Advertisement

ZDM

, Volume 50, Issue 7, pp 1237–1251 | Cite as

Elementary preservice teachers’ reasoning about statistical modeling in a civic statistics context

  • Rolf BiehlerEmail author
  • Daniel Frischemeier
  • Susanne Podworny
Original Article
  • 126 Downloads

Abstract

Elements of statistical modeling can be implemented already in primary school. A prerequisite for this approach is that teachers are well-educated in this domain. Content knowledge, pedagogical content knowledge and (pedagogical) content related technological knowledge are core components of teacher education. We designed a course for elementary preservice teachers with regard to developing statistical thinking including the mentioned knowledge facets. The course includes exploring data and modeling and simulating chance experiments with TinkerPlots. We use the ‘data factory metaphor’ in fictive contexts and in contexts stemming from civic statistics for supporting the idea of modeling. We interviewed four participants of the course to assess and analyze their reasoning. We analyze how they model a given civic statistics contextual problem using the TinkerPlots sampler and how they evaluate their model with regard to a civic statistics context (the situation of hospitals in Germany).

Keywords

Probability simulation and modeling Digital tools for learning Teacher education Context knowledge 

Notes

Acknowledgements

Many thanks go to Cliff Konold for proofreading and for providing very helpful comments on previous versions of this paper. We also thank the three anonymous reviewers for providing constructive feedback and helpful suggestions for revising the paper.

References

  1. Ainley, J., & Pratt, D. (2017). Computational modelling and children’s expressions of signal and noise. Statistics Education Research Journal, 16(2), 15–37.Google Scholar
  2. Arbeitskreis Stochastik der Gesellschaft für Didaktik der Mathematik. (2012). Empfehlungen für die Stochastikausbildung von Lehrkräften an Grundschulen. Retrieved from http://www.mathematik.uni-dortmund.de/ak-stoch/Empfehlungen_Stochastik_Grundschule.pdf.
  3. Aridor, K., & Ben-Zvi, D. (2017). The co-emergence of aggregate and modelling reasoning. Statistics Education Research Journal, 16(2), 38–63.Google Scholar
  4. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching what makes it special? Journal of Teacher Education, 59(5), 389–407.CrossRefGoogle Scholar
  5. Biehler, R., Frischemeier, D., & Podworny, S. (2015). Preservice teachers’ reasoning about uncertainty in the context of randomization tests. In A. S. Zieffler & E. Fry (Eds.), Reasoning about uncertainty: Learning and teaching informal inferential reasoning (pp. 129–162). Minnesota: Catalyst Press.Google Scholar
  6. Biehler, R., Frischemeier, D., & Podworny, S. (2017a). Design, realization and evaluation of a university course for preservice teachers on developing statistical reasoning and literacy with a focus on civic statistics. Paper presented at the World Statistics Congress 61, Marrakech, Morocco.Google Scholar
  7. 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
  8. Biehler, R., Frischemeier, D., & Podworny, S. (2018). Civic engagement in higher education: A university course in civic statistics for mathematics preservice teachers. Zeitschrift für Hochschulentwicklung, 13(2), 169–182.CrossRefGoogle Scholar
  9. Cobb, G. W. (2007). The Introductory Statistics course: A Ptolemaic curriculum? Technology Innovations in Statistics Education, 1(1), 1–15.Google Scholar
  10. Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.CrossRefGoogle Scholar
  11. Deutsche Mathematiker Vereinigung-Gesellschaft für Didaktik der Mathematik-Deutscher Verein zur Förderung des mathematischen und naturwissenschaftlichen Unterrichts. (2008). Standards für die Lehrerbildung im Fach Mathematik. Retrieved from http://madipedia.de/images/2/21/Standards_Lehrerbildung_Mathematik.pdf.
  12. Engel, J. (2017). Statistical literacy for active citizenship: A call for data science education. Statistics Education Research Journal, 16(1), 44–49.Google Scholar
  13. Engel, J., Gal, I., & Ridgway, J. (2016). Mathematical literacy and citizen engagement: The role of civic statistics. Paper presented at the 13th International Congress on Mathematical Education, Hamburg.Google Scholar
  14. Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2), 124–158.CrossRefGoogle Scholar
  15. Hasemann, K., & Mirwald, E. (2012). Daten, Häufigkeit und Wahrscheinlichkeit. In G. Walther, M. van den Heuvel-Panhuizen, D. Granzer & O. Köller (Eds.), Bildungsstandards für die Grundschule: Mathematik konkret (pp. 141–161). Berlin: Cornelsen Scriptor.Google Scholar
  16. Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39, 372–400.Google Scholar
  17. Jungwirth, H. (2003). Interpretative Forschung in der Mathematikdidaktik—ein Überblick für Irrgäste, Teilzieher und Standvögel. ZDM Mathematics Education, 35(5), 189–200.CrossRefGoogle Scholar
  18. Klein, F. (2016). Elementary mathematics from a higher standpoint: Arithmetic, algebra, analysis (Vol (1) [new English translation of the 1933 published 4th edition of the original German version]). Berlin: Springer.Google Scholar
  19. 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
  20. Konold, C., & Miller, C. (2011). TinkerPlots 2.0. Emeryville: Key Curriculum Press.Google Scholar
  21. Krummheuer, G., & Naujok, N. (1999). Grundlagen und Beispiele Interpretativer Unterrichtsforschung. Opladen: Leske + Budrich.CrossRefGoogle Scholar
  22. Langrall, C., Nisbet, S., Mooney, E., & Jansem, S. (2011). The role of context expertise when comparing data. Mathematical Thinking and Learning, 13(1), 47–67.CrossRefGoogle Scholar
  23. Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82–105.Google Scholar
  24. Makar, K., & Rubin, A. (2018). Learning about statistical inference. In D. Ben-Zvi, K. Makar & J. Garfield (Eds.), International handbook of research in statistics education (pp. 261–294). Cham: Springer.CrossRefGoogle Scholar
  25. Mishra, P., & Koehler, M. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. The Teachers College Record, 108(6), 1017–1054.CrossRefGoogle Scholar
  26. Pfannkuch, M., & Ben-Zvi, D. (2011). Developing teachers’ statistical thinking. In C. Batanero, G. Burrill & C. Reading (Eds.), Teaching statistics in school mathematics-challenges for teaching and teacher education (pp. 323–333). Dordrecht/Heidelberg/London/New York: Springer.CrossRefGoogle Scholar
  27. Podworny, S., Frischemeier, D., & Biehler, R. (2017). Design, Realization and Evaluation of a statistics course for preservice teachers for primary school in Germany. In A. Molnar (Ed.), IASE Satellite Conference 2017: Teaching Statistics in a Data Rich World. Rabat, Morocco: IASE.Google Scholar
  28. Pratt, D., & Kazak, S. (2018). Research on uncertainty. In D. Ben-Zvi, K. Makar & J. Garfield (Eds.), International handbook of research in statistics education (pp. 193–228). Cham: Springer.CrossRefGoogle Scholar
  29. Ridgway, J. (2016). Implications of the data revolution for statistics education. International Statistical Review, 84(3), 528–549.  https://doi.org/10.1111/insr.12110.CrossRefGoogle Scholar
  30. Rossman, A., Chance, B., Cobb, G. W., & Holcomb, R. (2008). Concepts of statistical inference: Approach, scope, sequence and format for an elementary permutation-based first course. http://statweb.calpoly.edu/bchance/csi/CSIcurriculumMay08.doc.
  31. Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.CrossRefGoogle 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.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2018

Authors and Affiliations

  1. 1.Paderborn UniversityPaderbornGermany

Personalised recommendations