Three Approaches for Modelling Situations with Randomness

Abstract

Three different approaches to the concept of probability dominate the teaching of stochastics: the classical, the frequentistic and the subjectivistic approach. Compared with each other they provide considerably different possibilities to interpret situations with randomness. With regard to teaching probability, it is useful to clarify interrelations and differences between these three approaches. Thus, students’ probabilistic reasoning in specific random situations could be characterized, classified and finally, understood in more detail. In this chapter, we propose examples that potentially illustrate both, interrelations and differences of the three approaches to probability mentioned above. Thereby, we strictly focus on an educational perspective.

At first, we briefly outline a proposal for relevant teachers’ content knowledge concerning the construct of probability. In this short overview, we focus on three approaches to probability, namely the classical, the frequentistic and the subjectivistic approach. Afterwards, we briefly discuss existing research concerning teachers’ knowledge and beliefs about probability approaches. Further, we outline our normative focus on teachers’ potential pedagogical content knowledge concerning the construct of probability. For this, we discuss the construct of probability within a modelling perspective, with regard to a theoretical perspective on the one side and with regard to classroom activities on the other side. We further emphasize considerations about situations which are potentially meaningful with regard to different approaches to probability. Finally, we focus on technological pedagogical content knowledge. Within the perspective of teaching probability, this kind of knowledge is about the question of how technology and, especially simulation, supports students understanding of probabilities.