The conceptual evolution of actual mathematical infinity

The different stages in the conceptual evolution of actual infinity are analyzed. We show how this concept occurs in high-school students at a prior, or at best, at the same level, as in Bernard Bolzano's conceptualization (as defined in his work The Paradoxes of Infinity). Furthermore, in terms of the historical development of the concept, the students' conceptualization has intra-objectal stage characteristics. Within the same framework, we show how Cantor's work fits into the inter-objectal stage, as well as presenting the difficulties encountered by students in order to reach this stage, given the current curricular structure. We conclude that such evidence should bring about a reconsideration of Piagetian ideas in education.