doi.org/10.52041/serj.v21i1.80Keywords:
Statistics education research, Statistical literacy, Design research, Learning trajectory, Critical literacyAbstract
Statistical literacy is a skill that will be required by all students, but only limited insights exist into how it can be developed in middle schools. Research is required that identifies design principles and provides didactic materials for developing statistical literacy in actual middle school classrooms, meaning classrooms in which statistics is only seen as a small part of mathematics. This study conceptualizes statistical literacy as not only the ability to read given statistical information, but also as the ability to imagine the often unreported data and underlying assumptions of this information. This allows the Design Research study to identify design principles for developing statistical literacy in which students actively engage with conflicting statistical information about the same data. The working mechanisms of the design principles are illustrated through didactic materials, and student responses show how the design principles can be used to develop statistical literacy in middle schools.
References
Arnold, P., Confrey, J., Jones, R. S., Lee, H. S., & Pfannkuch, M. (2018). Statistics learning trajectories. In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education (pp. 295–326). Springer. https://doi.org/10.1007/978-3-319-66195-7_9
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). Springer. https://doi.org/10.1007/1-4020-2278-6_7
Bakker, A., & van Eerde, D. (2015). An introduction to design-based research with an example from statistics education. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education (pp. 429–466). Springer. https://doi.org/10.1007/978-94-017-9181-6_16
Ben-Zvi, D., & Garfield, J. (Eds.) (2004). The challenge of developing statistical literacy, Reasoning and thinking. Springer. https://doi.org/10.1007/1-4020-2278-6
Ben-Zvi, D., Gravemeijer, K., & Ainley, J. (2018). Design of Statistics Learning Environments. In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education (pp. 473–502). Springer. https://doi.org/10.1007/978-3-319-66195-7_16
Biehler, R., Ben-Zvi, D., Bakker, A., & Makar, K. (2013). Technology for enhancing statistical rea- soning at the school level. In M. A. Clements, A. Bishop, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Third international handbook of mathematics education (pp. 643–690). Springer. https://doi.org/10.1007/978-1-4614-4684-2_21
Budgett, S., & Rose, D. (2017). Developing statistical literacy in the final school year. Statistics Education Research Journal, 16(1), 139–162. https://doi.org/10.52041/serj.v16i1.221
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., & Prediger, S. (2019). Students’ reflective concepts when reflecting on statistical measures: A design research study. Journal Für Mathematik-Didaktik, 40(2), 197–225. https://doi.org/10.1007/s13138-019-00142-2
Callingham, R., & Watson, J. M. (2017). The development of statistical literacy at school. Statistics Education Research Journal, 16(1), 181–201. https://doi.org/10.52041/serj.v16i1.223
Carmichael, C., Callingham, R., Watson, J., & Hay, I. (2009). Factors influencing the development of middle school students’ interest in statistical literacy. Statistics Education Research Journal, 8(1), 62–81. https://iase-web.org/documents/SERJ/SERJ8(1)_Carmichael.pdf?1402525008
Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81–89. https://doi.org/10.1207/s15327833mtl0602_1
Douady, R. (1985). The interplay between different settings. Tool-object dialectic in the extension of mathematical ability. In L. Streefland (Ed.), Proceedings of the ninth international conference for the psychology of mathematics education (Vol. 2, pp. 33–52). IGPME.
DWD Deutscher Wetterdienst (n.d.). Klimadaten Deutschland. Retrieved from https://www.dwd.de/DE/leistungen/klimadatendeutschland/klimadatendeutschland.html
Engel, J. (2017). Statistical literacy for active citizenship: A call for data science education. Statistics Education Research Journal, 16(2), 44–49. https://doi.org/10.52041/serj.v16i1.213
François, K., Monteiro, C., & Allo, P. (2020). Big-data literacy as a new vocation for statistical literacy. Statistics Education Research Journal, 19(1), 194–205. https://doi.org/10.52041/serj.v19i1.130
Gal, I. (2002). Adults’ statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1), 1–25. https://doi.org/10.2307/1403713
Gould, R. (2017). Data literacy is statistical literacy. Statistics Education Research Journal, 16(1), 22–25. https://doi.org/10.52041/serj.v16i1.209
Grant, R. (2017). Statistical literacy in the data science workplace. Statistics Education Research Journal, 16(1), 17–21. https://doi.org/10.52041/serj.v16i1.207
Hußmann, S., & Prediger, S. (2016). Specifying and structuring mathematical topics. Journal Für Mathematik-Didaktik, 37(S1), 33–67. https://doi.org/10.1007/s13138-016-0102-8
Jones, J. S., & Goldring, J. E. (2017). Telling stories, landing planes and getting them moving: A holistic approach to developing students’ statistical literacy. Statistics Education Research Journal, 16(1), 102–119. https://doi.org/10.52041/serj.v16i1.219
Krishnan, S. (2015). Fostering students’ statistical literacy through significant learning experience. Journal of Research in Mathematics Education, 4(3), 259. https://doi.org/10.17583/redimat.2015.1332
Lehrer, R., & English, L. (2018). Introducing children to modeling variability. In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education (pp. 229–260). Springer. https://doi.org/10.1007/978-3-319-66195-7_7
Lesh, R., & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2–3), 109–129. https://doi.org/10.1080/10986065.2003.9679996
Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13(1–2), 152–173. https://doi.org/10.1080/10986065.2011.538301
Organisation for Economic Co-operation and Development. (2018). Pisa 2022 Mathematics Framework (Draft). https://pisa2022-maths.oecd.org
Peschek, W., & Schneider, E. (2002). CAS in general mathematics education. ZDM, 34(5), 189–195. https://doi.org/10.1007/BF02655821
Poling, L., & Weiland, T. (2020). Using an interactive platform to recognize the intersection of social and spatial inequalities. Teaching Statistics, 42(3), 108–116. https://doi.org/10.1111/test.12234
Prediger, S. (2019). Theorizing in design research. Avances De Investigación En Educación Matemática. (15), 5–27. https://doi.org/10.35763/aiem.v0i15.265
Prediger, S., & Zwetzschler, L. (2013). Topic-specific design research with a focus on learning processes: The case of understanding algebraic equivalence in grade 8. In T. Plomp & N. Nieveen (Eds.), Educational design research: Part A: An introduction (pp. 409–423). SLO.
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
Prodromou, T., & Dunne, T. (2017). Statistical literacy in data revolution era: Building blocks and instructional dilemmas. Statistics Education Research Journal, 16(1), 38–43. https://doi.org/10.52041/serj.v16i1.212
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
Steen, L. A. (Ed.) (2001). Mathematics and democracy: The case for quantitative literacy. National Council on Education and the Disciplines.
The Concord Consortium. (2021). CODAP: Common Online Data Analysis Platform. https://codap.concord.org/
van den Akker, J. (1999). Principles and methods of development research. In J. van den Akker, R. M. Branch, K. Gustafson, N. Nieveen, & T. Plomp (Eds.), Design approaches and tools in education and training (pp. 1–14). Springer. https://doi.org/10.1007/978-94-011-4255-7
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). The contextualized situations constructed for the use of statistics by school mathematics textbooks. Statistics Education Research Journal, 18(2), 18–38. https://doi.org/10.52041/serj.v18i2.138
Wild, C. J. (2017). Statistical literacy as the Earth moves. Statistics Education Research Journal, 16(1), 31–37. https://doi.org/10.52041/serj.v16i1.211
Yolcu, E. (2014). Middle school students’ statistical literacy: Role of grade level and gender. Statistics Education Research Journal, 13(2), 118–131. https://doi.org/10.52041/serj.v13i2.285
Zieffler, A., Garfield, J., & Fry, E. (2018). What is statistics education? In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education (pp. 37–70). Springer. https://doi.org/10.1007/978-3-319-66195-7_2
