Students’ use of narrative when constructing statistical models in TinkerPlots

Abstract

Initial research has shown that simulating data from models created with computer software may enhance students’ understanding of concepts in introductory statistics; yet, there is little research investigating students’ development of statistical models. The research presented here examines small groups of students as they develop a model for a situation where a music teacher plays ten notes for a student who tries to guess each of the notes correctly. As students constructed their models and described their thinking, their descriptions were narrative in nature, focusing on the story of notes played and guessed. In this context, their focus on narrative appeared to support the development of productive statistical models. In addition, when students investigated pre-built TinkerPlots models, they preferred models that they perceived as more communicative or narrative in nature. These results have important pedagogical implications in terms of designing modeling curriculum.

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Notes

  1. 1.

    While some researchers distinguish between narrative and story (e.g., Fuchs, 2015), others use these terms interchangeably. In our work, we use stories and narrative interchangeably.

  2. 2.

    If the group came up with one of the three models shown then we did not show them that model, opting to show only the two models they did not use in their work.

  3. 3.

    Email the authors of this paper to obtain the entire problem solving session protocol.

  4. 4.

    We do not focus on quantitative summaries in this paper, however the majority of students did create models that focused on notes.

References

  1. Avraamidou, L., & Osborne, J. (2009). The role of narrative in communicating science. International Journal of Science Education, 31(12), 1683–1707. https://doi.org/10.1080/09500690802380695.

    Article  Google Scholar 

  2. Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101. https://doi.org/10.1191/1478088706qp063oa.

    Article  Google Scholar 

  3. Bruner, J. (1990). Acts of meaning. Cambridge: Harvard University Press.

    Google Scholar 

  4. Clark, M. C., & Rossiter, M. (2008). Narrative learning in adulthood. New Directions for Adult and Continuing Education, 119, 61–70. https://doi.org/10.1002/ace.306.

    Article  Google Scholar 

  5. Cobb, G. W. (2007). The introductory statistics course: A Ptolemaic curriculum? Technology Innovations in Statistics Education, 1(1). http://escholarship.org/uc/item/6hb3k0nz.

  6. Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. The American Mathematical Monthly, 104(9), 801–823. https://doi.org/10.2307/2975286.

    Article  Google Scholar 

  7. Doerr, H. M., 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 

  8. Doerr, H. M., & 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: Research syntheses (pp. 259–285). Charlotte: Information Age Publishing.

    Google Scholar 

  9. Fisher, W. R. (1987). Human communication as narration: Toward a philosophy of reason, value, and action. Columbia: University of South Carolina Press.

    Google Scholar 

  10. Fuchs, H. U. (2015). From stories to scientific models and back: Narrative framing in modern macroscopic physics. International Journal of Science Education, 37(5–6), 934–957. https://doi.org/10.1080/09500693.2015.1025311.

    Article  Google Scholar 

  11. Garfield, J., delMas, B., & Zieffler, A. (2012). Developing statistical modelers and thinkers in an introductory tertiary-level statistics course. ZDM – The International Journal on Mathematics Education, 44(7), 883–898. https://doi.org/10.1007/s11858-012-0447-5.

    Article  Google Scholar 

  12. Gil, E., & Ben-Zvi, D. (2011). Explanations and context in the emergence of students’ informal inferential reasoning. Mathematical Thinking and Learning, 13(1–2), 87–108. https://doi.org/10.1080/10986065.2011.538295.

    Article  Google Scholar 

  13. Hestenes, D. (2010). Modeling theory for math and science education. In R. Lesh, P. L. Galbraith, C. R. Haines & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies: ICTMA 13 (pp. 13–41). New York: Springer.

    Chapter  Google Scholar 

  14. Klassen, S. (2009). The relation of story structure to a model of conceptual change in science learning. Science & Education, 19, 305–317. https://doi.org/10.1007/s11191-009-9212-8.

    Article  Google Scholar 

  15. Konold, C., & Lehrer, R. (2008). Technology and mathematics education: An essay in honor of Jim Kaput. In L. D. English (Ed.), Handbook of international research in mathematics education (2nd edn., pp. 49–72). Philadelphia: Taylor & Francis.

    Google Scholar 

  16. Konold, C., & Miller, C. (2011). TinkerPlots™ Version 2.3 [Computer Software]. Amherst: Learn Troop.

    Google Scholar 

  17. Laina, V., & Wilkerson, M. (2017). Modeling data by visualizing it. Proceedings of the 10th of the international forum for statistical reasoning, thinking and literacy, Rotorua.

  18. Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life. New York: Cambridge University Press.

    Book  Google Scholar 

  19. 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 

  20. Lesh, R., & Doerr, H. M. (2003). Beyond constructivism: A models and modeling perspective on mathematics problem solving, learning and teaching. Mahwah: Lawrence Erlbaum Associates, Inc.

    Book  Google Scholar 

  21. Mair, M., Greiffenhagen, C., & Sharrock, W. W. (2015). Statistical practice: Putting society on display. Theory, Culture & Society, 33(3), 51–77. https://doi.org/10.1177/0263276414559058.

    Article  Google Scholar 

  22. Morgan, M. S. (2001). Models, stories and the economic world. Journal of Economic Methodology, 8(3), 361–384. https://doi.org/10.1080/13501780110078972.

    Article  Google Scholar 

  23. Nemirovsky, R. (1996). Mathematical narratives, modeling and algebra. In N. Bednarz, C. Kieran & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 197–220). Dordrecht: Kluwer Academic.

    Chapter  Google Scholar 

  24. Nolan, D., & Lang, D. T. (2010). Computing in the statistics curricula. The American Statistician, 64(2), 97–107. https://doi.org/10.1198/tast.2010.09132.

    Article  Google Scholar 

  25. Noll, J., & Kirin, D. (2016). Student approaches to constructing statistical models using TinkerPlots™. Technology Innovations in Statistics Education, 9(1). http://escholarship.org/uc/item/05b643r9.

  26. Norris, S. P., Guilbert, S. M., Smith, M. L., Hakimelahi, S., & Phillips, L. M. (2005). A theoretical framework for narrative explanation in science. Science Education, 89(4), 535–563. https://doi.org/10.1002/sce.20063.

    Article  Google Scholar 

  27. 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 

  28. Pfannkuch, M., & Wild, C. J. (2000). Statistical thinking and statistical practice: Themes gleaned from professional statisticians. Statistical Science, 15(2), 132–152.

    Article  Google Scholar 

  29. Segel, E., & Heer, J. (2010). Narrative visualization: Telling stories with data. IEEE Transactions on Visualization and Computer Graphics, 16(6), 1139–1148. https://doi.org/10.1109/TVCG.2010.179.

    Article  Google Scholar 

  30. Sinclair, N., Healy, L., & Sales, C. O. R. (2009). Time for telling stories: Narrative thinking with dynamic technology. ZDM - The International Journal on Mathematics Education, 41(4), 441–452. https://doi.org/10.1007/s11858-009-0180-x.

    Article  Google Scholar 

  31. van Oers, B. (1997). On the narrative nature of young children’s iconic representations: Some evidence and implications. International Journal of Early Years Education, 5(3), 237–245. https://doi.org/10.1080/0966976970050305.

    Article  Google Scholar 

  32. Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–248. https://doi.org/10.1111/j.1751-5823.1999.tb00442.x.

    Article  Google Scholar 

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Acknowledgements

The authors gratefully acknowledge the support of National Science Foundation for this CAREER project (NSF REC 1453822). Any conclusions expressed in this material are those of the authors and do not necessarily reflect the views of the NSF. We also wish to thank Andee Rubin for thoughtful feedback on students’ use of narrative.

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Correspondence to Jennifer Noll.

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Noll, J., Clement, K., Dolor, J. et al. Students’ use of narrative when constructing statistical models in TinkerPlots. ZDM Mathematics Education 50, 1267–1280 (2018). https://doi.org/10.1007/s11858-018-0981-x

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Keywords

  • Statistics education
  • Modeling
  • Simulation
  • Narrative
  • TinkerPlots