摘要：Maxine Pfannkuch a * & Stephanie Budgett a a Department of Statistics , The University of Auckland , Auckland , New Zealand CONTACT Maxine Pfannkuch m.pfannkuch@auckland.ac.nz Department of Statistics , The University of Auckland , Building 303, 38 Princes St, Auckland 1010 , New Zealand Finding ways to enhance introductory students' understanding of probability ideas and theory is a goal of many first-year probability courses. In this article, we explore the potential of a prototype tool for Markov processes using dynamic visualizations to develop in students a deeper understanding of the equilibrium and hitting times distributions. From the literature and interviews with practitioners, we identified core probability concepts, problematic areas, and possible solutions from which we developed design principles for the tool and accompanying tasks. The tool and tasks were piloted on six introductory probability students using a two-person protocol. The main findings highlight that our tool and tasks seemed to assist students to engage with probability ideas, to develop some intuition for Markov processes, to enhance their distributional ideas, to work between representations, and to see structure within the mathematics representations. The implications for teaching and learning are discussed.
关键词：Animations ; Equilibrium distribution ; Hitting times distribution ; Introductory probability students ; Statistics education
