Resumen

Context: Rethinking mathematics teaching practices in a university context is an emerging research theme. Objectives: In this article, we aim to discuss the limits and possibilities of using mathematical tasks in the teaching and learning processes of the concepts of Derivative, Integral and the Fundamental Theorem of Calculus. Design: The study is based on a qualitativeinterpretative perspective of research, with methodological procedures inspired by a DesignBased Research. Environment and participants: The research was developed with students attending a Functions of a Variable class in a public university in the state of São Paulo. Data collection and analysis: Data were collected through mathematical tasks on Differential and Integral Calculus solved by students. The protocols produced were analysed, pointing out the main aspects identified, which led us to organize categories of analysis and dimensions (i) knowledges mobilized and developed by students in relation to mathematical concepts; (ii) main errors and difficulties presented by students in the development of tasks; (iii) limits and possibilities of the practice of exploratory teaching in the university context. Results: The results reveal aspects that characterize a process of resignifying the mathematical concepts discussed with the students and a deepening of their knowledge about the concepts of the DIC. Conclusions: As future notes, we suggest rethinking university teaching practice, since the study indicated possibilities and potentialities of the use of exploratory tasks in the teaching of Differential and Integral Calculus.