As literature has reported, it is usual that university students in statistics courses, and even statistics teachers, interpret the confidence level associated with a confidence interval as the probability that the parameter value will be between the lower and upper interval limits. To confront this misconception, class activities have been designed with the aim of realizing that this application of confidence level violates the basic laws of probability, when considering two non-overlapping confidence intervals, that could plausibly correspond to two random samples from the same population, where the probability of events within this interpretation contradicts the probability rule for disjoint events and the rule of monotonicity (P[E] = P[F] if E ? F). Afterwards, we use simulation to help students shift to a frequentist interpretation of confidence intervals. Although the expected questioning was generated in students, it does not look like it is enough to establish a solid re-conceptualization of confidence level. We believe that this is due in part, to the slight language used in the teaching process and to incipient conceptions about the probability notion.