For more than a century, the academic community has been concerned with the training of Mathematics teachers, which often takes place isolated from the practice of basic school classrooms. When it comes to irrational numbers, the situation is no different. With a view to changing this scenario, we aim, in this experience report, to promote a debate on the content knowledge of irrational numbers, based on the reading of specific texts and a didactic activity with students from a public university. The work was conducted with seventeen students of the subject "Mathematics at School", of which fifteen were undergraduates and two were studying for a bachelor's degree. In two days of intervention, the collaborative observation, and the written productions of the students in the proposed activities were constituted as instruments for data collection. natural, integer and rational. Thus, we unveil such epistemological heterogeneity and warn that this, when not observed, can cause difficulties in student learning in Basic Education. [ABSTRACT FROM AUTHOR]