Visualizing chance in introductory probability

Research in the last thirty years has documented the challenges and difficulties in teaching probability and the many misconceptions prevalent in people’s reasoning. There is now a call to reform the approach to teaching probability from a traditional mathematical base to include more emphasis on modeling andinvestigations. Within this spirit of reform we undertook a two-part exploratory study. In the first part we interviewed seven practitioners in order to understand the probability concepts that need to be promoted and the areas of difficulties for students. Based on the first part of the study and the literature, we built and devised tasks for four interactive dynamic visualization tools, which we trialed on introductory probability students. The four tools trialed for the second part of the study were: an eikosogram, a pachinkogram, a Poisson processes tool and a Markov processes tool. In this talk I will briefly present findings from the practitioners’ interviews and the strategies used to develop the tasks accompanying the tools. The pachinkogram and Poisson processes tools will be demonstrated. The talk will then focus on the students’ interactions with the Markov processes tool. The main findings of our exploratory study suggested that our tools and tasks have the potential to enhance students’ probabilistic reasoning. The tools seemed to assist students to engage with and develop some intuition for probability ideas, to enhance their distributional ideas, to work flexibly between and within representations and to see mathematical structure.

https://www.stat.auckland.ac.nz/people/mpfa001