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Informal Inferential Reasoning and the Social: Understanding Students’ Informal Inferences Through an Inferentialist Epistemology

  • Maike SchindlerEmail author
  • Abdel Seidouvy
Chapter
Part of the ICME-13 Monographs book series (ICME13Mo)

Abstract

Informal statistical inference and informal inferential reasoning (IIR) are increasingly gaining significance in statistics education research. What has not sufficiently been dealt with in previous research is the social nature of students’ informal inferences. This chapter presents results from a study investigating seventh grade students’ IIR in an experiment with paper helicopters. It focuses on students’ reasoning on the best rotor blade length, addressing statistical correlation. We study how students draw inferences when working in a group; and how their inferences emerge socially in their IIR. For grasping the reasoning’s social nature and its normativity, we use inferentialism as background theory. The results illustrate how students’ informal inferences are socially negotiated in the group, how students’ perceived norms influence IIR, and what roles statistical concepts play in students’ IIR.

Keywords

Generalization from data Inferentialism Informal inferential reasoning (IIR) Informal statistical inference (ISI) Informal statistical reasoning Norms Social 

Notes

Acknowledgements

This work was supported by the Swedish Research Council (Vetenskapsrådet) [2012-04811]. We furthermore want to thank the anonymous reviewers and especially the editors of this book for their constructive feedback and their efforts improving this article.

References

  1. Ainley, J., Pratt, D., & Hansen, A. (2006). Connecting engagement and focus in pedagogic task design. British Educational Research Journal, 32(1), 23–38.CrossRefGoogle Scholar
  2. Ainley, J., Pratt, D., & Nardi, E. (2001). Normalising: Children’s activity to construct meanings for trend. Educational Studies in Mathematics, 45(1–3), 131–146.CrossRefGoogle Scholar
  3. Bakker, A., Ben-Zvi, D., & Makar, K. (2017). An inferentialist perspective on the coordination of actions and reasons involved in making a statistical inference. Mathematics Education Research Journal, 29(4), 455–470.CrossRefGoogle Scholar
  4. Bakker, A., Derry, J., & Konold, C. (2006). Using technology to support diagrammatic reasoning about center and variation. In A. Rossman & B. Chance (Eds.), Working Cooperatively in Statistics Education. Proceedings of the Seventh International Conference on Teaching Statistics, Salvador, Brazil. Voorburg, The Netherlands: International Association for Statistical Education and International Statistical Institute.Google Scholar
  5. Bakker, A., Kent, P., Noss, R., & Hoyles, C. (2009). Alternative representations of statistical measures in computer tools to promote communication between employees in automotive manufacturing. Technology Innovations in Statistics Education, 3(2).Google Scholar
  6. Bakker, A., & Derry, J. (2011). Lessons from inferentialism for statistics education. Mathematical Thinking and Learning, 13(1–2), 5–26.CrossRefGoogle Scholar
  7. Ben-Zvi, D., & Arcavi, A. (2001). Junior high school students’ construction of global views of data and data representations. Educational Studies in Mathematics, 45(1–3), 35–65.CrossRefGoogle Scholar
  8. Brandom, R. (1994). Making it explicit: Reasoning, representing, and discursive commitment. Cambridge, MA: Harvard University Press.Google Scholar
  9. Brandom, R. (2000). Articulating reasons: An introduction to inferentialism. Cambridge, MA: Harvard University Press.Google Scholar
  10. Brandom, R. (2001, July 12). Der Mensch, das normative Wesen. Über die Grundlagen unseres Sprechens. Eine Einführung. [The human, the normative being. About the foundations of our speech. An introduction.] Die Zeit. Retrieved from: https://www.zeit.de/2001/29/200129_brandom.xml.
  11. Burgess, T. A. (2006). A framework for examining teacher knowledge as used in action while teaching statistics. In A. Rossman & B. Chance (Eds.), Working Cooperatively in Statistics Education. Proceedings of the Seventh International Conference on Teaching Statistics, Salvador, Brazil. Voorburg, The Netherlands: International Association for Statistical Education and International Statistical Institute.Google Scholar
  12. Cobb, P., & McClain, K. (2004). Principles of instructional design for supporting the development of students’ statistical reasoning. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 375–395). Dordrecht, The Netherlands: Springer.CrossRefGoogle Scholar
  13. Dierdorp, A., Bakker, A., Eijkelhof, H., & van Maanen, J. (2011). Authentic practices as contexts for learning to draw inferences beyond correlated data. Mathematical Thinking and Learning, 13(1–2), 132–151.CrossRefGoogle Scholar
  14. Gal, I., Rothschild, K., & Wagner, D. A. (1990). Statistical concepts and statistical reasoning in school children: Convergence or divergence. Paper presented at the annual meeting of the American Educational Research Association, Boston, MA, USA.Google Scholar
  15. 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.CrossRefGoogle Scholar
  16. Groth, R. E. (2013). Characterizing key developmental understandings and pedagogically powerful ideas within a statistical knowledge for teaching framework. Mathematical Thinking and Learning, 15(2), 121–145.CrossRefGoogle Scholar
  17. Lehrer, R., & Romberg, T. (1996). Exploring children’s data modeling. Cognition and Instruction, 14(1), 69–108.CrossRefGoogle Scholar
  18. 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
  19. Makar, K., & Ben-Zvi, D. (2011). The role of context in developing reasoning about informal statistical inference. Mathematical Thinking and Learning, 13(1–2), 1–4.CrossRefGoogle Scholar
  20. Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82–105.Google Scholar
  21. 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.Google Scholar
  22. McClain, K., Cobb, P., & Gravemeijer, K. (2000). Supporting students’ ways of reasoning about data. US Department of Education, Office of Educational Research and Improvement, Educational Resources Information Center.Google Scholar
  23. 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
  24. Mokros, J., & Russell, S. J. (1995). Children’s concepts of average and representativeness. Journal for Research in Mathematics Education, 26(1), 20–39.CrossRefGoogle Scholar
  25. Moritz, J. (2004). Reasoning about covariation. In D. Ban-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 227–255). Dordrecht, NL: Springer.CrossRefGoogle Scholar
  26. Moritz, J. B. (2000). Graphical representations of statistical associations by upper primary students. In J. Bana & A. Chapman (Eds.), Mathematics Education Beyond 2000. Proceedings of the 23rd Annual Conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 440–447). Perth, WA: MERGA.Google Scholar
  27. Newen, A., & Schrenk, M. (2012). Einführung in die Sprachphilosophie [Introduction to the philosophy of language.]. WBG-Wissenschaftliche Buchgesellschaft.Google Scholar
  28. Nilsson, P., Schindler, M., & Bakker, A. (2018). The nature and use of theories in statistics education. In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education (pp. 359–386). Cham: Springer.Google Scholar
  29. Noorloos, R., Taylor, S., Bakker, A., & Derry, J. (2017). Inferentialism as an alternative to socioconstructivism in mathematics education. Mathematics Education Research Journal, 29(4), 437–453.CrossRefGoogle Scholar
  30. Peregrin, J. (2009). Inferentialism and the compositionality of meaning. International Review of Pragmatics, 1(1), 154–181.CrossRefGoogle Scholar
  31. Pfannkuch, M. (2006). Informal inferential reasoning. In A. Rossman & B. Chance (Eds.), Working cooperatively in statistics education. Proceedings of the seventh international conference on teaching statistics, Salvador, Brazil. Voorburg, The Netherlands: International Association for Statistical Education and International Statistical Institute.Google Scholar
  32. Pfannkuch, M. (2011). The role of context in developing informal statistical inferential reasoning: A classroom study. Mathematical Thinking and Learning, 13(1–2), 27–46.CrossRefGoogle Scholar
  33. Pollatsek, A., Lima, S., & Well, A. D. (1981). Concept or computation: Students’ understanding of the mean. Educational Studies in Mathematics, 12(2), 191–204.CrossRefGoogle Scholar
  34. Pratt, D. (1995). Young children’s active and passive graphing. Journal of Computer Assisted learning, 11(3), 157–169.CrossRefGoogle Scholar
  35. Pratt, D., & Ainley, J. (2008). Introducing the special issue on informal inferential reasoning. Statistics Education Research Journal, 7(2), 3–4.Google Scholar
  36. Rossman, A. (2008). Reasoning about informal statistical inference: One statistician’s view. Statistics Education Research Journal, 7(2), 5–19.Google Scholar
  37. Roth, W. M. (1996). Where is the context in contextual word problem?: Mathematical practices and products in grade 8 students’ answers to story problems. Cognition and Instruction, 14(4), 487–527.CrossRefGoogle Scholar
  38. Roth, W. M. (2016). The primacy of the social and sociogenesis. Integrative Psychological and Behavioral Science, 50(1), 122–141.CrossRefGoogle Scholar
  39. Rubin, A., Hammerman, J., & Konold, C. (2006). Exploring informal inference with interactive visualization software. In Proceedings of the Sixth International Conference on Teaching Statistics. Cape Town, South Africa: International Association for Statistics Education.Google Scholar
  40. Schindler, M., Hußmann, S., Nilsson, P., & Bakker, A. (2017). Sixth-grade students’ reasoning on the order relation of integers as influenced by prior experience: An inferentialist analysis. Mathematics Education Research Journal, 29(4), 471–492.CrossRefGoogle Scholar
  41. Shaughnessy, M. (2006). Research on students’ understanding of some big concepts in statistics. In G. Burrill (Ed.), Thinking and reasoning with data and chance: 68th NCTM yearbook (pp. 77–98). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  42. Watson, J. M. (2001). Longitudinal development of inferential reasoning by school students. Educational Studies in Mathematics, 47(3), 337–372.CrossRefGoogle Scholar
  43. Wittgenstein, L. (1958). Philosophical investigations. Basil Blackwell.Google Scholar
  44. 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

  1. 1.Faculty of Human SciencesUniversity of CologneCologneGermany
  2. 2.School of Science and TechnologyÖrebro UniversityÖrebroSweden

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