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.