Building on and Challenging Students' Intuitions about Probability: Can we Improve Undergraduate Learning?

Students in our first year probability and statistics course typically experience problems in learning formal probability. They also often fail to grasp the logic behind confirmatory methods. The premise of this paper is as follows: to enable students to understand and be comfortable with inferential (or even exploratory) statistics, they must be allowed to (1) experience the omnipresence of variation and (2) experience probability as a means to describe and quantify that variation. A pilot study to investigate the understanding of variability and probability of a small group of students enrolled in the 1994 course is described. These students have a strong tendency to think deterministically (especially in real world settings); they have little understanding of variability and its relationship to sample size; and they are generally unable to reconcile their intuitions with the formal probability they are taught. There were some initial indications that allowing students to experience variation personally made aware of their over-emphasis on causal explanations of variability. Lastly, it appears that students' awareness about probabilistic thinking can be raised by actively challenging and discussing their tacit intuitive models about chance.