From action to schema: A study on the construction of the concept of implicit derivation in engineering students

Abstract

This study proposes and empirically validates a genetic decomposition grounded in APOS theory to facilitate learning of implicit differentiation. The study analyzes the impact of a didactic intervention, developed using the genetic decomposition and implemented with 40 engineering students, that emphasizes coordination between graphical and analytical representations. Qualitative data were collected through questionnaires and clinical interviews. The results indicate that the intervention facilitated a transition from Action conceptions, characterized by mechanical application, to Process and Object conceptions, thereby resulting in greater conceptual flexibility and overcoming common errors. Additionally, the analysis revealed an unforeseen challenge in coordinating differentiation rules, prompting a refinement of the genetic decomposition to incorporate a new mental construction. The refined genetic decomposition is therefore considered a robust model for training, validating the APOS approach as an effective method to foster a structural understanding of implicit differentiation in engineers instruction.