Modeling the Growth of students’

covariational reasoning during an

introductory statistics course


Andrew S. Zieffler

University of Minnesota


Joan B. Garfield

University of Minnesota




This study examined students’ development of reasoning about quantitative bivariate data during a one-semester university-level introductory statistics course. There were three research questions of interest: (1) What is the nature, or pattern of change in students’ development in reasoning throughout the course?; (2) Is the sequencing of quantitative bivariate data within the course associated with differences in the pattern of change in reasoning?; and (3) Are changes in reasoning about foundational concepts of distribution associated with differences in the pattern of change? Covariational and distributional reasoning were measured four times during the course, across four cohorts of students. A linear mixed-effects model was used to analyze the data, revealing some interesting trends and relationships regarding the development of covariational reasoning.


Keywords: Statistics education research; Growth modeling; Topic sequencing




Statistics Education Research Journal, 8(1), 7-31,

Ó International Association for Statistical Education (IASE/ISI), May, 2009






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andrew s. zieffler

Educational Psychology

206 Burton Hall

178 Pillsbury Dr. SE

Minneapolis, MN 55455