Development of the concept of statistical variation: An exploratory study

Abstract

An appreciation of variation is central to statistical thinking, but very little research has focused directly on students' understanding of variation. In this exploratory study, four students from each of grades 4, 6, 8, and 10 were hlterviewed individually on aspects of variation present in three settings. The first setting was an isolated random sampling situation, whereas the other two settings were real world sampling situations. Four levels of responding were identified and described in relation to developing concepts of variation. Implications for teaching and future research on variation are considered.

Expectation versus variation: Students’ decision making in a sampling environment

“…Appreciation of variation is also important when considering the relationship of samples to populations. Although this topic does not attract as much attention in curriculum documents, it is beginning to generate much research in the statistics education community (Green, 1993;Konoid & Pollatsek, 2002;Shaughnessy, 1997;Shaughnessy, Watson, Moritz, & Reading, 1999;Torok & Watson, 2000;Watson & Kelly, 2004 expectation and variation and their potential conflict in statistical decision making is considered in this study, using a task adapted from early research in the field. Tversky and Kahneman (1971) employed the following question in an attempt to identify people's belief in the law of small numbers; that is, that a small sample is highly representative of a population and that a random process will correct itself if necessary to re-establish equilibrium with the population: "The mean IQ of the population of eighth graders in a city is known to be 100.…”

“…Alternatives included asking students for six values from repeated trials, for a range of values from repeated trials, and for a choice among several alternatives. Further to this research, interviews were carried out with students where they answered questions and were given the opportunity to carry out actual trials with candies to see if estimates would change (Kelly & Watson, 2002;Reading & Shaughnessy, 2000;Torok & Watson, 2000). A basic appreciation of variation was common, but the sophistication associated with an understanding of probability distributions was generally absent.…”

Preservice Secondary Mathematics Teachers' Statistical Literacy in Understanding of Sample

“…교차점은 미리 연습할 수 없는 맥락 과 자동적으로 발생하는 의사결정과 관련이 있는데, 이는 모두 통계적 도구, 일반적인 맥락적 지식, 비판적 소양 기술을 적용하는 능력에 기반을 둔다. " (Watson, 2013) 통계학은 공통적으로 표본 자료를 기반으로 하며, 표 본을 어떻게 추출하느냐에 따라서 자료의 질과 통계적 추론에 막대한 영향을 주기 때문에, 표본과 표집에 대한 이해는 통계적 소양의 매우 기초적인 요소이다 (Watson & Moritz, 2000b, p.109 2) 표집변이성에 대한 통계적 소양 한편, Watson & Moritz(2000a, 2000b)의 연구와 유사 하게 변이 개념에 대한 학생들의 이해를 범주화한 연구 또한 Watson과 그 동료들을 중심으로 이루어졌다 (Torok & Watson, 2000;Watson et al, 2003). 이에 따 르면 변이 개념에 대한 학생들의 이해는 네 가지로 범주 화되며 이 역시 Watson(1997) (Torok & Watson, 2000, p.155;Watson et al, 2003, p.20).…”

Structuring variability by negotiating its measure

“…An implication of the outcome view is that coming to see phenomena as part of a stochastic process is often challenging. Even when the repetition of a repeated random process is made explicit, and the sample space is relatively simple, students at all ages do not readily perceive relations between the mathematical structure of the random process and the distribution of variability that results from this repeated process (Shaughnessy, Canada, & Ciancetta, 2003;Shaughnessy, Watson, Moritz, & Reading, 1999;Torok & Watson, 2000;Watson, 2006).…”