The aim of this paper is to narrate a significant part of the experience of a professor over several semesters teaching fundamental ideas of the Theory of Calculus. The narrative explains how his didactic and mathematical mentality evolved as he witnessed students’ conceptual difficulties, as they were confronted with situations that generated tensions between their intuitions and the formal rigor of the theory of calculus. The evolving atmospheres in the classroom, the efforts to teach, and the deep obstacles to learning, indicate the existence of an epistemic fissure as one leaves the dynamic and geometric way of thinking and tries to adopt a mode of thinking developed from arithmetical rigor and the presence of infinity.

本文的目的是叙述教授在数个学期里教授微积分理论基本思想的重要经历。叙事解释了当他看到学生在概念上的困难时，他的教学和数学心态是如何演变的，因为他们面临着在直觉和微积分理论的严格性之间产生张力的情况。教室中不断变化的氛围，教学的努力以及学习的深层障碍，表明存在一种认知裂缝，因为人们离开了动态和几何思维方式，并尝试采用从数学严谨和严格的思维方式发展而来的思维方式。存在无穷大。