Conceptual Challenges in Coordinating Theoretical and Data-centered Estimates of Probability


Authors: 
Cliff Konold; Sandra Madden; Alexander Pollatsek; Maxine Pfannkuch; Chris Wild; Ilze Ziedins; William Finzer; Nicholas J. Horton; Sibel Kazak
Volume: 
13(1&2)
Pages: 
online
Year: 
2011
Publisher: 
Mathematical Thinking and Learning
URL: 
http://www.informaworld.com/smpp/title~db=all~content=g932654185
Abstract: 

A core component of informal statistical inference is the recognition that judgments based on sample data are inherently uncertain. This implies that instruction aimed at developing informal inference needs to foster basic probabilistic reasoning. In this article, we analyze and critique the now-common practice of introducing students to both "theoretical" and "experimental" probability, typically with the hope that students will come to see the latter as converging on the former as the number of observations grows. On the surface of it, this approach would seem to fit well with objectives in teaching informal inference. However, our in-depth analysis of one eighth-grader's reasoning about experimental and theoretical probabilities points to various pitfalls in this approach. We offer tentative recommendations about how some of these issues might be addressed

The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education

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