Exploring Probabilistic Reasoning : A Study of How Students Contextualise Compound Chance Encounters in Explorative Settings

Abstract: This thesis aims at exploring how probabilistic reasoning arises in explorative learning situations that are random in nature. The focus is especially on what learners with scant experience of formal theories of probability do and can do when dealing with compound random situations in which they are offered opportunities to integrate different probabilistic lines of reasoning. Three studies were carried out for the purpose of gaining an understanding of how learners’ probabilistic reasoning is organised and re-organised in explorative, random-dependent situations. In two of the studies 12 to 13 year-old students acted within a dice-game setting, which was based on the total of two dice. The third study examined 14 to 16 year-old students’ ways of dealing with ICT-versions of compound, independent events viewed in a random-dependent ramified structure. To uncover the basis and the content of the students’ reasoning, behaviour has been regarded in terms of intentions. That is, to understand and make sense of the students’ reasoning, their activities have been matched and re-matched with conjectures about their intents to fulfil certain goals. Although the students were acting on the same learning material, the analyses revealed various kinds of probabilistic reasoning among the students. It has been argued that students’ various ways of dealing with chance encounters may be understood and explained with reference to the ways in which they interpret the learning situations. Thus, this thesis suggests that probabilistic reasoning takes form through a process of contextualisation, i.e. through a compound process where the cognitive activity oscillates between interpretations and reflections about context, the focal event and new information that comes into play. This thesis reveals that students, prior to instruction, are able to devise ideas of an underlying probability distribution in the case of compound random phenomena. The students bring into the discussion geometrical and numerical considerations, as well as arguments reflecting principles of the law of large numbers.