I. Dražić , N. Črnjarić-Žic , A. Bašić-Šiško 

University of Rijeka, Faculty of Engineering (CROATIA)
Nowadays, hybrid forms of teaching are increasingly used, combining traditional face-to-face teaching with elements of e-learning. This form of teaching is optimal because it combines all the socio-educational advantages of traditional teaching with new technologies and methods of learning and teaching, such as flipped classroom and ubiquitous learning, where learning can take place anytime and anywhere without spatial or temporal constraints.

In traditional face-to-face teaching, data about the learning process is very difficult to access, there is very little of it, and it is rarely used to improve teaching. In e-learning, there are a handful of these data, and the e-learning systems themselves are often developed based on these data, with various machine learning algorithms guiding and optimizing the process of knowledge acquisition. However, in e-learning systems, the algorithms that drive the learning process are very often based on so-called black-box models that are outcome-oriented, without a deeper analysis and understanding of the problem. In both forms of teaching, and especially in the classical classroom model, the adaptation of the learning methodology is mainly based on the experience and intuition of the teacher and is therefore often subjective.

One of the important facts of which educators should be aware is that the development of science and technology requires more frequent and increasing interventions in the curriculum, both at the level of content and method, and that these interventions must be directed toward progress, that is, toward more efficient and better acquisition of new knowledge. What is happening in industry, i.e. the fourth industrial revolution, must have a corresponding impact on education and modern teaching should evolve within the concept now known as Education 4.0. It is clear that a subjective approach based on qualitative analysis and self-reflection is not the optimal tool for this and that a new method must be found that is, above all, extremely objective and fast.

In this paper, we explore the applications of classical data analysis methods such as correlation and cluster analysis, as well as the possibilities of modern approaches to data processing based on advanced data-driven algorithms. An example of such methods are techniques based on the Koopman operator. We pay special attention to the interpretation of the obtained results and the possibility of their implementation on concrete examples of hybrid educational systems.

As an example we take a hybrid model of mathematics education developed for students in the field STEM. The content focuses on the elements of differential and integral calculus and vector analysis with applications in engineering. We analyze the ways to improve the whole teaching process based on the data extracted from the corresponding e-learning system and the interpretation of the results of the mentioned analyzes. We focus on several important areas: Identifying key factors of the teaching process and detecting weaknesses, detecting clusters among students in terms of their performance and interests, and identifying necessary changes in the course content.