Law of Large Numbers: The Theory, Applications and Technology-Based Education

Abstract

Modern approaches for technology-based blended education utilize a variety of recently developed novel pedagogical, computational and network resources. Such attempts employ technology to deliver integrated, dynamically-linked, interactive-content and heterogeneous learning environments, which may improve student comprehension and information retention. In this paper, we describe one such innovative effort of using technological tools to expose students in probability and statistics courses to the theory, practice and usability of the Law of Large Numbers (LLN). We base our approach on integrating pedagogical instruments with the computational libraries developed by the Statistics Online Computational Resource (www.SOCR.ucla.edu). To achieve this merger we designed a new interactive Java applet and a corresponding demonstration activity that illustrate the concept and the applications of the LLN. The LLN applet and activity have common goals - to provide graphical representation of the LLN principle, build lasting student intuition and present the common misconceptions about the law of large numbers. Both the SOCR LLN applet and activity are freely available online to the community to test, validate and extend (Applet: http://socr.ucla.edu/htmls/exp/Coin_Toss_LLN_Experiment.html, and Activity: http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_LLN).

• Statistics education
• Technology-based blended instruction
• Applets
• Law of large numbers
• Limit theorems
• SOCR

Acknowledgements

These new SOCR LLN resources were developed with support from NSF grants 0716055 and 0442992 and from NIH Roadmap for Medical Research, NCBC Grant U54 RR021813. The authors are indebted to Juana Sanchez for her valuable comments and ideas. JSE editors and referees provided a number of constructive recommendations, revisions and corrections that significantly improved the manuscript.