Skip to main content
SpringerLink
Log in

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

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

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).

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • 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 

  • 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.

  • Aridor, K., & Ben-Zvi, D. (2017). The co-emergence of aggregate and modelling reasoning. Statistics Education Research Journal, 16(2), 38–63.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

  • 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 

  • 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.

    Article  Google Scholar 

  • Cobb, G. W. (2007). The Introductory Statistics course: A Ptolemaic curriculum? Technology Innovations in Statistics Education, 1(1), 1–15.

    Google Scholar 

  • Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.

    Article  Google Scholar 

  • 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.

  • Engel, J. (2017). Statistical literacy for active citizenship: A call for data science education. Statistics Education Research Journal, 16(1), 44–49.

    Google Scholar 

  • 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.

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • Jungwirth, H. (2003). Interpretative Forschung in der Mathematikdidaktik—ein Überblick für Irrgäste, Teilzieher und Standvögel. ZDM Mathematics Education, 35(5), 189–200.

    Article  Google Scholar 

  • 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 

  • Konold, C., Harradine, A., & Kazak, S. (2007). Understanding distributions by modeling them. International Journal of Computers for Mathematical Learning, 12(3), 217–230.

    Article  Google Scholar 

  • Konold, C., & Miller, C. (2011). TinkerPlots 2.0. Emeryville: Key Curriculum Press.

    Google Scholar 

  • Krummheuer, G., & Naujok, N. (1999). Grundlagen und Beispiele Interpretativer Unterrichtsforschung. Opladen: Leske + Budrich.

    Book  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82–105.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Mishra, P., & Koehler, M. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. The Teachers College Record, 108(6), 1017–1054.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

  • 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.

    Chapter  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

  • Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.

    Article  Google Scholar 

  • 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 

Download references

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.

Author information

Authors and Affiliations

  1. Paderborn University, Paderborn, Germany

    Rolf Biehler, Daniel Frischemeier & Susanne Podworny

Authors
  1. Rolf Biehler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Frischemeier
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Susanne Podworny
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rolf Biehler.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Biehler, R., Frischemeier, D. & Podworny, S. Elementary preservice teachers’ reasoning about statistical modeling in a civic statistics context. ZDM Mathematics Education 50, 1237–1251 (2018). https://doi.org/10.1007/s11858-018-1001-x

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-018-1001-x

Keywords

Search

Navigation