Tasks that require students to construct examples that meet certain constraints are frequently used in mathematics education. Although examples do not serve as proofs for general statements, they have a supporting role in the preliminary stages of making sense of a certain mathematical phenomenon as well as in the development of argumentation. We hypothesize that examples of the limit-confirming type could also support the initiation of arguments for refuting an existential claim. Although students may be able to construct this type of example, they rarely use it effectively in their argumentation. In this qualitative study, we analyze how teachers could scaffold students' awareness of the potential role of limit-confirming examples as tools for supporting argumentative processes and reflections on methods of construction of effective examples. We analyzed teacher's actions to explain and generalize this process by identifying and categorizing key moments that could characterize an approach fostering students' aware and effective use of examples to develop argumentations.