Abstract:

A lot of importance has been attached to a number as such throughout human history. The assertion that “number is the essence of things” was one of the most important philosophical principles of Pythagoras. The use of number systems, theorems and principles valid in number systems in connection with informatics is an area that we still explore and develop even today. The article deals with the identification of common mistakes that students make when solving problems in number theory. To identify mistakes, samples of student work were collected for each type of problem, the solutions of which the students developed without external suggestion. The analysis of methods of solution sought examples of correct solutions. Exceptions to these examples indicate a possible problem in mastering a given procedure or concept. The identified mistakes showed mainly procedural failures of students, which are, however, often caused by insufficient conceptual understanding of the basic notions of number theory. The identified mistakes, which were categorized according to their importance and frequency of occurrence, served as input in the creation of modules within the mastery learning concept. Knowing the frequently made mistakes will make it possible to create a relevant sequence of tasks within the mastery learning modules that will help students eliminate the shortcomings in the field of number theory. The created modules contain conceptual tasks in order to improve students' conceptual understanding of basic concepts of number theory. The individual modules correspond to the specified hierarchy of identified mistakes. The application of mastery learning in the teaching of mathematics will create suitable preconditions for students to be able to teach mathematics anytime, anywhere and at their own pace in the sense of the Education 4.0 educational concept.

Keywords:

Number systems, applications, mistakes identification, mastery learning, Education 4.0.