The scientific literature identifies five challenges related to training teachers: the basics of the constructivist approach, the problematization of mathematical knowledge to be taught, the promotion of interdisciplinarity, the use of digital pedagogical resources in planning teaching, and new skills to be developed due to the arrival of artificial intelligence. Considering the COVID-19 pandemic, it is appropriate to consider a sixth challenge, notably, training teachers capable of delivering mathematical distance learning courses focused on students’ conceptual understanding. It therefore is necessary to link the stakes of initial training with that of distance learning, which can enhance conceptual understanding. Linking the need to construct knowledge among students with technological tools used for distance learning allows new challenges faced in the planning of mathematics teaching to be highlighted. These new challenges give rise to the anticipation genesis that helps in situating the planning of mathematics teaching between three variables: artifact variables, arrangement variables, and variables related to the nature of the data to be used. These variables are a major asset for the training of the preservice mathematics teacher. Their study in this article allows us to recognize that the choice of technological tools to be used in mathematics distance learning depends greatly on the conceptual analysis of the mathematical knowledge to be taught. This study shows that it is important to rethink and question distance learning for each mathematical concept.