2013 Conference Proceedings - University of Nevada, Las Vegas

this study, it is important that we follow Groth’s lead and consider the types of nonmathematicalknowledge that students may be activating when conceptualizing appropriate sampling methods.While many studies have investigated students’ conceptions and misconceptions of average,variability, distributions, sampling distributions, and correlation (Shaughnessy, 2007), fewspecifically investigate students’ conceptualizations of sampling methods. To be sure, manystatistics education teaching resources contain quality tasks that challenge students to develop asound understanding of issues involved in selecting representative samples (Franklin et al., 2007;Rossman & Chance, 2008; Warton, 2007); however, it appears that most of these resources weredeveloped using authors’ experience and expertise in teaching statistics rather than empiricalstudies of student thinking.For example, Warton (2007) presents a task that requires students to estimate the size of theirvocabulary using a dictionary. In the process of completing this task, students must select arepresentative sample of words from the dictionary – a nontrivial subtask. The article mentionsthat it is important to discuss potential sampling methods (highlighting their strengths andweaknesses) and reports that students commonly ask questions such as "But how many samplesshould I take?", "How do I decide how precise I want my estimate to be?" and "Why not use asystematic sample rather than a random sample?" While these sample questions provide helpfulinsight regarding what to expect when this task is implemented with students, an analysis ofstudents’ conceptualization of the issues involved in sampling is not given. An analysis of thissort would provide helpful information to teachers who wish to implement this and other tasksfocused on sampling methods.MethodsThis study was conducted to better understand student ways of thinking related to samplingmethods misconceptions I have observed in 14 years of teaching introductory statistics courses.One prevalent misconception is the belief that samples must be very large (e.g. half the size ofthe population) to be representative. A second common misconception is the belief that aconvenience sample is an acceptable sampling method for gathering data useful for drawingsound inferences about the population of interest.Participants in this study included 22 members of an introductory statistics class. Thesestudents completed a pre-test for the course in which they were asked to answer a questionregarding the best way to take a sample from all students at a university in order to gauge theProceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 79