Task design fostering construction of limit confirming examples as means of argumentation

Tasks that require students to construct examples that meet certain constraints are known to be used in mathematics education. It is also well established that while examples are not proofs (for general statements), they have a supporting role in the preliminary stages of making sense of a certain mathematical phenomenon. In this study we examine a task design in which students are required to submit a supporting example to their explanation negating an existential statement. We introduce the idea of limit confirming examples and present their use in an analytical geometry task in a 10th grade class in Italy, along with the explanations they support in negating an existential statement. The results show that the design was effective in fostering the construction of limit confirming examples that could be considered as means of argumentation in the initial parts of proof construction.