Investigating Students’ Reasoning About Sampling Distributions Through a Resource Perspective

Abstract

Researchers have documented many misconceptions students hold about sampling variability. This study takes a different approach—instead of identifying shortcomings, we consider the productive reasoning pieces students construct as they reason about sampling distributions. We interviewed eight undergraduate students newly enrolled in an introductory statistics course. Taking a grounded theory style approach, we identified 10 resources that students used when reasoning about the sampling distribution for the average within two contexts: penny years and dice rolls. Students had varied success in their responses as they made choices about how to represent their resources in their constructions. Successful constructions exemplified careful blending of resources, while less successful constructions reflected disjoint perceptions and tensions between seemingly conflicting resources. Our findings stress the importance of framing students as capable reasoning agents by describing student resources that were used while solving tasks related to sampling distributions. We also discuss the influence of context and problem setting in students’ reasoning and resource elicitation. First published May 2019 at Statistics Education Research Journal Archives

How do students reason about statistical sampling with computer simulations? An integrative review from a grounded cognition perspective

“…Second, problems constructed regarding statistics (such as survey tasks) are easier to solve than probabilities (such as slot machines). Gok and Goldstone Cognitive Research: Principles and Implications (2024) 9:33 Findley and Lyford's (2019) study support Maxara and Biehler's conclusion that contextual familiarity influences students' reasoning about story problems. However, it challenges the conclusion that probabilistically presented contexts are necessarily more difficult.…”

“…In these cases, the focus on local changes in large sample simulations seems to have overridden students' size-confidence intuition and invoked the growing possibilities heuristic instead. Growing possibilities refer to the belief that more opportunities exist to deviate from the population parameters with larger samples as there are more unique observations (Findley & Lyford, 2019). By this line of reasoning, children believe that every data point in a large sample could deviate substantially from the population mean, and if even one data point is off, then the sample distribution is invalid.…”

“…Several studies indicate that students often fail to appreciate that variability decreases in sampling distributions as the sample size gets larger even after they observe it in the simulated distributions (Findley & Lyford, 2019;Konold & Kazak, 2008;Lehrer et al, 2014, van Dijke-Droogers et al, 2021b. Students continue to believe the variability in the sampling distribution of means does not change with the sample size, or that it gets larger with increases in sample size.…”

“…Prior research suggests that students are sensitive to the context in which sample size problems are presented whether they are trained with simulations (Abrahamson et al, 2006;Maxara & Biehler, 2006) or not (Findley & Lyford, 2019).…”

Factors Influencing Students’ Understanding of Basic Statistical Concepts

“…Statistical concepts are the basis of learning statistics, and therefore, should be given due attention by every educational institution. Research on understanding basic concepts of statistics that has been conducted includes the following three areas: (1) reasoning about distributions and graphical representations of distributions (Bakker & Gravemeijer, 2004;Ben-Zvi, 2004;Hammerman & Rubin, 2004;Whitaker & Jacobbe, 2017); (2) understanding concepts related to statistical variation, such as measures of variability (DelMas & Liu, 2005;Mathews & Clark, 1997;Turegun & Reeder, 2011); and (3) sampling distributions (Braham & Ben-Zvi, 2017;delMas et al, 1999;Findley & Lyford, 2019;Saldanha & Thompson, 2001).…”