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ZDM

, Volume 50, Issue 7, pp 1295–1309 | Cite as

Statistics students’ identification of inferential model elements within contexts of their own invention

  • Matthew D. BeckmanEmail author
  • Robert delMas
Original Article
  • 83 Downloads

Abstract

Statistical thinking partially depends upon an iterative process by which essential features of a problem setting are identified and mapped onto an abstract model or archetype, and then translated back into the context of the original problem setting (Wild and Pfannkuch, Int Stat Rev 67(3):223–248, 1999). Assessment in introductory statistics often relies on tasks that present students with data in context and expects them to choose and describe an appropriate model. This study explores post-secondary student responses to an alternative task that prompts students to clearly identify a sample, population, statistic, and parameter using a context of their own invention. The data include free-text narrative responses of a random sample of 500 students from a sample of more than 1600 introductory statistics students. Results suggest that students’ responses often portrayed sample and population accurately. Portrayals of statistic and parameter were less reliable and were associated with descriptions of a wide variety of other concepts. Responses frequently attributed a variable of some kind to the statistic, or a study design detail to the parameter. Implications for instruction and research are discussed, including a call for emphasis on a modeling paradigm in introductory statistics.

Keywords

Statistics education Statistical modeling Statistical inference Assessment Parameter 

Notes

Acknowledgements

The authors wish to express their sincere gratitude to Joan Garfield for her thoughtful direction and influence on development of early research leading to this work. The authors are also grateful for the thoughtful feedback and constructive suggestions of colleagues during the SRTL-10 forum.

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Copyright information

© FIZ Karlsruhe 2018

Authors and Affiliations

  1. 1.Pennsylvania State UniversityUniversity ParkUSA
  2. 2.University of MinnesotaMinneapolisUSA

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