The theoretical nature of probability in the classroom

This chapter presents an epistemological analysis of the nature of stochastical knowledge. In particular, the mutual relationship between the elementary concept of probability (in its empirical form of relative frequency and in its theoretical form of Laplace's approach) and the basic idea of chance is demonstrated. An important consequence for teaching elementary probability is that there cannot be a logical and deductive course for introducing the basic concepts and then constructing the theory upon them; developing stochastic knowledge in the classroom has to take into account a holistic and systematic perspective. The concept of task system is elaborated as an appropriate curricular means for treating the theoretical nature of stochastic knowledge in the classroom.