Facilitating factors and obstacles in the coordination of theoretical probability and relative frequency estimates of probability

Coordination of theoretical probability and relative frequency estimates is challenging in probability teaching and learning. Modeling is one of the ways of teaching and learning that facilitates inquiry between these two perspectives. Given that, we designed a modeling activity to support fifteen secondary students in investigating theoretical probabilities, relative frequencies, and the corresponding relationship and in estimating the true probability. We analyzed how the design of a modeling activity can afford students’ coordination of the two probability perspectives and the difficulties in the process. This analysis shows that adopting an asymmetric random process and having students extend their models of a simple event to a compound event are helpful for students to coordinate probability perspectives. However, potential obstacles to coordination include an authority issue and statistical bias.