Comparisons between formal and informal arguments

The aim of this study is to explore the attention foci and cognitive obstacles that underlie in the process of deciding whether a Formal proof is Based on an Informal argument (FBI judgement). Examining what students consider when making these types of judgments, it is possible to gain some insights about the way in which they construe mathematical formalization. Overall, it was observed that those who make successful FBI judgements show more robust conceptions about the aspects involved in mathematical proof and how conceptual breaches seem to influence the transition from informal to formal arguments. To this effect, Zazkis and Villanueva's (2016) model of attention foci and the notions of structural and concept distances is used to explain difficulties students face when making FBI judgments.