Volume 12 - Issue 62
/ February 2023
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http:// www.amazoniainvestiga.info ISSN 2322- 6307
DOI: https://doi.org/10.34069/AI/2023.62.02.35
How to Cite:
Nichyshyna, V., & Voinalovych, N. (2023). Integration of methods and means of distance learning of mathematics during the
process of training future teachers of mathematics. Amazonia Investiga, 12(62), 345-352. https://doi.org/10.34069/AI/2023.62.02.35
Integration of methods and means of distance learning of mathematics
during the process of training future teachers of mathematics
Integración de métodos y medios de aprendizaje a distancia de las matemáticas durante el
proceso de formación de futuros profesores de matemáticas
Received: February 10, 2023 Accepted: March 19, 2023
Written by:
Viktoriia Nichyshyna1
https://orcid.org/0000-0003-3771-1589
Nataliia Voinalovych2
https://orcid.org/0000-0002-0523-7889
Abstract
The article aims to study the peculiarities of
applying different distance education methods
and tools in training future teachers of
mathematics. The task of the article can be
conditionally divided into two stages:
differentiation of means and methods of distance
education in the conditions of higher education
institutions; searching for a model (combination
of social, pedagogical, and other elements) of
forming professional competence through a
combination of distance education tools and
methods. The methodological basis of the study
was scientific and pedagogical methods. The
results of the study highlight the elements of
distance education, capable in their totality to
provide full and high-quality training of future
teachers of mathematics in the digital
environment of universities.
Keywords: modern education, mathematics
education, distance learning tools, digital
didactics, vocational training.
Introduction
The relevance of the study is due to the need to
solve problems of improving the quality of
distance learning in mathematics in the
preparation of future teachers of mathematical
disciplines, which is caused by the need to
organize the work of students in the course. In
1
Ph.D.in Pedagogical Sciences, Associate Professor of the Department of Mathematics and its Teaching Methods Faculty of
Mathematics, Natural Sciences and Technologies, Central Ukrainian State University named after Volodymyr Vinnichenko, Ukraine.
2
Ph.D.in Pedagogical Sciences, Associate Professor of the Department of Mathematics and its Teaching Methods Faculty of
Mathematics, Natural Sciences and Technologies, Central Ukrainian State University named after Volodymyr Vinnichenko, Ukraine.
this regard, the improvement of distance learning
is possible through the introduction of new tools
that can provide solutions to the problems of
improving the academic performance of
students. Distance learning based on Internet
technologies is considered a progressive form of
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professional education, aimed at the personal
requirements of students and their qualifications,
and also allows you to constantly increase the
professional level, taking into account personal
qualities. In the process of studying mathematical
and pedagogical disciplines, the student of
pedagogical HEIs in the online mode without any
assistance is mastering learning materials, being
tested (Catalano, Torff & Anderson, 2021). One
of the directions of the informatization process of
modern society is the informatization of the
training process of future specialists in the
educational sphere. This process consists in the
research and provision of the educational sphere
with the methodology, practice of development
and optimal use of innovative technologies
focused on the implementation of psychological
and pedagogical goals of professional training of
future teachers of mathematics. Among the
innovative technologies, based on which the new
learning environment should be created in HEIs,
there are e-learning technologies, the use of
which is able to make the learning process
available at any time and in any place, to
encourage students to self-education throughout
life, while learning will become more attractive,
democratic, comfortable. The use of modern
technologies in the educational process of future
teachers of mathematics promotes the quality of
their professional training and competitiveness in
the labor market (Karjanto, 2021). Distance
learning technologies not only facilitate access to
information and open up opportunities for the
variability of learning activities, its
individualization, and differentiation, but also
allow the organizing interaction of subjects of
learning at a new level, building an educational
system in which students will be active and equal
participants of educational activities. Distance
learning technologies, based on the use of
information and communication technologies,
confidently enter the practice of many
educational institutions of different forms and
levels. Since one of its main features is
independence from geographical location, from
the distance between the teacher and students, it
is called distance learning, that is learning at a
distance (Chen, Liu & Tretheway, 2022). The
purpose of the article is to update the methods
and means of distance educational technologies
in the process of forming the professional
competence of future teachers of mathematical
disciplines Based on the purpose of the study, the
following problems have been identified:
1) Determination of means of distance education
in the conditions of higher education institutions.
2) Search for the optimal model of coexistence of
innovative and traditional educational
technologies in the conditions of distance
education.
Literature review
The question of the effectiveness of distance
education arises against the background of socio-
political shifts that have recently engulfed the
whole world. The question arises of ensuring the
effective training of future specialists in the
pedagogical sphere, despite the challenges of an
uncertain environment. It is with this duty that
distance education facilities are increasingly
being introduced to provide unimpeded access to
educational services despite the dispersal of
students from the educational institution.
Tsekhmister (2021) examines the
implementation of pedagogical innovation in the
educational process. This is necessary to match
the education system to the modern challenges of
society associated with the development of
technology, the emergence of new socio-
economic relations. The introduction of
pedagogical innovations, according to the author,
brings with it the need to revise the existing
traditional paradigms of the educational process
organization. The new paradigm must take into
account the need for asynchronous organization
of the educational process by means of
computerization and digitalization. Melnychuk
(2022) discusses the methodological foundations
for organizing teacher training in the conditions
of distance education. The author notes the need
to introduce innovative technologies as a tool to
ensure quality teacher education. Also, the work
of Korostiianets (2022) should be mentioned.
The author considers the effectiveness of the use
of modern didactic tools in the process of
formation of professional competence of future
teachers of mathematics in the conditions of
higher education institutions.
In the process of preparing a future teacher of
mathematics by means of distance education,
special attention should be paid to specialized
software for simulation and visualization of
phenomena and processes. To this end, special
attention needs the work of Karjanto & Husain
(2021). The authors considered the peculiarities
of using the wxMaxima software package in the
process of training future teachers of
mathematics. Together with researchers
Velychko Stopkin & Fedorenko (2019), the
authors of the article try to analyze the
importance of computer algebra packages in the
process of organizing the training of modern
teachers of mathematics in distance education.
Nichyshyna and Voinalovich (2022) were
interested in the issue of the integrity of the
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formation of mathematical knowledge. The
authors substantiate the practicality of the
application of opposition in the process of the
formation of integrated systems of mathematical
knowledge. Also, the work of Botuzova,
Nichyshina and Rizhnyak (2022) is interesting
for this study. The authors devoted their work to
studying a complex integrative approach to the
study of problem-solving methods by students of
higher education institutions. Thus, despite the
existence of a large number of studies, there are
still a low number of unresolved issues. Firstly,
the problem of organizing distance learning for
future mathematics teachers by combining
several methods and tools is still insufficiently
covered. Secondly, the data from existing studies
are still insufficient to draw conclusions about
the optimal mechanisms and methods of distance
learning for future mathematics teachers.
Materials and methods
The analysis of the integration of methods and
means of distance learning in mathematics in the
conditions of pedagogical HEIs has historical,
didactic, and psychological peculiarities.
Therefore, there is a need for a thorough analysis
of the existing systems of distance learning
organization in pedagogical HEIs taking into
account the features of harmonization of the
distance education system of training future
teachers of mathematics. The methodological
means that can provide analysis of the
peculiarities of methods and means of teaching
mathematics in the Ukrainian educational
environment are general scientific methods
(analysis, systematization, prediction,
comparison) and scientific and pedagogical
special methods (pedagogical observation,
educational experiment). The didactic practice of
introducing distance learning methods of
mathematical disciplines in the pedagogical HEIs
testifies to the high effectiveness of such a
solution. However, there is still a certain lack of
data for a full and comprehensive analysis of the
effectiveness of popular methods of organizing
distance learning of mathematical disciplines in
the conditions of pedagogical HEIs. The study
uses the methodological principle of systems
theory to analyze the diversity of existing
distance learning tools for mathematics. These
difficulties are associated with the peculiarities
of the transfer of theoretical knowledge in the use
of computer tools in the educational process in
the practice of teaching future teachers of
mathematics and are due to the following factors:
• insufficient number of special studies in the
training of future teachers of mathematics in
the modern paradigm by means of distance
education;
• orientation of digital educational resources
not on the specific requirements for the
future specialist, but on the implemented
private author's concepts and the lack of
taking into account their variability in
accordance with the curricula of various
pedagogical HEIs;
• psychological difficulties faced by future
teachers of mathematics in the practice of
using new computer tools in the study of
mathematics.
The organization of the study was carried out in
several stages. At the first stage the analysis of
philosophical, psychological and pedagogical,
scientific, and methodological literature on the
topic of research, the study of the experience of
HEIs, the identification of conditions for the
formation of future teachers of mathematics
readiness for professional activity, the definition
of directions, methods of research. At the second
stage, the existing models of distance learning for
future teachers of mathematics were studied. The
organizational and pedagogical conditions for the
formation of professional competencies were
determined, the criteria and indicators of the
effectiveness of the formation of readiness for
professional activities of future teachers of
mathematics were determined. At the third stage,
the processing and analysis of the results of the
study were carried out. Conclusions on the
results of the study are made.
Results
Future teachers of mathematics, starting to carry
out professional activities, must be prepared to
use the entire arsenal of teaching tools that
modern didactics possesses. Of course, it is
impossible to imagine modern education without
innovative educational tools. To understand how
important it is to pay attention to the use of a
variety of distance learning tools in the
professional training of future teachers of
mathematics, it is necessary to find out what
place of computer tools in the modern
educational process. This study should consider
their features and advantages over other means of
education. By teaching aids (didactic means) we
mean teaching and visual aids, demonstration
devices, tools, etc. Didactic means are objects
that provide students with sensorimotor stimuli
that can affect their senses, facilitate their direct
and indirect knowledge of reality.
The means of learning include: used in the
process of training equipment, machinery, tools
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and devices, rooms for classes (classrooms,
laboratories), means of communication, means of
obtaining and storing information. Modern
didactics defines learning tools as instruments of
activity of a teacher and students (as material and
ideal objects), which are involved in the
educational process as carriers of information
and activity tools.
Material means of learning - teaching and visual
aids (textbooks, didactic material, test material),
didactic equipment, educational equipment,
technical means of learning. Ideal learning tools
- language (oral language), writing (written
language), diagrams, drawings, works of art,
opinion, training computer programs, etc. Of all
the means of learning that have found use in
distance education can include the following:
• audiovisual (educational videos, slides,
educational films);
• electronic educational resources
(multimedia textbooks, educational films on
digital media, software for subjects often
referred to as educational multimedia,
educational and methodological programs);
• online educational resources, interactive
whiteboards, etc.
The technical means of education (TTE), which
are used in the organization of distance learning
of future teachers of mathematics, can include
the achievements of new information technology
- computers and computer networks, media
education, training equipment based on
electronic equipment, and specialized software.
Modern technical means that provide distance
learning, called the means of new information
technology. This notion should be understood as
software, hardware, and software and technical
means and devices that are based on
microprocessor technology, modern systems,
and means of information transfer, information
exchange, providing access to information
resources of computer networks (including
global). This makes it possible to collect,
accumulate, process, store, produce, transmit,
use information (Martin, Harbour & Polly,
2022).
Computers as a medium of instruction have many
characteristics of traditional teaching tools, but
what makes them different is that they allow for
a kind of student-computer dialogue, which is an
undeniable advantage of this educational tool in
terms of organizing and perceiving teaching
material and controlling and assessing
knowledge.
To achieve the goals of training future teachers
of mathematics in a distance learning
environment is possible to use such types of
computer tools:
• general-purpose service software tools;
• software tools for mathematical and
simulation modeling;
• software to control and measure the
academic performance of future teachers of
mathematics;
• electronic simulators;
• information retrieval and reference systems;
• software for remote access laboratories and
virtual laboratories;
• expert learning systems (ELS);
• automated Learning Systems (ALS);
• electronic textbooks (ET);
• means of professional activity automation;
• intellectual learning systems (ILC);
• specialized training web-portals;
• training applications;
• learning forums and chatbots in social
networks and messengers (Cano &
Lomibao, 2022).
It is impossible to overestimate the benefits of the
limitless possibilities of modern multimedia
technology. Using computer tools in distance
learning, it is possible to change the way visual
and audio information is formed. Specificity is
important when choosing an object of study to
demonstrate with the help of traditional
visualization, while the use of distance means
provides the possibility of dynamic interpretation
of both real objects and theories, scientific
regularities, concepts (Sapiński & Ciupka, 2021).
All of the above has allowed us to identify the
essence of distance learning in the informational
and productive approaches. The informational
approach of distance education of future teachers
of mathematics should be formed based on
informational postulates, the method of
informational modeling of the essence. The
purpose of training is to form an information
model of the student's brain with a given volume
and quality of the thesaurus, the development of
its knowledge as a mechanism for perception and
extraction of information from natural and
artificial sources. Productive learning is
connected with the concept of socially significant
result of student's activity. This result can be both
internal, manifested in qualitative changes in the
nature of the mental activity, and external,
expressed in the creation of a product - a material
or informational result of human activity. The
peculiarities of the process of productive activity
and its products can be used in diagnosing the
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development of skills, student skills,
development of cognitive processes, formation
of the ability to plan their activities (Martin,
Harbour & Polly, 2021).
For further consideration of the problem of
providing distance education for future teachers
of mathematics, it is necessary to define the
structure of the concept of professional
competence in order to make an idea of the ways
of its formation on this basis. Based on the
research on the named problem, we can say that
competence as a professional quality is defined
by the presence of three groups of attributes:
technical competencies, subject, and
methodological competencies (Table 1).
Table 1.
The structure of the professional competence of the future teacher of mathematics in distance education
Components
Competence of a mathematics teacher
Technical
Subject
Methodological
Logistical and
organizational
components
Providing appropriate
technology. Providing
access to high-speed
Internet
Providing e-learning
tools
Ability to create work
programs, lesson plans,
educational-methodical
complexes
Theoretical component
Awareness of the
capabilities of modern
digital learning and
communication tools
Possessing the subject
at a high level
Awareness of
methodological
principles of teaching
in the full-time,
distance, and mixed
forms of education.
Awareness of the basic
sanitary-hygienic and
informational safety
requirements for the
organization of the
educational process
Practical component
Know how to use
digital technology and
create, edit, and share
learning materials
remotely.
Using digital
materials in their work
Mastery of
methodological
fundamentals of
creating and using
electronic educational
resources
Personality component
Awareness of the
capabilities of
technology and
computer-based
learning tools; keep up
to date with new tools
and opportunities
Prospects for the use
of distance methods in
work
Participation in
webinars, online
courses, electronic
conferences for the
purpose of methodical
qualification
improvement
Source: Authors’ development.
Technical competencies are a prerequisite for
working in a remote format, which is the ability
to use digital educational technology and
techniques, IT-communications to mediate and
fully implement the educational process. Subject
competencies - the foundation of the professional
skill of the teacher, his duty to know well the
subject, the field of science in which it belongs,
the application of this knowledge to solve
professional and other problems. Methodological
competencies - mastery of the basics of
educational theory and methodology, the ability
to “adjust” the methodological system of
teaching to work in a remote format in
compliance with appropriate pedagogical
principles (Higgins, Huscroft-D'Angelo &
Crawford, 2019).
Each of the attributes is defined by a number of
descriptors categorized into four groups:
logistical and instructional organization,
theoretical component, practical component, and
personal qualities of the teacher. Let us illustrate
the structure of competence of a future teacher of
mathematics during distance learning on the
example of the subject area “Mathematics”. The
peculiarities of this field of knowledge are that
the use of distance technologies until recently
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were limited by technical conditions. The
situation has changed with the replenishment of
the arsenal of digital devices. Logistical support
for the learning process should include the
necessary technical means and a point of access
to high-speed Internet. Technical means should
include office computer equipment with installed
standard software and video communication
means; software packages for mathematical
calculations (Excel, Statistica, etc.); graphic
tablet (for handwriting input of mathematical
information, formulas, drawings). The basis of
subject support are the elements of the electronic
educational-methodical complex: electronic
textbook, work (possibly interactive) workbooks
for practical work, electronic lecture notes,
visualization tools of educational material
(presentations, tables), control tools (tests, cards,
individual assignments), etc.).
The creation of a set of teaching and learning
materials should be distributed among the
teachers of the discipline for sufficient time and
constantly maintained. The organizational
component of methodological competencies is
also formed: course work programs, syllabi, and
class schedules are created. These documents, as
a rule, are placed in the electronic information
and educational environment of the university. It
is also important to decide on ways to
communicate with students and administration:
social networks, messengers, digital platforms,
etc. The teacher needs to be able to inform
students quickly and massively about upcoming
events, and students need to be able to provide
feedback (Martin, Polly & Ritzhaupt, 2020).
Discussion
Analysis of the works on the topic of research
showed that the authors pay much attention to the
issues of the distance learning organization,
tools, and platforms for distance learning
organization, problems of forming mathematical
concepts with the support of electronic learning
tools, and implementation of visual support of
the educational process in mathematics,
problems of assessing knowledge in
mathematics. in distance learning format
(Sherman, Puhovskiy, Kambalova & Kdyrova,
2022). In general, based on the analysis of the
results of research literature, personal teaching
experience, and accepted practice it is possible to
highlight the following tools, especially popular
in the organization of distance learning (Fig. 1):
Fig. 1. Keyways to support distance learning for future mathematics teachers
Source: Authors’ development.
The remote format of the educational process
imposes an obligation on teachers to have a high
degree of digital competence. Computer literacy
ensures the use of innovative digital technologies
and the latest didactic tools in the work. In
addition, a high level of digital competence of
both students and teachers can ensure a high level
of communication during distance learning.
Mastering digital technologies makes it possible
to use a wide range of software aimed at
organizing the distance learning process. This is
especially true for the study of mathematics.
(Higgins, Huscroft-D'Angelo & Crawford,
2019).
Means of organizing the educational process
Means of teaching individual mathematical disciplines
Means of controlling academic performance
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Today, specialized software for performing
special mathematical calculations is gaining
popularity. This software is called mathematical
processors and is aimed at using both numerical
and symbolic calculations. At the same time,
such software requires users to have not only
special mathematical knowledge, but also to have
technical means of sufficient power. Until
recently, this problem prevented the use of some
special mathematical software in the educational
process. It is known that the technical equipment
of higher education institutions does not always
meet the requirements of modern software,
especially the one that requires large RAM
resources, a modern powerful video card, a
processor of the latest generations, etc. The
solution to this problem came naturally. With the
advent of cloud computing, the entire computing
process, which has been performed on hardware,
has now been moved to a cloud server. Thus, a
significant technical resource has been saved.
Large companies such as Google or Microsoft
provide their own cloud computing capacities for
educational purposes to universities absolutely
free of charge. Thus, the problem of outdated
equipment becomes irrelevant (Martin, Polly &
Ritzhaupt, 2020).
But since the comfortable use of an online board
determines the availability of a touchscreen, and
in other cases, its use is less convenient, some
additional features have to be sought. In the
context of this study, Boiaryshcheva, Herych,
Pohoriliak, Syniavska & Tehza (2022) are
interesting. Researchers remain committed to
traditional methods of education and see the only
possibility of using distance learning
technologies and methods in combination with
face-to-face learning. Hodges, Lockee, Moore,
Trust & Bond (2020) cite data fully confirming
the full ability of distance education methods in
the formation of professional competencies of
future educational specialists.
Conclusions
Analyzed the experience of using distance means
of organizing professional training of future
teachers of mathematics, investigating the
coverage of this topic in the scientific literature,
the following conclusions are made. Distance
form of education is a response to the challenges
of the modern world, its task is to ensure
continuous and quality education. In pedagogical
practice, there are a large number of methods and
means of organizing the educational process
through the introduction of distance technology.
As evidenced by the results of the study, the
optimal result is achieved by a complex
combination of several methods and means. The
effectiveness of the distance form of education is
determined by the level of formation of
professional competence, which is reflected in
the indicators of academic success of future
teachers of mathematics. We can conclude that
the use of distance form of education is a global
trend and at this stage of pedagogical science
development, we need to look for ways to
improve its effectiveness.
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