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.

Using InteractiveShinyApplications to Facilitate Research-Informed Learning and Teaching

“…Wild and Pfannkuch (1999) argued that the iterative exploration of data, as supported by the applets, software tools and games discussed above, mirrors statistical practice and helps develop a "habit of enquiry." Studies such as those in Lane and Tang (2000), Lunsford et al (2006), and Hagtvedt et al (2007) reveal that technological enhancement in Statistics courses can also improve student performance significantly. In terms of teaching Statistics, Doi et al (2016) commented on the benefit of Shiny apps in in-class demonstrations, as they can offer "… a much more fluid and dynamic presentation than one may typically experience by using the standard R console.…”

Distinguishing Between Binomial, Hypergeometric and Negative Binomial Distributions

“…In particular it is recommended that activities do not lead students step by step but rather allow students to discuss and think critically about the problem at hand (GAISE College Report 2005). Lunsford, Rowell, and Goodson-Espy (2006) discuss how lectures, or just merely demonstrations by the professor, are not as effective as hands-on activities for developing student understanding. Mills (2002) found that students who were actively collecting and analyzing data developed a better understanding of the concepts.…”

Learning Survival Models with On-Line Simulation Activities in the Actuarial Science Degree

“…The most significant experiences in Higher Education in this area integrate interactive resources with IT using interactive learning tools that help with the understanding and assimilation of abstract concepts, which are more difficult to teach and learn in the traditional classroom, [7], [12], [6]. One of the most common tools in this field is the Java applet embedded in an html document, [14], [7], [1], [16].…”

“…There are a number of examples in the field of Statistics education that combine new pedagogical approaches with technological infrastructure allowing instructors and students to improve motivation and enhance the learning process, [10], [12], [15], or [7]. The most significant experiences in Higher Education in this area integrate interactive resources with IT using interactive learning tools that help with the understanding and assimilation of abstract concepts, which are more difficult to teach and learn in the traditional classroom, [7], [12], [6].…”