In the period of digitalization of education, the creation of interactive learning environments is one of the most urgent tasks of this system. However, education is still dominated by the use of theoretical and concrete-practical texts, in which the hermeneutical potential of the studied science, embedded in reflexive teaching methods, is poorly manifested. In this regard, the study aimed to provide theoretical and methodological support for the design of interactive learning environments that include innovative educational technologies in mathematics, created in the course of the hermeneutical approach. In this case, methods are used that develop students 'and students' self-awareness, as well as humanitarianization of their thinking. Relying on this approach can provide the creation of new educational technologies for reflexive work with scientific and practical texts, their integration into electronic educational resources posted on the Internet, the intensification of innovative activities of teachers by combining them in creative educational clusters. As a result of the research, the following conclusions were made: reliance on the hermeneutical approach to the educational process will create conditions for the transition from the existing attitude to "ready knowledge" in education to the attitude to independent and active mental activity of students, which will stimulate the reflexive process of mastering the studied theories; the use of models and technologies of innovative computer didactics based on the HTML software platform provides electronic resources with the properties required by GOST R 53620-2009: interactivity, multi-media, the ability to modify content and software components, functionality, independence from the computer operating systems used. Thanks to these properties, it is possible to optimize the process of designing computer didactics technologies following the tasks of digitalization of the education system.
1
The new technological era is inevitably the reason for cardinal changes in all areas of
human society. There are a lot of changes in the educational process at all levels of
education since the innovative type of educational process must also correspond to an
innovative economy [
The creation of interactive training environments caused changes in the teaching
methodology of many disciplines. It led to forming a new teaching system with its own
specific theoretical and methodological basis - computer didactics. It is the field of
modern didactics. It explores the theoretical aspects and practice of e-learning and
creates the means for digital full-time and distance learning [
The concept «computer technology» has not yet received a clear definition, but is widely used in the theory of distance education. The authors of many scientific works use various terms as synonyms of this concept: electronic educational environment, virtual learning environment, digital educational environment, but these structures are different from interactive educational environments (IEE).
Many authors also refer to interactive educational environments as various types of electronic educational materials: electronic educational resources, electronic laboratory and task workshops, electronic supplements to training courses, electronic libraries, etc.
Others consider that interactive educational environments also are social networks
and social repositories, network offices and diaries, social media and databases, mental
maps as a technique for visualizing thinking, etc. However, the above-mentioned
electronic constructions have different aims and perform different functions in the
educational space [
There are different approaches to describe the IEE structure. For example, I.K.
Sirotina, S.I. Berezyuk, A.V. Faley teaching mathematics to point out the following
components: interactive content, presented by interactive texts, reference material,
workshop, and tests; interactive text with dialogical interaction with the student through
comments, tips, pictures, diagrams, and animation; an interactive workshop that
includes key tasks and tabs «Knowledge Update» and «Solution»; an interactive online
reference book with a base of theoretical material; a test component with two modes of
operation: control and interact with material for self-study [
This structure is typical for most of the subject educational environments presented on the Internet. There is no unified IEE classification; we cannot refer to a unified definition of this concept.
That’s why we use ready-made software components in the structure of IEE, and the functions of teachers are in developing educational content (this is the way «from a computer to the content of education»).
Our research follows a different way, it is «from the content of learning to the computer», i.e. we create the software component of interactive technologies IEE independently. We define IEE as a subject software-content structure for studying scientific theory with the help of digital interactive technologies which can be individual and implemented in line with the hermeneutic approach to creating IEE. 2 2.1
The term «hermeneutics» comes from the Greek «Hermeneuo». It means «I explain,
interpret» [
At present, hermeneutics is in demand as a certain methodology for mastering the phenomena of modern knowledge, based on the idea of influencing a person's consciousness to obtain various information, on his thinking and types of activity, including forecasting, modeling, design, diagnostics.
Pedagogical hermeneutics is the theory and practice of interpreting and interpretation
pedagogical knowledge. The key idea of this science is in developing the
self-consciousness of students in the process of reading and interpreting scientific texts, the
humanization of their world outlook and thinking. The urgency of this problem is
emphasized by the majority of school teachers and university teachers, believing that many
students do not have the ability of formal logical and dialectical thinking [
The process of understanding the studied text must be accompanied by the
transformation of knowledge into the mental experience of the learner. Therefore, it is
important to rely on the hermeneutic potential of scientific texts when designing IEE,
which is usually ignored in teaching physical and mathematical disciplines, where
computational and practical methods dominate. At the same time, by hermeneutic potential
we mean those properties of the text, based on which it is possible to organize the
mental activity of pupils and students, formulating a hermeneutic task for its study and the
subsequent development of a didactic (textual) version of educational technology, as
well as the creation of computer programs [
There are three groups of IEE technologies: technologies for mastering the content and analysis of theoretical educational texts, technologies for forming practical skills, recreational technologies focused on preventing mental fatigue, for example, computer educational games. Fig. 1 shows the components of the design process for an interactive educational environment. Each component has its characteristics and is invariant for any subject area (see Fig. 1).
Extrapolating the ideas of hermeneutics to the field of didactics, interactive digital technologies for processing scientific text were created in the structure of IEE. For example, at the first level of understanding, the following items were used: - «SLD» (structural and logical diagram), preliminary analysis of the entire topic as a whole; the method of the hermeneutic circle is implemented («from the whole text to separate parts, from parts to the whole»);
- «Blind scheme», the establishment of a sequence and connection within the studied
theory and self-filling of the scheme [
- text analysis and synthesis is used in many IEE technologies, for example, in the
Internet technology «Formula of knowledge» using symbols of the algebra logic, a
definition of a concept is made from elementary statements; Internet technology
«Disappearing text» («Fast reading» or «Visual dictation») is also based on the analysis of the
text and its correlation with the studied didactic objects [
Understanding scientific texts involve the step-by-step implementation of a complex system of cognitive operations: defining keywords, highlighting the main thing, proposing to continue the thought, find the cause and establish a consequence, draw conclusions, draw up abstracts, find an analogy, choose an adequate pictogram, establish a sequence of events, or algorithm of actions, correlate text with a picture, etc.
Technologies were created that reveal the internal structure of concepts: «Reconstruction»; «Insert symbol», «Find meaning», etc. They implement the principle of «didactic iteration», multiple variable repetitions.
The second level of understanding is syntactic, reflecting the understanding of sentences in the generalizing Internet technology «Matrix of knowledge».
The third level - semantic (contextual) - forms an understanding of the meaningful
parts of the text, as well as the text as a whole - the technology «Synopsisscroll» (with
a gradual unfolding the synopsis), «Concepts-meaning» (concepts are revealed by
interactive modules), «Synopsis-meaning», (symbolic designations of concepts and their
lexical meanings) [
The peculiarity of IEE technologies is that their aims are not to percept in-formation
directly, but the logical and dialectical understanding of information. In our opinion,
the phenomenon of understanding arises at the moment when it becomes possible to
connect a new information object with subject relations that are already presented in
the individual experience of the student. This provision of pedagogical hermeneutics
was implemented in the text-component IEE, in training blocks, for example, in the
Textbookcom program (textbook + computer) [
The use of game situations in the IEE texts is essential for developing concepts since
intellectual games involve the transformation of texts into various operations with
concept elements that are absent in scientific texts [
The stated theoretical provisions were implemented through a complex of innovative
technologies using the Power of Knowledge Internet constructor on the site of the same
name http://ya-znau.ru/ [
The process of monitoring the didactic efficiency of IEE digital technologies took place parallel with the study. So, during 2017-2019 years to identify the effectiveness of using interactive technologies of IEE, an experiment was carried out based on the study of the section of mathematics «Elements of linear algebra» for 2nd-year students of the Faculty of Continuing Education of training judicial system specialists of the SCF FSBEI HE «Russian State University of Justice». The control and experimental groups were selected by random sampling. The topic «Matrixes and actions on them» was studied using the interactive technologies of IEE, created in the program of the Internet constructor «Power of Knowledge» (see Fig. 2).
Algorithm of the experiment and statistical processing of the data obtained during the experiment.
1. Students of the experimental group were provided with a lecture course in the form of a web presence for self-study (see Fig. 3). Lectures were held traditionally for the students of the control group.
2. For the experimental group, various interactive tasks were organized through the corresponding web-forms on «the Power of Knowledge» website (see Fig.4 and see Fig. 5), namely: technologies for working with text, hermeneutic techniques (the concept of understanding), local learning technologies. Interactive exercises are aimed at the practical application of the knowledge gained during the study of the corresponding educational text and are equipped with operational verification of the results. The control group students performed the tasks presented in the methodological manual, traditionally on paper. 3. The study of the topic in the computer program «Textbookcom» is allocated to voluminous, complex educational tasks (in one task there can be up to 36 questions-tasks). Each such question-task is evaluated by a certain number of points. In our case, the maximum number of points is 141. When completing the tasks, the students' answers were recorded in the assessment tables, the number of points scored was calculated, the assessment scale was built, and, using the rating system, the mark was set (Table 1). The rating system may be changed depending on the complexity of the tasks. Table 2 presents the data of the experimental group (students are encoded with serial numbers) on the topic «Matrixes and manipulations with them», performed using the computer shell of the Textbookcom program. 4. For each group, bar graphs were constructed, illustrating the average score for each of the tasks of interactive technologies. Graphically, the data in Table 2 are presented in the form of a diagram (see fig. 6). 5. At the end of the experiment, a final control work was carried out to generalize and systematize knowledge about the main issues of the section with the use of innovative didactic technologies for the experimental group. The final work was carried out in the traditional form in the control group. The tasks were arranged in ascending order of difficulty; each was evaluated by a point corresponding to its ordinal number in the task (from one to five).
28 26 27 23 22 15
9 Average Tasks 1 and 3 contain two tasks, so the total number of points for the work is 19. The results of the final work for the experimental and control groups are shown in Table 1 and Table 1, respectively, where the number of students who solved each of the tasks is calculated, the total percentage of the task is shown, as the ratio of the number of completed tasks to the total number of tasks. A graphical interpretation of the statistics of the control task performance is given in the comparative diagram in Fig. 7. The diagram is based on the data in Table 1 and Table 1. The average score for the control task in the experimental group (201 g.) is 16.0, in the control group (202 g.) is 10.88, and it means that the experimental group coped with the task more successfully.
As a result of statistical processing of the data of the pedagogical experiment according
to the Fisher slope method, conducted in groups of students when studying the topic
«Matrixes and manipulations with them», during the period of training a positive effect
was observed in the experimental group using technologies integrated into an
interactive environment learning and using the author's program «Texbookcom» [
The results of our research can be used both in full-time education and in distance
learning, as well as in the independent work of students (pupils). New digital teaching
means are being created within the framework of the scientific direction - innovative
computer didactics - at the Kuban State University (KubSU), where dozens of
dissertations in this direction have been done. Published 75 issues of the scientific and
methodological journal «School Years» with electronic applications [
IEE innovative technologies have been created over a long period, therefore, their
discussion was held many times and in various forms: at international conferences
(Moscow - 2016, 2018; Derbent - 2017, 2018; Yalta - 2017, 2018 2019; Krasnodar - 2018),
at the regional seminars of mathematics teachers held by the Regional Institute of the
Development of Education (Krasnodar, Armavir, Tikhoretsk, Yeisk,
Primorsko-Akhtarsk 2016-2020), in the process of performing dissertation research by graduate
students of KubSU (2000-2018). Initially, IEE technologies were created to be included
in a new model of the textbook, which was the winner of federal competitions of
projects: «Informatization of the education system», Moscow - 2006; «The best IT solution
for distance learning», Yalta - 2017. The textbook is named technological because 80%
of its volume is innovative technologies of IEE. For creating a new model of the
textbook, its author, Professor A.I. Arkhipova, was awarded the medal of K. D. Ushinsky.
But it is practically impossible to introduce new models of textbooks into schools,
therefore IEE technologies began to develop autonomously, entering the structures of
other types of electronic resources, in particular, into interactive learning environments.
Since 2014, 12 of these technologies have been created on the Internet using the Power
of Knowledge constructor on the popular site of the same name [
The results of the discussion by teachers of innovative technologies for teaching mathematics (2016-2020) are reflected in the questionnaires, their numerical and graphic interpretation are displayed on the KubSU portal. 5
The study confirmed the legitimacy and productivity of the authors' initial position that a hermeneutic approach to the process of designing digital technologies for an interactive educational environment can create favorable conditions for teaching and educating not just literate, but an intelligent and highly moral person. It is this scientific and pedagogical foundation that we consider as an incentive for the positive development of the digitalization process in Russian education.
In conclusion, the authors express their gratitude to the administration of the Kuban State University, which created a comfortable environment for the scientific and pedagogical activities of the university teachers; Dean of the Faculty of Mathematics and Computer Science, Doctor of Pedagogical Sciences, Professor S.P. Grushevsky, who created conditions for the productive activity of students; software engineer, Ph.D., R.I. Zolotarev, who created four sites with high traffic free of charge; teachers I.G. Knyazeva and S. B. Nuzhnova, actively introducing IEE technology into school practice.