Mathematical practices when solving problems involving joint and conditional probabilities without prior instruction

Resumen

Given the significance of probability, its various interpretations, and the challenges associated with teaching it, this article presents the findings of a study that explores the strategies employed by participants when faced with a problem involving joint and conditional probabilities during the final round of the XXX Aragon Mathematical Olympiad. The onto-semiotic approach (OSA) serves as the theoretical framework for this study, with particular emphasis on the levels of algebraization. The methodology is qualitative, centred on analysing the problem statement and the participants' approaches to solving it. This allows for the observation of emerging probability meanings, the language utilized, the algebraic activity conducted, and the problem’s difficulty throughout the resolution process. Our findings reveal that different levels of algebraization were observed in the resolution of each problem subsection, not necessarily correlated with the a priori difficulty.