Advertisement

ZDM

, Volume 50, Issue 7, pp 1197–1212 | Cite as

Developing a statistical modeling framework to characterize Year 7 students’ reasoning

  • Anne Patel
  • Maxine PfannkuchEmail author
Original Article

Abstract

Some researchers advocate a statistical modeling approach to inference that draws on students’ intuitions about factors influencing phenomena and that requires students to build models. Such a modeling approach to inference became possible with the creation of TinkerPlots Sampler technology. However, little is known about what statistical modeling reasoning students need to acquire. Drawing and building on previous research, this study aims to uncover the statistical modeling reasoning students need to develop. A design-based research methodology employing Model Eliciting Activities was used. The focus of this paper is on two 11-year-old students as they engaged with a bag weight task using TinkerPlots. Findings indicate that these students seem to be developing the ability to build models, investigate and posit factors, consider variation and make decisions based on simulated data. From the analysis an initial statistical modeling framework is proposed. Implications of the findings are discussed.

Keywords

Statistics education Middle school students Statistical modeling reasoning TinkerPlots Model eliciting activities 

References

  1. 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). Dordrecht: Springer.Google Scholar
  2. Ben-Zvi, D. (2006). Scaffolding students’ informal inference and argumentation. In A. Rossman & B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching of Statistics, Salvador, Brazil. Voorburg, The Netherlands: International Statistical Institute.Google Scholar
  3. Blum, W., Galbraith, P., Henn, H.-W., & Niss, M. (Eds.). (2007). Modeling and Applications in Mathematics Education: The 14th ICMI Study. New York: Springer.Google Scholar
  4. Carlson, M., Larsen, S., & Lesh, R. (2003). Integrating a Models and Modeling Perspective with Existing Research and Practice. In R. Lesh & H. Doerr (Eds.), Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching (pp. 465–478). Mahwah: Lawrence Erlbaum Associates.Google Scholar
  5. Charmaz, K. (2014). Constructing Grounded Theory. Thousand Oaks: Sage.Google Scholar
  6. Dierdorp, A., Bakker, A., Eijkelhof, H., & van Maanen, J. (2011). Authentic practices as contexts for learning to draw inferences beyond correlated data. Mathematical Thinking and Learning, 13(1&2), 132–151.CrossRefGoogle Scholar
  7. 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
  8. Gil, E., & Ben-Zvi, D. (2010). Emergence of reasoning about sampling among young students in the context of informal inferential reasoning. In C. Reading (Ed.), Data and context in statistics education: Towards an evidence-based society. Proceedings of the Eighth International Conference on Teaching Statistics, Ljubljana, Slovenia. Voorburg, The Netherlands: International Statistical Institute.Google Scholar
  9. Kaiser, G., Blum, W., & Ferri, Borromeo, R., & Stillman, G. (Eds.). (2011). Trends in Teaching and Learning of Mathematical Modelling: ICTMA 14. New York: Springer.Google Scholar
  10. Konold, C., & Harradine, A. (2014). Contexts for highlighting signal and noise. In T. Wassong, D. Frischemeier, P. Fischer, R. Hochmuth & P. Bender (Eds.), Mit Werkzeugen Mathematik und Stochastik lernen: Using Tools for Learning Mathematics and Statistics (pp. 237–250). Wiesbaden: Springer.CrossRefGoogle Scholar
  11. 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
  12. Konold, C., & Kazak, S. (2008). Reconnecting data and chance. Technology Innovations in Statistics Education, 2(1). http://repositories.cdlib.org/uclastat/cts/tise/vol2/iss1/art1. Accessed 25 Feb 2013.
  13. Konold, C., & Miller, C. (2011). TinkerPlots™ Version 2.3 [Computer Software]. Amherst: Learn Troop.Google Scholar
  14. Lehrer, R. (2015). Developing practices of model-based informal inference. In Proceedings of the Ninth International Research Forum on Statistical Reasoning, Thinking, and Literacy (SRTL9, 26 July3 August, 2015) (pp. 76–86). Paderborn, Germany: University of Paderborn.Google Scholar
  15. 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.CrossRefGoogle Scholar
  16. 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
  17. Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for Developing Thought-Revealing Activities for Students and Teachers. In A. Kelly & R. Lesh (Eds.), Handbook of Research Design in Mathematics and Science Education (pp. 591–646). Mahwah: Lawrence Erlbaum.Google Scholar
  18. Pfannkuch, M., Budgett, S., Fewster, R., Fitch, M., Pattenwise, S., Wild, C., & Ziedins, I. (2016). Probability modeling and thinking: What can we learn from practice? Statistics Education Research Journal, 15(2), 11–37.Google Scholar
  19. Pfannkuch, M., & Ziedins, I. (2014). A modeling Perspective on Probability. In E. Chernoff & B. Sriraman (Eds.), Probabilistic Thinking: Presenting Plural Perspectives (pp. 101–116). Dordrecht: Springer.CrossRefGoogle Scholar
  20. Pratt, D. (2011). Re-connecting probability and reasoning from data in secondary school teaching. Proceedings of the 58th International Statistical Institute World Statistical Congress, Dublin, (pp. 890–899). The Hague, The Netherlands: International Statistical Institute.Google Scholar
  21. Stillman, G., Galbraith, P., Brown, J., & Edwards, I. (2007). A Framework for Success in Implementing Mathematical Modeling in the Secondary Classroom. In J. Watson & K. Beswick (Eds.), Proceedings of the 30th Annual Conference of the Mathematics Education Research Group of Australasia, (vol. 2, pp. 688–697). Adelaide, Australia: MERGA Inc.Google Scholar
  22. Watson, A., & Ohtani, M. (Eds.). (2015). Task Design in Mathematics Education. New York: Springer.Google Scholar
  23. Wild, C., Pfannkuch, M., Regan, M., & Horton, N. (2011). Towards more accessible conceptions of statistical inference. Journal of the Royal Statistical Society. Series A: Statistics in Society, 174(2), 247–295.CrossRefGoogle Scholar
  24. Yoon, C., & Patel, A. (2011). Students’ Communication Abilities in Model Eliciting Activities. In H. Dixon, E. van Til, & R. Williams (Eds.), Proceedings of the Conference of the New Zealand Association for Research in Education (pp. 87–94), Auckland, New Zealand: NZARE.Google Scholar
  25. Yoon, C., Patel, A., Radonich, P., & Sullivan, N. (2011). Learning environments with mathematical modeling activities. Teacher Learning Research Initiative. Wellington, New Zealand: New Zealand Council for Educational Research. http://www.tlri.org.nz/sites/default/files/projects/9274_finalreport.pdf. Accessed 10 Jul 2015.
  26. Yoon, C., Patel, A., & Sullivan, N. (2016). LEMMA (Learning Environments with Mathematical Modeling Activities): Mathematics Tasks that Promote Higher Order Thinking. Mixing Ratios. Wellington: New Zealand Council for Educational Research.Google Scholar

Copyright information

© FIZ Karlsruhe 2018

Authors and Affiliations

  1. 1.The University of AucklandAucklandNew Zealand

Personalised recommendations