The Impact of an Instructional Intervention Designed to Support Development of Stochastic Understanding of Probability Distribution

Abstract

Stochastic understanding of probability distribution undergirds development of conceptual connections between probability and statistics and supports development of a principled understanding of statistical inference. This study investigated the impact of an instructional course intervention designed to support development of stochastic understanding of probability distribution. Instructional supports consisted of supplemental lab assignments comprised of anticipatory tasks designed to engage students in coordinating thinking about complementary probabilistic and statistical notions. These tasks utilized dynamic software simulations to elicit stochastic conceptions and to support development of conceptual connections between empirical distributions and theoretical probability distribution models along a hypothetical learning trajectory undergirding stochastic understanding of probability distribution. The study employed a treatment-control design, using a mix of quantitative and qualitative research methods to examine students' understanding after a one-semester course. Participants were 184 undergraduate students enrolled in a lecture/recitation, calculus-based, introductory probability and statistics course who completed lab assignments addressing either calculus review (control) or stochastic conceptions of probability distribution (treatment). Data sources consisted of a student background survey, a conceptual assessment, ARTIST assessment items, and final course examinations. Student interviews provided insight into the nature of students' reasoning and facilitated examination of validity of the stochastic conceptual assessment. Logistic regression analysis revealed completion of supplemental assignments designed to undergird development of stochastic conceptions had a statistically significant impact on students' understanding of probability distribution. Students who held stochastic conceptions indicated integrated reasoning related to probability, variability, and distribution and presented images which support a principled understanding of statistical inference.