Abstract:

Meaningful learning has an important role in improving any educational activity. From this perspective, the integral concept can consciously be learned and applied in the context of physical science. Particularly, this type of learning is crucial in non-Physics degree courses. In this paper, our goal is to develop a procedure to facilitate the acquisition of this type of learning. For this reason, we have developed a five-stage procedure. First, we find out if potentially meaningful knowledge exists. Second, we reconstruct and/or reinforce what the student already knows and relate the integral concept to others such as the limit and derivative of functions. Third, we pass from the derivative concept to the differential of a function. Taking into account the strong relation among previous concepts, we highlight that dynamic changes in the limit definition and its cumulative character are key for understanding the integral as the sum of infinite elements where each one has an infinitesimal character. Fourth, we present properties and typical operations with the integral concept and give its interpretation. Fifth, we apply this concept to different problems with two levels of difficulty. Less complication arises when we have the derivative of a physical magnitude. As the first derivative and the differential of a function are related concepts, it is possible to calculate the integral when variables can be separated. More complication will occur if we have to solve a problem from another perspective in which we need to decompose a given magnitude in infinitesimal quantities. However, this last difficulty has an advantage, a feedback process in learning can be observed. In addition, in all stages, our method considers the principles of meaningful learning and the theory of conceptual fields. The procedure has been applied in the Applied Physics course in the degree of Pharmacy and the Foundation Physics course in the Computer Engineering and Design and Development of Videogames degrees in Universidad San Jorge, Spain. Our main results are as follow. First, a methodology that allows to obtain meaningful learning of the integral concept and its applications to a variety of problems of diverse nature. Second, the procedure is verifiable during the metacognitive process. Third, students show significant learning cues when they do the exam. Theoretically, our method is compatible with previous papers and can be implemented in different areas of knowledge in the physics field.

Keywords:

Meaningful learning, learning strategies, conceptual fields.