Understanding the Formal Limit Definition: a study in preservice Mathematics’ teacher education

Abstract In this paper, we analyze Brazilian preservice mathematics teachers’ understanding on the formal limit definition of a function in a point, during a didactic intervention aiming at the learning of this mathematical concept with understanding. The data, collected from participant observation with audio and video recording of the classes and the written productions of these students in solving the proposed tasks, were qualitatively and interpretatively analyzed considering three elements involved in understanding: the meanings and the representations of limit and its application in problem-solving. The results showed that students, in general, assigned different meanings to the limit, which emerged from their concept-image and showed an adequate conception of the symbols present on the formal limit definition. They were also able to recognize and represent the limit, both algebraic and geometrically with records based on the symbols of this definition and to apply it correctly in the errors analysis and when solving problems involving conjecture validation. Thus, they unveiled comprehension of the formal limit definition.