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Mathematics Education Research Journal

, Volume 31, Issue 4, pp 485–505 | Cite as

Primary school students’ reasoning when comparing groups using modal clumps, medians, and hatplots

  • Daniel FrischemeierEmail author
Original Article

Abstract

Comparing groups is a fundamental activity in statistics since it includes many basic concepts like center, variability, and representation and can pave the way to inferential statistics. Preliminary work involving group comparisons can be undertaken at an early age, e.g., at primary school using proto-concepts like modal clumps, precursor representations like hatplots, or formal concepts like medians. We have designed and implemented a teaching unit using modal clumps, medians, and hatplots to guide primary school students (grade 4, aged 10–11) to compare groups with TinkerPlots. Consequently, a case study with six of these primary school students was conducted to investigate how our primary school students compare groups in large authentic data sets using TinkerPlots. One finding is that all six primary school students make sophisticated use of modal clumps, medians, and hatplots to compare groups in large and authentic data with TinkerPlots.

Keywords

Primary school education Statistical reasoning Comparing groups Digital tools TinkerPlots 

Notes

Acknowledgments

I am very grateful to Cliff Konold for very helpful and constructive comments and feedback on this manuscript. Furthermore, I am very grateful to Rebecca Breker and Christina Schäfers who have been collaborators on the design and the implementation of the instructional unit on group comparisons. Many thanks also to the three anonymous reviewers who provided helpful feedback and suggestions on previous versions of this article.

References

  1. Bakker, A. (2004). Design research in statistics education - on symbolizing and computer tools. (Dissertation), University of Utrecht.Google Scholar
  2. Bakker, A., & Gravemeijer, K. (2004). Learning to reason about distributions. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 147–168). Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
  3. Bakker, A., Biehler, R., & Konold, C. (2005). Should young students learn about box plots? In G. Burrill & M. Camden (Eds.), Curricular development in Statistics Education: International Association for Statistical Education (pp. 163–173). Voorburg: International Statistical Institute.Google Scholar
  4. Ben-Zvi, D. (2004). Reasoning about variability in comparing distributions. Statistics Education Research Journal, 3(2), 42–63.Google Scholar
  5. Biehler, R., Ben-Zvi, D., Bakker, A., & Makar, K. (2013). Technology for enhancing statistical reasoning at the school level. In M. A. Clements, A. J. Bishop, C. Keitel-Kreidt, J. Kilpatrick, & F. K.-S. Leung (Eds.), Third international handbook of mathematics education (pp. 643–689). New York: Springer Science + Business Media.Google Scholar
  6. Biehler, R., Frischemeier, D., Reading, C., & Shaughnessy, M. (2018). Reasoning about data. In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International Handbook of Research in Statistics Education (pp. 139–192). Cham: Springer International.Google Scholar
  7. Burrill, G., & Biehler, R. (2011). Fundamental statistical ideas in the school curriculum and in training teachers. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics-Challenges for teaching and teacher education (pp. 57–69). Dordrecht/Heidelberg/London/New York: Springer.CrossRefGoogle Scholar
  8. Camtasia Studio Version 6.0.3. (2011). Okemos: Techsmith.Google Scholar
  9. Cobb, P. (1999). Individual and collective mathematical development: The case of statistical data analysis. Mathematical Thinking and Learning, 1(1), 5–43.CrossRefGoogle Scholar
  10. Eichler, A., & Vogel, M. (2013). Leitidee Daten und Zufall. Wiesbaden: Springer Spektrum.CrossRefGoogle Scholar
  11. Engel, J. (2017). Statistical literacy for active citizenship: A call for data science education. Statistics Education Research Journal, 16(1), 44–49.Google Scholar
  12. Fielding-Wells, J. (2018). Dot plots and hat plots: Supporting young students emerging understandings of distribution, center and variability through modeling. ZDM Mathematics Education, 50(7), 1125–1138.CrossRefGoogle Scholar
  13. Frischemeier, D. (2014). Comparing groups by using TinkerPlots as part of a data analysis task - Tertiary students’ strategies and difficulties. In: K. Makar, B. de Sousa & R. Gould (Eds.), Sustainability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics. Voorburg: International Statistical Institute.Google Scholar
  14. Frischemeier, D., & Biehler, R. (2016). Preservice teachers´ statistical reasoning when comparing groups facilitated by software. In K. Krainer & N. Vondrova (Eds.), Proceedings of the 9th Congress of the European Society for Research in Mathematics Education (pp. 643–650). Prague: Charles University in Prague, Faculty of Education and ERME.Google 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. Jungwirth, H. (2003). Interpretative Forschung in der Mathematikdidaktik—ein Überblick für Irrgäste, Teilzieher und Standvögel. ZDM Mathematics Education, 35(5), 189–200.CrossRefGoogle Scholar
  17. Jungwirth, H. (2005). Interpretative Mathematikdidaktik: methodisches und methodologisches am Beispiel von Normen im Mathematikunterricht. Retrieved from:http://psydok.sulb.uni-saarland.de/volltexte/2005/449/pdf/jungwirth.pdf. Accessed 5 Sept 2018.
  18. Konold, C. (2002). Hat Plots?. Unpublished manuscript. University of Massachusetts.Google Scholar
  19. Konold, C. (2007). Designing a data tool for learners. In M. Lovett & P. Shah (Eds.), Thinking with data: The 33rd Annual Carnegie Symposium on Cognition (pp. 267–292). Hillside: Lawrence Erlbaum Associates.Google Scholar
  20. Konold, C., & Higgins, T. L. (2003). Reasoning about data. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A Research Companion to Principles and Standards for School Mathematics (pp. 193–215). Reston: National Council of Teachers of Mathematics.Google Scholar
  21. Konold, C., & Miller, C. (2011). TinkerPlots 2.0. Emeryville: Key Curriculum Press.Google Scholar
  22. Konold, C., & Pollatsek, A. (2002). Data analysis as the search for signals in noisy processes. Journal for Research in Mathematics Education, 33(4), 259–289.CrossRefGoogle Scholar
  23. Konold, C., Robinson, A., Khalil, K., Pollatsek, A., Well, A. D., Wing, R., et al. (2002). Students’ use of modal clumps to summarize data. In B. Phillips (Ed.), Proceedings of the International Conference on Teaching Statistics [CD-ROM], Cape Town. Voorburg: International Statistics Institute.Google Scholar
  24. Konold, C., Higgins, T., Russell, S. J., & Khalil, K. (2014). Data seen through different lenses. Educational Studies in Mathematics, 88(3), 305–325.CrossRefGoogle Scholar
  25. Kuckartz, U. (2012). Qualitative Inhaltsanalyse. Methoden, Praxis, Computerunterstützung. Weinheim: Beltz Juventa.Google Scholar
  26. Leavy, A., Meletiou-Mavrotheris, M., & Paparistodemou, E. (2018). Statistics in early childhood and primary education: Supporting early statistical and probabilistic thinking. Singapore: Springer.CrossRefGoogle Scholar
  27. Makar, K., & Allmond, S. (2018). Statistical modelling and repeatable structures: Purpose, process and prediction. ZDM Mathematics Education, 50(7), 1139–1150.CrossRefGoogle Scholar
  28. MAXQDA 11 software für qualitative Datenanalyse. (2013). Berlin: Sozialforschung GmbH.Google Scholar
  29. Pfannkuch, M. (2007). Year 11 students’ informal inferential reasoning: A case study about the interpretation of box plots. International Electronic Journal of Mathematics Education, 2(3), 149–167.Google Scholar
  30. Voigt, J. (1984). Interaktionsmuster und Routinen im Mathematikunterricht: theoret. Grundlagen u. mikroethnograph. Falluntersuchungen. Weinheim: Beltz.Google Scholar
  31. Watson, J. M., & Moritz, J. B. (1999). The beginning of statistical inference: Comparing two data sets. Educational Studies in Mathematics, 37(2), 145–168.CrossRefGoogle Scholar
  32. Watson, J., Fitzallen, N., Wilson, K., & Creed, J. (2008). The representational value of HATS. Mathematics Teaching in Middle School, 14(1), 4–10.Google Scholar
  33. Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–248.CrossRefGoogle Scholar
  34. Yin, R. (2014). Case study research: Design and methods (5th ed.). Thousand Oaks: Sage.Google Scholar

Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2019

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of PaderbornPaderbornGermany

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