Dificultades en las prácticas del cálculo diferencial: una mirada desde la teoría de los obstáculos y los conflictos semióticos

Abstract

This book, which the reader holds in his or her hands, constitutes a dense and in-depth work on the initial teaching methods of differential calculus. It studies the interactions between students and teachers without judging the phenomena as "good" or "bad." It attempts to infer the teachers' purposes, methods, and techniques and compares them with what their students learn or don't learn well, or understand or don't understand well, or at least repeat well after one or several semesters of classes. Regarding the epistemological aspects, the author manages to penetrate the tangle of terms, definitions, and interpretations circulating in the literature on mathematics education regarding the obstacles, errors, conflicts, difficulties, and conceptions or "my conceptions" of students. Emphasizing that research into the transition or break from school algebra to differential calculus, and the epistemological, semiotic, didactic or cultural difficulties, conflicts or obstacles that arise in this transition, constitute crucial points in research on the teaching and learning of Differential and Integral Calculus in secondary and higher education.