=Paper=
{{Paper
|id=Vol-2770/paper13
|storemode=property
|title=Digitalization of Mathematical Education and its Influence on the Formation of Stochastic Worldview through the Development of Probabilistic Thinking Style
|pdfUrl=https://ceur-ws.org/Vol-2770/paper13.pdf
|volume=Vol-2770
|authors=Sergey Shcherbatykh,Kseniya Lykova
}}
==Digitalization of Mathematical Education and its Influence on the Formation of Stochastic Worldview through the Development of Probabilistic Thinking Style==
https://ceur-ws.org/Vol-2770/paper13.pdf
Digitalization of Mathematical Education and its
Influence on the Formation of Stochastic Worldview
through the Development of Probabilistic Thinking Style*
Sergey Shcherbatykh1 [0000-0001-9737-2473] , and Kseniya Lykova1 [0000-0001-9312-7040]
1
Bunin Yelets State University, Kommunarov, 28, 399770 Yelets, Russia
shchersv@elsu.ru, ksli1024@mail.ru
Abstract. The digitalization in education has started the process of social and
economic transformation which has entailed not only cardinal changes in ap-
proaches to training, principles of interaction of subjects of educational rela-
tions, but also has led to reconstruction of methodical system of schools. As a
result, in the system of secondary general education the process of integration
of digital educational environment into traditional education is being imple-
mented in order to provide unlimited access to information of any form. The
digital environment directly influences consciousness of the person, expanding
his cognitive abilities, changing system of values, world understanding and
world outlook of the person of schoolboy. In this regard, it is important during
school years to develop an "objective" world view of students, designed to help
substantiate the cause and effect of the surrounding reality. In our opinion, this
is the stochastic worldview formed through the development of students' proba-
bilistic thinking style.
Keywords: digitalization of mathematical education, probabilistic thinking
style, stochastic worldview, secondary general education, digital educational
environment, digital technologies.
1. Introduction
Modern society is characterized by high speed, an abundance of events and changes
that entail states of instability and instability, misunderstanding of oneself, one's atti-
tude towards events and changes. The daily increasing flow of all kinds of infor-
mation and falling on a person is so great that its constructive perception and analysis
in this environment becomes difficult. Therefore, it is important, in the context of the
digitalization of mathematical education, to develop in students a probabilistic style of
thinking that promotes knowledge of the phenomena around them that cannot be di-
rectly perceived. The probabilistic style of thinking is characterized by flexibility,
criticality, adaptability, dynamism, ability to act in conditions of uncertainty, is de-
fined by the possibility of designing non-standard patterns of actions, refusal of tradi-
*
Supported by the Russian Science Foundation, grant No. 20-313-90019
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0
International (CC BY 4.0).
Proceedings of the 4th International Conference on Informatization of Education and E-learning Methodology:
Digital Technologies in Education (IEELM-DTE 2020), Krasnoyarsk, Russia, October 6-9, 2020.
tional schemes of thinking, harmonious display of interconnected links of the objec-
tive world [1].
Analysis of probability and statistical data, ability to make decisions in situations
of uncertainty will help students to model natural and social patterns, predict random
phenomena and processes. Establishing the probabilistic thinking style of high school
students while studying elements of stochastics will allow them to form a complex,
structural vision of the world, i.e., to approach such a phenomenon of thinking as
stochastic worldview. N. D. Andreeva believes that the scientific worldview of stu-
dents formed during school years: "under the conditions of the ambiguity and contra-
dictions of the modern world, it may play the role of a 'fulcrum point' in solving a
variety of problems, namely, to perform an information-reflective, orientation-
regulatory, and evaluation function" [2, pp. 8-9].
The digitalization of the education system defines the application of the newest
methods and means of education, construction of individual educational trajectories,
influences qualitative change of the content of education and increase of its techno-
logical level: possibilities of management and control of the results of education,
work in virtual and supplemented reality. Digital technologies provide huge educa-
tional opportunities to organize effective learning: instant access to learning applica-
tions and materials, work with visual learning tools and electronic simulators, mobile
learning technology, virtual and augmented reality technology. A variety of digital
technologies used in the learning process: training and simulation programs, infor-
mation resources, interactive modules, cognitive programs, social services Web 2.0,
3.0, etc., there is a manifestation of them in the form of private individual environ-
ments. New educational technologies are aimed at improving the culture of thinking
of students, the disclosure of intellectual potential.
In the framework of the national project "Education", which includes such federal
projects as "Modern School", "Digital Educational Environment", "New Opportuni-
ties for Everyone", one of the main goals is the full-scale digitalization of schools. As
a result, the education system is making a smooth transition to the digital era.
Despite the wide spread and introduction of digital technologies among researchers
abroad (Bersin J., Janice L, Koole M, Kuiper K., McMurtrie C, Ronald G.) there is no
unequivocal point of view on the effectiveness of digital learning, the possibilities to
improve its quality, content and control. Fatherland scientists (A.A. Andreev, S.A.
Beshenkov, I.P. Gladilina, M.V. Voropaeva, E.V. Minzayeva, A.V. Morozov, S.S.
Neustroev, V.A. Pleshakova, I.N. Turkulova, T.S. Shikhnabieva, M.I. Shutikova, etc.)
have no unequivocal opinion on the effectiveness of digital learning, its content and
control. ) are of the opinion that digital technologies have both positive and negative
impact on the development of a student's personality, their use in the learning process
is carried out spontaneously, and most importantly, the latent nature of information
means in teaching is noted. On this basis, the task of research and clarification of the
features of the influence of digitalization of mathematical education on the develop-
ment of probabilistic thinking style in order to form a stochastic worldview of high
school students is extremely important.
2. Results
For the modern younger generation, the "children of the digital age", digital technolo-
gy is a connecting link in the relationship between people, and the virtual world ex-
tends their social life. They spend a lot of time on the Internet, not sharing their own
identity in the digital and real world, actively use information technology to express
themselves, interact with each other, access all kinds of sources of information, result-
ing in the formation of new knowledge and creative work of a new type. As a result,
the functioning of the environment in which human life is intertwined with technolo-
gy is constantly evolving and improving.
According to J. Palfrey's research: "The children of the digital age fundamentally
transform many sectors of the economy, education system and world politics" [3].
This situation generates a lot of problems, including the development of orientation
skills in the information space and the formation of a critical attitude towards infor-
mation. That is why it is necessary to learn how to make samples of qualitative and
reliable information, to be able not to give in to manipulation and disinformation. The
National Project "Education" provides for the development of students' skills in data
processing and analysis, which is closely related to the process of developing the
probabilistic thinking style of students in the framework of mathematical education.
Probabilistic thinking style of students contributes to the objective analysis of con-
ditions and situations, the correct interpretation of trends that give rise to their func-
tioning. Skills of statistical information processing are an indispensable condition for
vision of integrity and objectivity of the world picture: determination of industrial
production index; estimation of living standards of population; analysis of pricing
theory; identification of factors influencing economic interest; possibility of estab-
lishment of gross regional product volume, etc.
Formed stochastic worldview lays the guidelines for creative and practical activi-
ties, helps to create favorable conditions for the development of intellectual potential
of the student. The specifics of the stochastic worldview are revealed in its character-
istics: "flexibility" of thinking due to the ability to quickly switch attention; improve-
ment of thinking actions and operations (abstraction, analysis, analogy, generaliza-
tion, concretization, synthesis, etc.); predominance of creativity in the use of elements
of stochastics - the ability to use associations to objects, to go beyond the scope of the
problem under study, to generate original ideas and apply them in specific tasks. Due
to the unique features of stochastic worldview: the formation of a positive attitude to
chance, the ability to identify mutually intertwined connections of the world, to pre-
dict the behavior of objects in the environment, students will succeed in learning
about the world around them, will be able to better navigate in it and adapt (in particu-
lar, "adapt") to constant changes in it.
By studying the elements of mathematical statistics, combinatorial science, proba-
bility theory, high school students get ideas about the influence of random events on
the regularities in the result of the experiments, visualization of which is extremely
useful. Thus interactive models, software of cognitive character, board Smart serve as
a tool basis at training and allow to reach efficiency of educational process by stimu-
lation of conscious cognitive activity of pupils, as a result of integration of availabil-
ity, memorability and interactivity inherent in the specified means. Digital technolo-
gies in the study of the probability-statistical line of a school mathematics course
provide access to new sources of information (interactive tables, meteorological ser-
vice sites, election commissions, sports statistics, etc.). The functionality of statistical
application packages (Statistica, Stadia, SyStat, etc.) facilitates fast and accurate pro-
cessing of statistical information: sorting, grouping of data, and demonstration of
results in the form of histograms, diagrams, and polygons. The applied tools and
technologies facilitate unconventional organization of classes and other management
of the educational process.
In conditions of digitalization of mathematical education the basis of information
support is orientation on effective application of information or digital technologies
and work in the digital educational environment by creation of optimum conditions of
development of each schoolboy's personality. Applied means and technologies in-
crease motivation for learning, allow organizing classes in a different way and manag-
ing the educational process. Local, network databases are created for realization of
collective forms of work and realization of training courses; development of training
programs and computer games (as the tool of diagnostics and rehabilitation) for de-
velopment of sensory, perceptual and cognitive functions of the person, studying and
improvement of thought functions of the person is carried out [4].
The digital environment realized in educational institutions provides new possibili-
ties for display of creativity of the person of the schoolboy, repeatedly raises efficien-
cy of independent work of pupils, realization of essentially new forms and methods of
the organization of educational activity is carried out (for example, joint educational,
creative and research work in profile network communities and projects; preparation
for olympiads and examinations; work with gifted children). The digital environment
operates continuously, regardless of the user, is not limited by time or geographical or
any other framework, contains huge amounts of data, supports various forms of com-
munication, in particular, interactive communication. Given that the digital environ-
ment has a direct impact on a student's mind by changing their cognitive abilities and
value systems. In turn, the stochastic worldview is a mechanism that determines the
personal position of the student to the world and to himself in this world, and has
specific capabilities: building his worldview on the basis of stochastic knowledge,
methods and ways of knowing reality, overcoming situations of uncertainty in the
conditions of multiple choices, individual adaptation to a constantly changing envi-
ronment in the direction of further activities.
The multidimensional digital environment and the diversity of its aspects is mani-
fested in the presence of basic tools necessary for its normal operation, and in infor-
mation and communication technologies and interactive components.
Thus, to achieve the development of stochastic worldview of high school students
through the development of components of probabilistic thinking style in the condi-
tions of digitalization of mathematical education can be achieved through the imple-
mentation of a holistic, comprehensive organization of educational process: intellec-
tual and sensory knowledge of reality and its practical development. A triadic system
of principles based on the ideas of synergy [1, pp. 249-250] was introduced into the
theory and practice of mathematics education by the example of studying the stochas-
tic line using digital technologies. The study used the following triad of principles:
problems - clarity - flexibility and adaptability of organizational structure; saturation
of educational environment - individualization and personalization of educational
routes - intelligent control.
The principle of problem solving is aimed at the development of both intellectual
and motivational spheres of activity, as well as at the formation of thinking abilities,
cognitive needs and high independence of students, carries a pattern that leads to the
comprehension of early experience, to the familiarization with knowledge and meth-
ods of creative activity. In turn, the principle of clarity in learning the elements of
stochastics eliminates ambiguity and impedes the implementation of a linear gap of
semantically related components. The principle of flexibility and adaptability of the
organizational structure is responsible for the implementation of various options for
building an individual educational strategy depending on the personal characteristics
and capabilities of the learner. The principle permeates all aspects of the educational
process: content, forms of organization, methods, technologies and means of learning.
Adaptive learning system is aimed at qualitative changes of individual features and
abilities of students, favors the strengthening of the speed of thought processes, in-
creasing the level of knowledge and skills, work capacity, the level of cognitive and
practical activity in educational activities, etc. The principle of flexibility is designed
to respond quickly to changes in the content of learning, taking into account the needs
and interests of students, constantly changing requirements of the educational para-
digm. The adaptive digital educational process, which includes a system of diagnos-
tics of individual learning styles and strategies, automatically adjusts to the needs of
each individual student, provides an opportunity to create unique educational pro-
grams that adapt and adapt to the psychological and pedagogical features (determin-
ing the order, method and pace of presentation of educational material, the level of
complexity of tasks, identifying the level of knowledge and skills, diagnosis of short-
comings in understanding, pedagogical assistance and advice, etc.). This principle is
inherent in an effective restructuring of the educational structure: multilevel,
multifunctionality, multistage.
The principle of saturation of the educational environment brings redundancy of
resource opportunities when choosing elements of the content of educational material
and the level of its development [5]. Such resource redundancy is created in the uni-
form information educational environment filled with components of the probability
theory and mathematical statistics. The principle of individualization and personaliza-
tion of educational routes allows organizing the educational process in such a way
that it was directed to the formation of creatively active, initiative-organized personal-
ity of a student as a result of the development of probability thinking style, social and
communicative abilities, intellectual abilities. The learning digital environment helps
to implement, build an individual educational route for the development of a student's
personality and adjust it through the use of automated learning, testing, and superviso-
ry systems. The principle of intellectual management characterizes the management
of a complex technological process. This principle is based on the elements of artifi-
cial intelligence, in particular, the active use of modeling or virtual reality models;
planning of trajectories of movement in the information environment; recognition of
images by external information; diagnostics of the system status.
3. Conclusions
Experience in the use of digital technology: interactive models, software, interactive
panel Smart, when studying the elements of stochastics shows that their use is charac-
terized by clarity and interactivity, promotes not only visual perception, but also the
organization of problem-search activities, activates cognitive interest in the subject,
increases the efficiency of learning. Thus, training of mathematics (on an example of
a stochastic line) in the general school, carried out with application of specially se-
lected (developed) means of educational digital technologies, allows to raise level of
formation of stochastic world outlook of high school students by development of
components of probabilistic style of thinking: logic, intuition, creativity, criticality of
thinking.
Digital technologies, on the one hand, increase productivity and efficiency, and on
the other hand, promote the use of unique means of learning and implementation of
individual approach. Their rapid development and improvement is directly related to
constantly updated software, characterized by the construction of complex processes
in three-dimensional space. For example, in many schools, students are able to see
and apply in practice the functionality of 3D printing, individual parts made on this
device, sometimes problematic to get in the traditional production.
Digital technologies arouse interest in their use in learning not by themselves, but
only as a tool for learning the world around them and solving various tasks. It is im-
possible to do without them in the modern reality.
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