Developing Concepts of Sampling

A key element in developing ideas associated with statistical inference involves developing concepts of sampling. The objective of this research was to understand the characteristics of students' constructions of the concept of sample. Sixty-two students in Grades 3, 6, and 9 were interviewed using open-ended questions related to sampling; written responses to a questionnaire were also analyzed. Responses were characterized in relation to the content, structure, and objectives of statistical literacy. Six categories of construction were identified and described in relation to the sophistication of developing concepts of sampling. These categories illustrate helpful and unhelpful foundations for an appropriate understanding of representativeness and hence will help curriculum developers and teachers plan interventions. How do children develop the intuitions that form the foundation for sampling in statistics? Many educators appear to assume students understand the part-whole relationship of sample to sampled and the purpose of seeing what the whole is like. Is there a need to make more explicit the transition from out-of-school connotations of sampling, such as in supermarkets or medical contexts in which variation is not usually an issue, to representative sampling required for inference, sampling that must depict the underlying population without bias? This question reflects one of the educational issues underlying the research reported in this article. Another issue is associated with the goal of students' achieving, before they leave school, a level of statistical literacy that will allow them to contribute meaningfully to social decision making based on quantitative data. In the context of sampling, meeting this goal requires that students develop both an understanding of sampling methods and the motivation to be able to question claims based on biased sampling methods.