EXPLORING STUDENTS’ CONCEPTIONS OF THE STANDARD DEVIATION

By R. delMas, Yan Liu. 2005

138 citations recorded by the source corpus.

SUMMARY This study investigated introductory statistics students’ conceptual understanding of the standard deviation. A computer environment was designed to promote students’ ability to coordinate characteristics of variation of values about the mean with the size of the standard deviation as a measure of that variation. Twelve students participated in an interview divided into two primary phases, an exploration phase where students rearranged histogram bars to produce the largest and smallest standard deviation, and a testing phase where students compared the sizes of the standard deviation of two distributions. Analysis of data revealed conceptions and strategies that students used to construct their arrangements and make comparisons. In general, students moved from simple, one-dimensional understandings of the standard deviation that did not consider variation about the mean to more mean-centered conceptualizations that coordinated the effects of frequency (density) and deviation from the mean. Discussions of the results and implications for instruction and further research are presented.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cc982ee6481b257cfdcc03f645adfe495e467ee7

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Citations in the corpus

ASSESSING STUDENTS’ CONCEPTUAL UNDERSTANDING AFTER A FIRST COURSE IN STATISTICS (2007, background): “…Statistical Education (IASE/ISI), November, 2007 2000), and understanding concepts related to statistical variation such as measures of variability (delMas & Liu, 2005; Mathews & Clark, 1997; Shaughnessy, 1977), sampling variation (Reading & Shaughnessy, 2004; Shaughnessy, Watson, Moritz, &…”
A FRAMEWORK FOR TEACHING AND ASSESSING REASONING ABOUT VARIABILITY (2005, background): “Keywords: Variability; Variation; Learning and teaching statistics; Assessment; Statistics curriculum; Statistics education; Reasoning and thinking; Deep understanding”
Students’ misconceptions of statistical inference: A review of the empirical evidence from research on statistics education (2007, methodology): “Third, with regard to the data gathering methodology, interviews (e.g., delMas & Liu, 2005), and mixture of multiple-choice and open-answer items can be found (e.g., Vallecillos, 1995, 1996, 2000, 2002).”
Development and Validation of a Scale for Measuring Instructors' Attitudes toward Concept-Based or Reform-Oriented Teaching of Introductory Statistics in the Health and Behavioral Sciences (2010, background): “…are experiencing difficulties with introductory statistics, and emerge with a lack of understanding of core concepts, such as statistical variation (delMas & Liu, 2005), chance (Garfield, 2003), graphical representations of distributions (Bakker & Gravemeijer, 2004), sampling variation (Reading &…”
A Rasch Model Analysis on Secondary Students' Statistical Reasoning Ability in Descriptive Statistics (2014, background): “…including reasoning about measures of central tendency (Cooper & Shore, 2008; Huck, 2009; Olani et al., 2011), representations of data (Lee and Meletiou-Mavrothesis, 2003; Sharma, 2005; Cooper and Shore, 2008), variability (delMas and Liu, 2005; Matthew and Clark, * Corresponding author.”
What Does Research Suggest About the Teaching and Learning of Introductory Statistics at the College Level? A Review of the Literature (2008, methodology): “In a related study, delMas and Liu (2005) studied students’ development of reasoning about standard deviation.”