EXPLORING STUDENTS’
CONCEPTIONS OF
THE STANDARD DEVIATION
ROBERT DELMAS
University of Minnesota
delma001@umn.edu
YAN LIU
Vanderbilt University
yan.liu@vanderbilt.edu
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.
Keywords: Standard deviation; Variability; Conceptions;
Strategies; Interviews
__________________________
Statistics Education Research
Journal, 4(1), 55-82, http://www.stat.auckland.ac.nz/serj
Ó International Association for Statistical Education (IASE/ISI), May, 2005
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ROBERT DELMAS
University of Minnesota
354 Appleby Hall
128 Pleasant Street SE
Minneapolis, MN 55455
USA