DYNAMICAL TEACHING FOR THE NEW AGE: EXAMPLE OF THE TEACHING AND LEARNING OF FEATURES OF DERIVATIVE
Keywords:
Differential calculus, derivative, GeoGebra, dynamical materialsAbstract
Differential calculus represents a very important field of mathematics, primarily because of the possibility
of its application. The derivative of a function, a key element of differential calculus, finds its application not only in
mathematics but also in most other natural sciences. By its very nature, differential calculus is an abstract and, to
understand, rather complicated and demanding theory for students. Due to the presence of highly abstract concepts,
students have difficulties understanding the true meaning of differential calculus, and especially seeing a little
further, i.e. recognizing situations where that theory can be applied. In higher education, differential calculus,
primarily the derivative of a function, is an unavoidable moment in the teaching of mathematics, and it is very
important how it will be presented to students. In teaching mathematics, it is very important that students have
properly formed ideas about mathematical concepts. This is especially related to the concept of the derivative of a
function, which is necessary for students not only as a concept that occurs in the teaching of mathematics but as a
necessary tool for many other fields and sciences. Successful organization of the process of formation of
mathematical concepts and successful management of their adoption can be achieved through the modernization of
the teaching process. Special attention in this paper is devoted to the improvement of the teaching process through
the application of modern computer technologies. The GeoGebra software, which was used for the purpose of
preparing the material for this work, is described and shown. The GeoGebra software was chosen for its ability to
create animations and simulations. The dynamic nature of the GeoGebra software answer the demands of modern
teaching and fits perfectly into the students’ habits for the active learning process. For the purposes of this work, a
dynamical material containing moving images, illustrations, and graphs which through its interesting story illustrates
the features of the derivative of the function in a very interesting way was designed by the authors of the paper.
Presenting the basic content related to the concept of the derivative of a function in this way enables students to
understand and acquire these concepts more quickly. The material presented in the paper was realized using
GeoGebra software. All the elements of the used GeoGebra material were explained in detail. The impressions of
teachers and students about the effects of applying such materials in teaching mathematics and science were more
than positive. Our mission for the future is to continue with the development and improvement of teaching materials
and techniques by using modern technologies.
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