An exploratory study of the difficulties related to the probabilistic modeling process

This study is a contribution to efforts to promote practices for dealing with the difficulties encountered by learners in probabilistic modeling situations. We attempt to elucidate as precisely as possible the types of difficulties that secondary school students face in the process of modeling with probability tools. By referring to a large and extensive literature on the specific difficulties of modeling, we have been able to establish a typology of possible difficulties that may emerge during the implementation of the modeling process by secondary school students. We determined sub-categories for the probabilistic modeling stages. Based on this typology, we constructed a test and we administered it to a random sample of secondary school students. The analysis of the responses via a grid developed for this purpose, we were able to deduce that the sub-categories of difficulties we identified are both positively correlated. With regard to student performance, some particular difficulties were encountered in the implementation of the modeling stages. We also observed that the choice of the appropriate probabilistic model is hampered by a lack of conceptual understanding of the probabilistic situation, while the stage of probabilistic calculations is mainly affected by the failure to choose the correct mathematical methods and techniques.