This research documents the impact of a teaching interview aimed at developing a critical attitude in students, and focused on a particular topic: radiocarbon dating. This teaching interview is designed to observe students' reaction to limited written explanations of the phenomenon under study, and their possible frustration or intellectual satisfaction in relation to these texts. We aim to document the possible link between students' developing conceptual understanding of a topic and their ability to express their frustration when presented with very incomplete explanations, or their intellectual satisfaction when presented with complete explanation. As a side product, we intend to observe some of their a priori ideas concerning this topic. Ten teaching interviews conducted with fourth-year University students were recorded, transcribed and coded. Beyond a series of results concerning students' a priori understanding of the domain, the analysis of the interviews suggests that, when students are presented with texts of increasing completeness and discuss these with the interviewer, their critical reactions evolve in time in a very specific way. We propose a tentative model for this co-evolution of student conceptual command and critical stance. The discussion bears on possible interpretations for the "anesthesia of judgment" observed in most students at the beginning of the interview, and for a few of them throughout the discussion. Keeping in mind the "competence vs concepts" current alternative, the conditions that seem to free students' critical potential are analyzed in relation to their evolving command of the topic and their degree of intellectual satisfaction.