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Pre-service Teachers and Informal Statistical Inference: Exploring Their Reasoning During a Growing Samples Activity

  • Arjen de VettenEmail author
  • Judith Schoonenboom
  • Ronald Keijzer
  • Bert van Oers
Chapter
Part of the ICME-13 Monographs book series (ICME13Mo)

Abstract

Researchers have recently started focusing on the development of informal statistical inference (ISI) skills by primary school students. However, primary school teachers generally lack knowledge of ISI. In the literature, the growing samples heuristic is proposed as a way to learn to reason about ISI. The aim of this study was to explore pre-service teachers’ reasoning processes about ISI when they are engaged in a growing samples activity. Three classes of first-year pre-service teachers were asked to generalize to a population and to predict the graph of a larger sample during three rounds with increasing sample sizes. The content analysis revealed that most pre-service teachers described only the data and showed limited understanding of how a sample can represent the population.

Keywords

Informal inferential reasoning Informal statistical inference Initial teacher education Primary education Samples and sampling Statistics education 

References

  1. Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools. Utrecht, The Netherlands: CD-ß Press, Center for Science and Mathematics Education.Google Scholar
  2. Bakker, A., & Derry, J. (2011). Lessons from inferentialism for statistics education. Mathematical Thinking and Learning, 13(2), 5–26.CrossRefGoogle Scholar
  3. 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
  4. Batanero, C., & Díaz, C. (2010). Training teachers to teach statistics: What can we learn from research? Statistique et enseignement, 1(1), 5–20.Google Scholar
  5. Ben-Zvi, D. (2006). Scaffolding students’ informal inference and argumentation. Paper presented at the Seventh International Conference on Teaching Statistics, Salvador, Brazil.Google Scholar
  6. Ben-Zvi, D., Aridor, K., Makar, K., & Bakker, A. (2012). Students’ emergent articulations of uncertainty while making informal statistical inferences. ZDM—Mathematics Education, 44(7), 913–925.CrossRefGoogle Scholar
  7. Ben-Zvi, D., Bakker, A., & Makar, K. (2015). Learning to reason from samples. Educational Studies in Mathematics, 88(3), 291–303.CrossRefGoogle Scholar
  8. Ben-Zvi, D., Gil, E., & Apel, N. (2007). What is hidden beyond the data? Young students reason and argue about some wider universe. In D. Pratt & J. Ainley (Eds.), Proceedings of the Fifth International Forum for Research on Statistical Reasoning, Thinking and Literacy (SRTL-5). Warwick, UK: University of Warwick.Google Scholar
  9. Burgess, T. (2009). Teacher knowledge and statistics: What types of knowledge are used in the primary classroom? Montana Mathematics Enthusiast, 6(1&2), 3–24.Google Scholar
  10. Canada, D., & Ciancetta, M. (2007). Elementary preservice teachers’ informal conceptions of distribution. Paper presented at the 29th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Stateline, NV.Google Scholar
  11. Cobb, P., & Tzou, C. (2009). Supporting students’ learning about data creation. In W.-M. Roth (Ed.), Mathematical representation at the interface of body and culture (pp. 135–171). Charlotte, NC: IAP.Google Scholar
  12. De Vetten, A., Schoonenboom, J., Keijzer, R., & Van Oers, B. (2018). Pre-service primary school teachers’ knowledge of informal statistical inference. Journal of Mathematics Teacher Education.  https://doi.org/10.1007/s10857-018-9403-9.
  13. Garfield, J., & Ben-Zvi, D. (2007). How students learn statistics revisited: A current review of research on teaching and learning statistics. International Statistical Review, 75(3), 372–396.CrossRefGoogle Scholar
  14. Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. Dordrecht, The Netherlands: Springer.Google Scholar
  15. Garfield, J., Le, L., Zieffler, A., & Ben-Zvi, D. (2015). Developing students’ reasoning about samples and sampling variability as a path to expert statistical thinking. Educational Studies in Mathematics, 88(3), 327–342.CrossRefGoogle Scholar
  16. Groth, R. E., & Bergner, J. A. (2006). Preservice elementary teachers’ conceptual and procedural knowledge of mean, median, and mode. Mathematical Thinking and Learning, 8(1), 37–63.CrossRefGoogle Scholar
  17. Harradine, A., Batanero, C., & Rossman, A. (2011). Students and teachers’ knowledge of sampling and inference. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), Joint ICMI/IASE study: Teaching statistics in school mathematics. Challenges for teaching and teacher education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference (pp. 235–246). Dordrecht, The Netherlands: Springer.CrossRefGoogle Scholar
  18. Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., et al. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430–511.CrossRefGoogle Scholar
  19. Jacobbe, T., & Carvalho, C. (2011). Teachers’ understanding of averages. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), Joint ICMI/IASE study: Teaching statistics in school mathematics. Challenges for teaching and teacher education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference (pp. 199–209). Dordrecht, The Netherlands: Springer.CrossRefGoogle Scholar
  20. 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
  21. Leavy, A. M. (2006). Using data comparison to support a focus on distribution: Examining preservice teacher’s understandings of distribution when engaged in statistical inquiry. Statistics Education Research Journal, 5(2), 89–114.Google Scholar
  22. Leavy, A. M. (2010). The challenge of preparing preservice teachers to teach informal inferential reasoning. Statistics Education Research Journal, 9(1), 46–67.Google Scholar
  23. Liu, Y., & Grusky, D. B. (2013). The payoff to skill in the third industrial revolution. American Journal of Sociology, 118(5), 1330–1374.CrossRefGoogle Scholar
  24. Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13(1–2), 152–173.CrossRefGoogle Scholar
  25. Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82–105.Google Scholar
  26. Makar, K., & Rubin, A. (2014). Informal statistical inference revisited. Paper presented at the Ninth International Conference on Teaching Statistics (ICOTS 9), Flagstaff, AZ.Google Scholar
  27. Meletiou-Mavrotheris, M., Kleanthous, I., & Paparistodemou, E. (2014). Developing pre-service teachers’ technological pedagogical content knowledge (TPACK) of sampling. Paper presented at the Ninth International Conference on Teaching Statistics (ICOTS9), Flagstaff, AZ.Google Scholar
  28. Meletiou-Mavrotheris, M., & Paparistodemou, E. (2015). Developing students’ reasoning about samples and sampling in the context of informal inferences. Educational Studies in Mathematics, 88(3), 385–404.CrossRefGoogle Scholar
  29. Mooney, E., Duni, D., VanMeenen, E., & Langrall, C. (2014). Preservice teachers’ awareness of variability. In K. Makar, B. De Sousa, & R. Gould (Eds.), Proceedings of the Ninth International Conference on Teaching Statistics (ICOTS9). Voorburg, The Netherlands: International Statistical Institute.Google Scholar
  30. Rivkin, S. G., Hanushek, E. A., & Kain, J. F. (2005). Teachers, schools, and academic achievement. Econometrica, 73(2), 417–458.CrossRefGoogle Scholar
  31. Schön, D. A. (1983). The reflective practitioner: How professionals think in action. London, UK: Temple Smith.Google Scholar
  32. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.CrossRefGoogle Scholar
  33. Watson, J. M. (2001). Profiling teachers’ competence and confidence to teach particular mathematics topics: The case of chance and data. Journal of Mathematics Teacher Education, 4(4), 305–337.CrossRefGoogle Scholar
  34. Zieffler, A., Garfield, J., delMas, R., & Reading, C. (2008). A framework to support research on informal inferential reasoning. Statistics Education Research Journal, 7(2), 40–58.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Arjen de Vetten
    • 1
    Email author
  • Judith Schoonenboom
    • 2
  • Ronald Keijzer
    • 3
  • Bert van Oers
    • 1
  1. 1.Section of Educational SciencesVrije Universiteit AmsterdamAmsterdamThe Netherlands
  2. 2.Department of EducationUniversity of ViennaViennaAustria
  3. 3.Academy for Teacher Education, University of Applied Sciences iPaboAmsterdamThe Netherlands

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