The study of new approaches to teaching Science has become important to understand how these new methodologies can enhance student learning. In this context, the investigative approach and the STEAM approach have been gaining more and more strength and notoriety in the research literature in this area. In order to investigate the potential of these approaches for teaching physics in high school classes, the workshop entitled "Building an Artificial Muscle" was created by the “Ciência em Foco” extension project, linked to the Physics Department at Federal University of Pará and to “REPENSE” Studies Center. As it is interdisciplinary in nature, the workshop has three areas of science as strands: Biology, Physics and Biophysics – which are addressed in three different moments. During the first implementations of the workshop, when mathematical concepts linked to the physical concepts that were being worked on were discussed (Hooke's Law), the great difficulty of the participants was evident: understanding the proportionality between physical quantities. From this observation, we sought to understand the root of the problem and, after conducting a bibliographic survey on the teaching-learning process having cognitive development as a theoretical foundation, we arrived at the neo-Piagetian cognitive theory called Theory of Conceptual Fields, proposed by Gérard Vergnaud. Thus, in this work, based on Vergnaud's theory, the following were analyzed: 1. The conceptual fields named “multiplicative structures”, which are related to knowledge involving mathematical concepts in Physics (proportionality); 2. The configuration of a conceptual field, being described by four pillars (concepts, situations, schemes and operative invariants) whose domain requires time and acquired experience; 3. The construction of scientific knowledge through the learner's personal experiences. In the application of the workshop in the online model, concepts and situations inherent to the mathematical construction of Hooke's Law were identified. The results were given through the analysis of dialectical oral discussions between the workshop participants and applicators. Through the responses to the questionnaires applied at the end of each moment and these discussions throughout the workshop, there were signs that the participants improved their mastery of the concepts covered, demonstrating the potential of using an investigative approach and STEAM in teaching science concepts.
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