Developing Concepts of Sampling

By Jane Watson, J. Moritz. 2000

163 citations recorded by the source corpus.

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.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6f97b0672eb578608fbcac505ff6a1764f864d6c

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Citations in the corpus

Development of the concept of statistical variation: An exploratory study (2000, methodology): “Rubin, Bruce, and Tenney (1991) found that high school students tended to overestimate representativeness in small samples and variability in large samples. Watson and Moritz (2000a) report that,”
Conceptions of sample and their relationship to statistical inference (2002, background): “Other conceptual analyses of sampling (Schwartz et al., 1998; Watson and Moritz, 2000) characterized the relationship between population and a randomly selected subset of it in a way that did not entail images of the repeatability of the sampling process nor of the variability that we can expect…”
Learning to reason from samples (2015, unknown): “However, they have difficulty making the transition to the formal statistical meaning of sample (Watson & Moritz, 2000), understanding the behavior of samples when they study statistics, how they relate to a population, and what happens when many samples are drawn and their statistics accumulated…”
Models of Development in Statistical Reasoning (2004, methodology): “Research in this area has examined the development of students’ statistical reasoning, not only in relation to the concept of sample, sample size, and sampling procedures (Watson, Chapter 12; Watson & Moritz, 2000b ) but also in relation to more sophisticated ideas like sampling distributions (Chap”
REASONING ABOUT SHAPE AS A PATTERN IN VARIABILITY (2004, unknown): “documented (Konold & Higgins, 2003; McGatha, Cobb, & McClain, 2002; Mokros & Russell,”
STATISTICAL LITERACY: A COMPLEX HIERARCHICAL CONSTRUCT (2003, methodology): “As well, largescale surveys have added to the store of information on understanding of these topics (Watson & Moritz, 1998, 1999a, 2000b, 2002; Zawojewski & Shaughnessy, 2000).”