Abstract:

Successful learning is characterized by being meaningful and that should also be the aim of any educational activity. The meaningful learning of the derivative concept is crucial to be consciously applied in science and engineering. Such application is difficult in specialities other than Physics and Mathematics. Our goal is to develop a method to facilitate conscious learning of this concept and its applications in science problems. In this paper, our methodology takes into account the observations and the difficulties previously indicated. First, through a simulation, the derivative is presented as a quality of the dynamic change in respect to the independent variable. Second, the interpretations of this concept must be systematically used in all operations with derivatives. The first point is useful to introduce the physical and geometric meanings of the derivative. The second point is useful to interpret the rules and calculations with the derivatives. In addition, our method considers the principles of meaningful learning and presents a set of procedures to achieve this type of learning. This method is broken in five steps. First, the concepts of function and function limit are used as potentially meaningful knowledge. The procedure incorporates experimental demonstrations to establish the relationship between a concrete fact (reality of a situation) and the concept abstraction process. In that way, the secant line is not introduced ad hoc. Second, the processes of progressive differentiation and integrative reconciliation of the mathematical concepts are related to physical magnitudes frequently used in science. Those processes are performed according to the theory of conceptual fields. Third, the interpretations of the derivative are related to the definitions and rules that allow to calculate the derivatives. Fourth, the concept of differential of a function is introduced and its interpretation takes as reference the concept of derivative. Fifth, physical and geometric interpretations are applied in different types of problems and its effectiveness is verified. The procedure has been applied in the course of Calculus and Analysis of the Bioinformatics degree of Universidad San Jorge, Spain. Our main results are indicated as follow. First, a methodology that allows meaningful learning of the interpretations of the derivative concept and its applications to problems of diverse nature is presented. Second, the procedure is verifiable during the metacognitive process. Third, students successfully pass the exam of derivative and their applications.

Keywords:

Meaningful learning, learning strategies, conceptual fields.