The purpose of this study is to investigate the ways in which Swedish seventh grade students (12 and 13 years old) handle chance encounters. Four groups of students working in pairs participated in the study. In the group discussions, which were taperecorded and fully transcribed, the students were encouraged to explore strategies for winning a specifically designed dice game based on the sum of two dice. The dice game included four different set-ups of dice designed to bring to the fore different aspects of probability modelling and to offer the student the opportunity to encounter small differences in the mathematical structure of the sample space and of the probability distribution between the four different set-ups. The study describes strategies that the students use when confronted with these different set-ups, what their activities imply in terms of resources in handling random phenomena and what the dice game offers in terms of opportunities for learning probability. In order to explain such meaning-making processes the students' activities are viewed from a perspective that takes into consideration how the students' understanding varies with their interpretations of the situation they are confronted with, i.e., how they contextualize the different set-ups of the dice game. The results show how the students, during the course of the game, reorganize their interpretations of the mathematical content confronting them, and how a variation of guiding principles becomes the object of exploration. Approaches of extremes and a number model are described as a means for the students to identify and assign probabilities for the total of two dice.

The aim of this article is to develop analytical tools for studying mathematical communication in collaborative activities. The theoretical construct of contextualization is elaborated methodologically in order to study diversity in individual thinking in relation to effective communication. The construct of contextualization highlights issues of diversity in collaborative activities as it emphasizes how students may struggle differently with a learning activity. The interaction of students (12 to 13 years old), playing a specifically designed dice game, is used as an example for illustration. The article shows how accounting for the focal events of the interlocutors, and the contexts in which they contextualize these events, help in organizing our thinking about mathematically effective communication in collaborative activities.

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