Advertisement

ZDM

, Volume 50, Issue 7, pp 1113–1123 | Cite as

Innovations in statistical modeling to connect data, chance and context

  • Maxine Pfannkuch
  • Dani Ben-Zvi
  • Stephanie Budgett
Survey Paper
First Online:

Abstract

Statistical modeling is emerging as a fertile research environment in which to promote and learn about student statistical reasoning processes. We outline a paradigm shift toward a modeling perspective that is occurring in statistics education research and how statistical modeling processes involve connecting data, chance and context. The innovative task and software designs and theoretical frameworks that are under development for explicating student reasoning and pedagogy are discussed. In conclusion, we reflect on statistics education research.

This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

We thank Michal Dvir for her thorough feedback and comments on the paper and assistance in drawing out the main framework themes presented at SRTL-10.

References

  1. Abelson, R. (1995). Statistics as principled argument. Hillsdale: Lawrence Erlbaum.Google Scholar
  2. Abrahamson, D. (2014). Rethinking probability education: Perceptual judgment as epistemic resource. In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic thinking: Presenting plural perspectives (pp. 239–260). Dordrecht: Springer.CrossRefGoogle Scholar
  3. Ainley, J., Aridor, K., Ben-Zvi, D., Manor, H., & Pratt, D. (2013). Children’s expressions of uncertainty in statistical modelling. In J. Garfield (Ed.), Proceedings of the eighth international research forum on statistical reasoning, thinking, and literacy (SRTL8) (pp. 49–59). Minneapolis: University of Minnesota.Google Scholar
  4. Ainley, J., & Pratt, D. (2017). Computational modeling and children’s expressions of noise and signal. Statistics Education Research Journal, 16(2), 15–37.Google Scholar
  5. Aridor, K., & Ben-Zvi, D. (2017). The co-emergence of aggregate and modeling reasoning. Statistics Education Research Journal, 16(2), 38–63.Google Scholar
  6. Aridor, K., & Ben-Zvi, D. (2018). Statistical modeling to promote students’ aggregate reasoning with sample and sampling. ZDM Mathematics Education (this issue).Google Scholar
  7. Beckman, M., & delMas, R. (2018). Students’ emergent understanding of statistical modeling through parametric inference. ZDM Mathematics Education (this issue).Google Scholar
  8. 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
  9. Ben-Zvi, D., & Garfield, J. (Eds.). (2004). The challenge of developing statistical literacy, reasoning and thinking. Dordrecht: Kluwer Academic Publishers.Google Scholar
  10. 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). New York: Springer.CrossRefGoogle Scholar
  11. Biehler, R., Frischemeier, D., & Podworny, S. (2017a). Reasoning about models and modeling in the context of informal statistical inference. Statistics Education Research Journal, 16(2), 8–12.Google Scholar
  12. Biehler, R., Frischemeier, D., & Podworny, S. (2017b). Elementary preservice teachers’ reasoning about modeling a “family factory” with TinkerPlots—a pilot study. Statistics Education Research Journal, 16(2), 244–286.Google Scholar
  13. Biehler, R., Frischemeier, D., & Podworny, S. (2018). Elementary preservice teachers’ reasoning about setting up models in civic statistics contexts. ZDM Mathematics Education (this issue).Google Scholar
  14. Blum, W., Galbraith, P., Henn, H.-W., & Niss, M. (Eds.). (2007). Modeling and applications in mathematics education: The 14th ICMI Study. New York: Springer Science + Business Media, LLC.Google Scholar
  15. Budgett, S., & Fergusson, A. (2017). Modelling and linking the Poisson and exponential distributions in the real world and in the model world. In Proceedings of the 10th statistical reasoning, thinking and literacy forum, Rotorua, New Zealand (pp. 118–134). Auckland, SRTL.Google Scholar
  16. Budgett, S., & Pfannkuch, M. (2018). Modelling and linking the Poisson and exponential distributions. ZDM Mathematics Education (this issue).Google Scholar
  17. Büscher, C., & Schnell, S. (2017). Students’ emergent modeling of statistical measures—a case study. Statistics Education Research Journal, 16(2), 144–162.Google Scholar
  18. Cobb, G. (2007). The introductory statistics course: A ptolemaic curriculum? Technology Innovations in Statistics Education, 1(1), 1–16.Google Scholar
  19. Cobb, G., & Moore, D. (1997). Mathematics, statistics and teaching. The American Mathematical Monthly, 104(9), 801–823.CrossRefGoogle Scholar
  20. Doerr, H., delMas, R., & Makar, K. (2017). A modeling approach to the development of students’ informal inferential reasoning. Statistics Education Research Journal, 16(2), 86–115.Google Scholar
  21. Doerr, H., & Pratt, D. (2008). The learning of mathematics and mathematical modeling. In M. K. Heid & G. W. Blume (Eds.), Research on technology and the teaching and learning of mathematics: A research synthesis (pp. 259–286). Charlotte: Information Age Publishing.Google Scholar
  22. Dvir, M., & Ben-Zvi, D. (2018). The role of model comparison in young learners’ reasoning with statistical models and modeling. ZDM Mathematics Education.  https://doi.org/10.1007/s11858-018-0987-4.CrossRefGoogle Scholar
  23. Eichler, A., & Vogel, M. (2014). Three approaches for modelling situations with randomness. In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic thinking: Presenting plural perspectives (pp. 75–99). Dordrecht: Springer.CrossRefGoogle Scholar
  24. Fielding-Wells, J. (2018). Dot plots and hat plots: Supporting young students emerging understandings of distribution, center and variability through modeling. ZDM Mathematics Education.  https://doi.org/10.1007/s11858-018-0961-1.CrossRefGoogle Scholar
  25. Garfield, J., & Ben-Zvi, D. (2008). Learning to reason about statistical models and modeling. In J. Garfield & D. Ben-Zvi (Eds.), Developing students’ statistical reasoning: Connecting research and teaching practice (pp. 143–163). New York: Springer.CrossRefGoogle Scholar
  26. Garfield, J., & Ben-Zvi, D. (2015). Foreword. In A. Zieffler & E. Fry (Eds.), Reasoning about uncertainty: Learning and teaching informal inferential reasoning (pp. xv–xviii). Minneapolis: Catalyst Press.Google Scholar
  27. Garfield, J., delMas, R., & Zieffler, A. (2012). Developing statistical modelers and thinking in an introductory, tertiary-level statistics course. ZDM - The International Journal on Mathematics Education, 44(7), 883–898.CrossRefGoogle Scholar
  28. Gil, E., & Gibbs, A. (2017). Promoting modeling and covariational reasoning among secondary school students in the context of big data. Statistics Education Research Journal, 16(2), 163–190.Google Scholar
  29. Gould, R., Bargagliotti, A., & Johnson, T. (2017). An analysis of secondary teachers’ reasoning with participatory sensing data. Statistics Education Research Journal, 16(2), 305–334.Google Scholar
  30. Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1(2), 155–177.CrossRefGoogle Scholar
  31. Justice, N., Zieffler, A., Huberty, M., & delMas, R. (2018). Narration, comparison, and variation: Secondary teachers’ reasoning about statistical models. ZDM Mathematics Education (this issue).Google Scholar
  32. Kaiser, G., Blum, W., & Ferri, B., R., & Stillman, G. (Eds.). (2011). Trends in teaching and learning of mathematical modelling: ICTMA 14. New York: Springer.Google Scholar
  33. Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302–310.CrossRefGoogle Scholar
  34. Kazak, S., & Pratt, D. (2017). Pre-service mathematics teachers’ use of probability models in making informal inferences about a chance game. Statistics Education Research Journal, 16(2), 287–304.Google Scholar
  35. Kazak, S., Pratt, D., & Gökce, R. (2018). Sixth grade students’ emerging practices of data modelling. ZDM Mathematics Education.  https://doi.org/10.1007/s11858-018-0988-3.CrossRefGoogle Scholar
  36. Konold, C., Finzer, W., & Kreetong, K. (2017). Modeling as a core component of structuring data. Statistics Education Research Journal, 16(2), 191–212.Google Scholar
  37. Konold, C., Harradine, A., & Kazak, S. (2007). Understanding distributions by modeling them. International Journal of Computers for Mathematical Learning, 12(3), 217–230.CrossRefGoogle Scholar
  38. Konold, C., & Kazak, S. (2008). Reconnecting data and chance. Technology Innovations in Statistics Education, 2(1), 1–37.Google Scholar
  39. Konold, C., & Lehrer, R. (2008). Technology and mathematics education: An essay in honor of Jim Kaput. In L. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 49–72). New York: Routledge.Google Scholar
  40. Konold, C., Madden, S., Pollatsek, A., Pfannkuch, M., Wild, C., Ziedins, I., Finzer, W., Horton, N., & Kazak, S. (2011). Conceptual challenges in coordinating theoretical and data-centered estimates of probability. Mathematical Thinking and Learning, 13(1&2), 68–86.CrossRefGoogle Scholar
  41. Konold, C., & Miller, C. (2011). TinkerPlots™ Version 2.3 [computer software]. Amherst: Learn Troop.Google Scholar
  42. Lehrer, R. (2017). Modeling signal-noise processes supports student construction of a hierarchical image of sample. Statistics Education Research Journal, 16(2), 64–85.Google Scholar
  43. Lehrer, R., & English, E. (2018). Introducing children to modeling variability. In D. Ben-Zvi, J. Garfield & K. Makar (Eds.), International handbook of research in statistics education (pp. 229–260). New York: Springer.CrossRefGoogle Scholar
  44. Lesh, R., & Doerr, H. (Eds.). (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahwah: Lawrence Erlbaum Associates.Google Scholar
  45. Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763–802). Greenwich: Information Age Publishing.Google Scholar
  46. Lightner, J. (1991). A brief look at the history of probability and statistics. Mathematics Teacher, 84(8), 623–630.Google Scholar
  47. Makar, K., & Allmond, S. (2018). Statistical modeling and repeatable structures: Purpose, process and prediction. ZDM Mathematics Education (this issue).Google Scholar
  48. Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13(1&2), 152–173.CrossRefGoogle Scholar
  49. Makar, K., & Rubin, A. (2018). Research on inference. In D. Ben-Zvi, J. Garfield & K. Makar (Eds.), International handbook of research in statistics education (pp. 261–294). New York: Springer.CrossRefGoogle Scholar
  50. Manor Braham, H., & Ben-Zvi, D. (2017). Students’ emergent articulations of statistical models and modelling in making informal statistical inferences. Statistics Education Research Journal, 16(2), 116–143.Google Scholar
  51. Noll, J., Clement, K., Dolor, J., & Petersen, M. (2018). Students’ use of narrative when constructing statistical models in TinkerPlots™. ZDM Mathematics Education.  https://doi.org/10.1007/s11858-018-0981-x.CrossRefGoogle Scholar
  52. Noll, J., & Kirin, D. (2017). TinkerPlots™ model construction approaches for comparing two groups: Student perspectives. Statistics Education Research Journal, 16(2), 213–243.Google Scholar
  53. Patel, A., & Pfannkuch, M. (2018). Developing a statistical modeling framework to characterize Year 7 students’ reasoning. ZDM Mathematics Education.  https://doi.org/10.1007/s11858-018-0960-2.CrossRefGoogle Scholar
  54. Pfannkuch, M. (2011). The role of context in developing informal statistical inferential reasoning: A classroom study. Mathematical Thinking and Learning, 13(1&2), 27–46.CrossRefGoogle Scholar
  55. Pfannkuch, M., & Budgett, S. (2016). Markov processes: Exploring the use of dynamic visualizations to enhance student understanding. Journal of Statistics Education, 24(2), 63–73.CrossRefGoogle Scholar
  56. Pfannkuch, M., Budgett, S., Fewster, R., Fitch, M., Pattenwise, S., Wild, C., & Ziedins, I. (2016). Probability modelling and thinking: What can we learn from practice? Statistics Education Research Journal, 15(2), 11–37.Google Scholar
  57. Pfannkuch, M., & Ziedins, I. (2014). A modelling perspective on probability. In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic thinking: Presenting plural perspectives (pp. 101–116). New York: Springer.CrossRefGoogle Scholar
  58. Pratt, D. (2011). Re-connecting probability and reasoning from data in secondary school teaching. In Proceedings of the 58th International Statistical Institute World Statistical Congress, Dublin (pp. 890–899). The Hague: International Statistical Institute.Google Scholar
  59. Pratt, D., & Noss, R. (2010). Designing for mathematical abstraction. International Journal of Computers for Mathematical Learning, 15(2), 81–97.CrossRefGoogle Scholar
  60. Resnick, L. (1988). Treating mathematics as an ill-structured discipline. In R. Charles & E. Silver (Eds.), The teaching and assessing of mathematical problem solving (pp. 32–60). Reston: National Council of Teachers of Mathematics.Google Scholar
  61. Shinohara, M., & Lehrer, R. (2017). Narrating lines of practice: Students’ views of their participation in statistical practices. In Proceedings of the 10th Statistical Reasoning, Thinking and Literacy Forum, Rotorua, New Zealand (pp. 15–33). Auckland: SRTL.Google Scholar
  62. Stillman, G., Kaiser, G., Blum, W., & Brown, J. (Eds.). (2013). Teaching mathematical modeling: Connecting research to practice. Dordrecht: Springer.Google Scholar
  63. Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry (with discussion). International Statistical Review, 67(3), 223–265.CrossRefGoogle Scholar
  64. Wild, C. J., Pfannkuch, M., Regan, M., & Parsonage, R. (2017). Accessible conceptions of statistical inference: Pulling ourselves up by the bootstraps. International Statistical Review, 85(1), 84–107.CrossRefGoogle Scholar
  65. Wilkerson, M., & Laina, V. (2018). Middle school students’ reasoning about data, context, and chance through storytelling with repurposed local data. ZDM Mathematics Education.  https://doi.org/10.1007/s11858-018-0974-9.CrossRefGoogle Scholar
  66. Zapata-Cardona, L. (2018). Students’ construction and use of models for informal inferential reasoning. ZDM Mathematics Education.  https://doi.org/10.1007/s11858-018-0967-8.CrossRefGoogle Scholar
  67. Zieffler, A. (2017). Panel presentation communication at the 10th statistical reasoning, thinking and literacy forum, Rotorua, New Zealand.Google Scholar

Copyright information

© FIZ Karlsruhe 2018

Authors and Affiliations

  1. 1.The University of AucklandAucklandNew Zealand
  2. 2.The University of HaifaHaifaIsrael

Personalised recommendations

Cite article

Buy options