Teaching Students to Estimate Probabilities: The Frequentist Approach and Its Relationship with Statistical Understanding (original) (raw)

2011, International Group for the Psychology of Mathematics Education

Theoretical Background The Three Views of Probability There are three main views of probability: classical, frequentist, and subjective (Shaughnessy, 1992). Using the classical view, one first partitions a sample space into equally likely outcomes. The probability of an event is simply the ratio of the number of outcomes in which that event occurs to the total number of outcomes. In contrast, the frequentist approach to probability involves repeated trials. A person using a frequentist approach might conduct a simulation with a large number of trials, examine the data, and assert probabilities based on the observations. If the number of trials is large enough, and if the results are repeated in other contexts, then the probability is judged reliable. A classical approach examines a priori how different arrangements of events could happen in order to develop a uniform distribution model. The frequentist approach is mathematically more related to statistics, since it involves the sear...