Resumen

This paper considers the different ways in which students make use of empirical evidence as they attempt to write valid mathematical proofs. Examples of students’ proof constructions related to both algebra and geometry activities are presented to illustrate how that type of evidence can play a variety of different roles in the proving process. For example, it can act as tests of a conjectured conditionality, as generic examples in deductive arguments and as special cases to highlight particular properties when more inductive arguments are developed. It is suggested that involvement in the construction of mathematical objects during computer interaction can encourage students to identify general structures when they manipulate particular cases.