, Volume 50, Issue 7, pp 1165–1181 | Cite as

Statistical modeling to promote students’ aggregate reasoning with sample and sampling

  • Keren AridorEmail author
  • Dani Ben-Zvi
Original Article


While aggregate reasoning is a core aspect of statistical reasoning, its development is a key challenge in statistics education. In this study we examine how students’ aggregate reasoning with samples and sampling (ARWSS) can emerge in the context of statistical modeling activities of real phenomena. We present a case study on the emergent ARWSS of two pairs of sixth graders (age 11–12) involved in statistical data analysis and informal inference utilizing TinkerPlots. The students’ growing understandings of various statistical concepts is described and five perceptions the students expressed are identified. We discuss the contribution of modeling to these progressions followed by conclusions and limitations of these results. While idiosyncratic, the insights contribute to the understanding of students’ aggregate reasoning with data and models, with regards to samples and sampling.


Exploratory data analysis Informal statistical inference Aggregate statistical reasoning Statistical model and modeling Sample and sampling 



This research was supported by the University of Haifa and the I-CORE Program of the Planning and Budgeting Committee and the Israel Science Foundation Grant 1716/12. We deeply thank the Connections research team and the anonymous reviewers of earlier versions of this manuscript.


  1. Ainley, J., Pratt, D., & Hansen, A. (2006). Connecting engagement and focus in pedagogic task design. British Educational Research Journal, 32(1), 23–38.CrossRefGoogle Scholar
  2. Aridor, K., & Ben-Zvi, D. (2017). The co-emergence of aggregate and modelling reasoning. Statistics Education Research Journal, 16(2), 38–63.Google Scholar
  3. Aridor, K., & Ben-Zvi, D. (2018). Students’ aggregate reasoning with covariation. In G. Burrill & D. Ben-Zvi (Eds.), Topics and trends in current statistics education research: International perspectives. New York: Springer (in press).Google Scholar
  4. Bakker, A., & Gravemeijer, K. P. E. (2004). Learning to reason about distributions. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 147–168). Dordrecht: Kluwer.CrossRefGoogle Scholar
  5. Ben-Zvi, D., & Arcavi, A. (2001). Junior high school students’ construction of global views of data and data representations. Educational Studies in Mathematics, 45(1–3), 35–65.CrossRefGoogle Scholar
  6. Ben-Zvi, D., Aridor, K., Makar, K., & Bakker, A. (2012). Students’ emergent articulations of uncertainty while making informal statistical inferences. ZDM - The International Journal on Mathematics Education, 44(7), 913–925.CrossRefGoogle Scholar
  7. Ben-Zvi, D., Bakker, A., & Makar, K. (2015). Learning to reason from samples. Educational Studies in Mathematics, 88(3), 291–303.CrossRefGoogle Scholar
  8. 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). Cham: Springer Cham.CrossRefGoogle Scholar
  9. Biehler, R., Ben-Zvi, D., Bakker, A., & Makar, K. (2013). Technology for enhancing statistical reasoning at the school level. In M. A. Clements et al. (Eds.), Third international handbook of mathematics education (pp. 643–690). New York: Springer.Google Scholar
  10. Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. New York: Springer.Google Scholar
  11. Hancock, C., Kaput, J. J., & Goldsmith, L. T. (1992). Authentic enquiry with data: Critical barriers to classroom implementation. Educational Psychologist, 27(3), 337–364.CrossRefGoogle Scholar
  12. Konold, C. (2002). Teaching concepts rather than conventions. New England Journal of Mathematics, 34(2), 69–81.Google Scholar
  13. Konold, C., Higgins, T., Russell, S.-J., & Khalil, K. (2015). Data seen through different lenses. Educational Studies in Mathematics, 88(3), 305–325.CrossRefGoogle Scholar
  14. Konold, C., & Kazak, S. (2008). Reconnecting data and chance. Technology innovations in statistics education, 2(1), 1, (article 1).Google Scholar
  15. Konold, C., & Miller, C. (2015). TinkerPlots™ (Version 2.2) [Computer software]. Amherst: University at Massachusetts.Google Scholar
  16. 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.CrossRefGoogle Scholar
  17. 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). Cham: Springer Cham.CrossRefGoogle Scholar
  18. Lehrer, R., & Schauble, L. (2004). Modelling natural variation through distribution. American Educational Research Journal, 41(3), 635–679.CrossRefGoogle Scholar
  19. Lehrer, R., & Schauble, L. (2005). Developing modeling and argument in the elementary grades. In T. Romberg, T. Carpenter & F. Dremock (Eds.), Understanding mathematics and science matters (pp. 29–53). Mahwah: Erlbaum.Google Scholar
  20. Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13(1), 152–173.CrossRefGoogle Scholar
  21. Makar, K., & Rubin, A. (2018). Learning about statistical inference. In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International handbook on research in statistics education. (pp. 261–294). Cham: Springer Cham.CrossRefGoogle Scholar
  22. Manor, H., & Ben-Zvi, D. (2017). Students’ emergent articulations of statistical models and modeling in making informal statistical inferences. Statistics Education Research Journal, 16(2), 116–143.Google Scholar
  23. Moore, D. S. (2010). The basic practice of statistics. New York: Freeman.Google Scholar
  24. Pfannkuch, M., Ben-Zvi, D., & Budgett, S. (2018). Innovations in statistical modeling to connect data, chance and context. ZDM Mathematics Education, 1, 1–11.Google Scholar
  25. Rubin, A., Bruce, B., & Tenney, Y. (1991). Learning about sampling: Trouble at the core of statistics. In D. Vere-Jones (Ed.), Proceedings of the Third International Conference on Teaching Statistics (Vol. 1, pp. 314–319). Amsterdam: ISI Publications in Statistical Education.Google Scholar
  26. Rubin, A., Hammerman, J. K. L., & Konold, C. (2006). Exploring informal inference with interactive visualization software. In Proceedings of the Seventh International Conference on Teaching Statistics. Salvador, Brazil.Google Scholar
  27. Schoenfeld, A. H. (2007). Method. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 69–107). Charlotte: Information Age Publishing.Google Scholar
  28. Shaughnessy, M., & Chance, B. (2005). Statistical questions from the classroom. Reston: NCTM.Google Scholar
  29. Siegler, R. S. (2006). Microgenetic analyses of learning. In D. Kuhn & R. S. Siegler (Eds.), Handbook of child psychology: Cognition, perception, and language (Vol. 2, 6th edn., pp. 464–510). Hoboken: Wiley.Google Scholar

Copyright information

© FIZ Karlsruhe 2018

Authors and Affiliations

  1. 1.LINKS I-CORE, Faculty of EducationThe University of HaifaHaifaIsrael

Personalised recommendations