Classroom Research: Assessment of Student Understanding of Sampling Distributions of Means and the Central Limit Theorem in Post-Calculus Probability and Statistics Classes

Abstract

We applied a classroom research model to investigate student understanding of sampling distributions of sample means and the Central Limit Theorem in post-calculus introductory probability and statistics courses. Using a quantitative assessment tool developed by previous researchers and a qualitative assessment tool developed by the authors, we embarked on data exploration of our students' responses on these assessments. We observed various trends regarding their understanding of the concepts including results that were consistent with research completed previously (by other authors) for algebra-based introductory level statistics students. We also used the information obtained from our data exploration and our experiences in the classroom to examine and conjecture about possible reasons for our results.

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• Action Research

Acknowledgements

In developing the foundations of this classroom-based research, we appreciate the direct support of the National Science Foundation Division of Undergraduate Education (NSF DUE) matching grants (DUE-126401, 0126600, 0126716, and 0350724) and our institutions. The views and opinions expressed here are those of the authors and do not necessarily reflect the views and opinions of the National Science Foundation. We also sincerely appreciate the willingness of Drs. Allan Rossman, Beth Chance, California Polytechnic University, and Dr. Kyle Siegrist, University of Alabama in Huntsville, to share the educational materials they have developed through NSF-supported projects (DUE-9950476 and 9652870). Drs. Rossman and Chance were especially generous with their time and expertise in training us in appropriate pedagogy for using their educational materials. Furthermore, we are grateful for the willingness of Drs. Robert delMas and Joan Garfield, University of Minnesota, and Dr. Beth Chance, California Polytechnic University, to share their assessment instrument, learning activities, and research developed in part with support of NSF DUE-9752523 grant, “Tools for Teaching and Assessing Statistical Inference,” in which the software Sampling SIM was developed and its usefulness was tested. Some of the results for the Math 300 class found in this paper were also presented by the authors at the 2005 Joint Statistical Meetings at the presentation, “Applying an Action Research Model to Assess Student Understanding of the Central Limit Theorem in Post-Calculus Probability and Statistics Courses,” and are published in the corresponding proceedings. Finally, we would like to thank the three anonymous referees for their many valuable comments and suggestions which greatly improved the presentation of our results.