=Paper=
{{Paper
|id=Vol-2879/paper17
|storemode=property
|title=The support of the process of training pre-service mathematics teachers by means of cloud services
|pdfUrl=https://ceur-ws.org/Vol-2879/paper17.pdf
|volume=Vol-2879
|authors=Vladyslav Ye. Velychko,Elena H. Fedorenko,Nataliia V. Kaidan,Vladimir N. Soloviev,Olga V. Bondarenko
}}
==The support of the process of training pre-service mathematics teachers by means of cloud services==
https://ceur-ws.org/Vol-2879/paper17.pdf
The support of the process of training pre-service
mathematics teachers by means of cloud services
Vladyslav Ye. Velychko1 , Elena H. Fedorenko1 , Nataliia V. Kaidan1 ,
Vladimir N. Soloviev2 and Olga V. Bondarenko2
1
Donbas State Pedagogical University, 19 Heneral Batiuk Str., Sloviansk, 64122, Ukraine
2
Kryvyi Rih State Pedagogical University, 54 Gagarin Ave., Kryvyi Rih, 50086, Ukraine
Abstract
The training of pre-service mathematics teachers is a complex process due to the specifics of the field.
Informatization of education affects all the areas, and pre-service mathematics teachers can not be
left out. The article is devoted to the problem of supporting the process of professional training of
pre-service mathematics teachers by means of cloud services. Examples of the use of cloud technologies
are given. The analysis of a survey of pre-service mathematics teachers on the use of information and
communication technologies in the training process is done.
Keywords
training of pre-service teachers, cloud services, mathematics teachers, training system
1. Introduction
During the constraints caused by the COVID-19 pandemic, education was forced to switch
to e-learning as a matter of urgency [1, 2, 3, 4, 5]. The transition revealed problems not only
in the material part of the organization of education (lack of access to digital technologies
for a significant number of both students and teachers) in the lack of electronic educational
resources needed for educational activities. There were problems with the appropriate training
of pre-service teachers. It cannot be said that this issue has not been raised by the educational
community and government agencies, however, the results indicate a formality in resolving
these issues.
2. Statement of the problem in general
News reports, social networks, reports at webinars of teachers and educators speak not only
about the possibility of achieving the goal of learning through e-learning. It also speaks to
Cloud Technologies in Education 2020, December 18, 2020, Kryvyi Rih, Ukraine
" vladislav.velichko@gmail.com (V. Ye. Velychko); fedorenko.elena1209@gmail.com (E. H. Fedorenko);
kaydannv@gmail.com (N. V. Kaidan); vnsoloviev2016@gmail.com (V. N. Soloviev); bondarenko.olga@kdpu.edu.ua
(O. V. Bondarenko)
0000-0001-9752-0907 (V. Ye. Velychko); 0000-0002-1897-874X (E. H. Fedorenko); 0000-0002-4184-8230
(N. V. Kaidan); 0000-0002-4945-202X (V. N. Soloviev); 0000-0003-2356-2674 (O. V. Bondarenko)
© 2020 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
318
the problems that arise. These questions concern each of the subjects of educational activity:
students, teachers, parents and the administration of educational institutions.
Let’s consider what problems teachers have when moving to the online space. Going online
and transferring even one course taught in a higher education institution or a general secondary
education institution is a huge long-term work of a whole team of professionals. The examples
are Cousera or Prometheus resource courses. All videos are recorded by professional cameramen
in the studios, with a professional overlay voice of the lecturer of the presentation on the video,
with a very careful and competent distribution of information over time. The course consists
of 20-30 minute informative videos, for which tests, a large amount of materials for self-study,
tasks such as peer to peer review and so on are prepared.
In order to implement such functionality, it is not enough for a teacher to have information
and communication technologies, to have the necessary material base for shooting, editing
videos, informational material, etc. Such work takes much more time than preparing for lectures
or conducting a lesson and creating presentations for them. The results of mastering the material
from most subjects, disciplines or courses cannot be assessed by passing tests, there is a need
to check written works, listen to auditions and so on. It significantly increases the amount
of mechanical work that is added to the responsibilities of a teacher or lecturer. For clarity
purposes, you can, for example, open 20 e-mails, download 20 completed works and save them
in the appropriate folder. We see that even such primitive mechanical operations are very time
consuming.
In addition, there is a big psychological problem if during online classes students are a passive
cluster that is not even displayed on the screen. Not every teacher is able to tell 40 minutes on
the black screen without any impact on the audience, even if from time to time there are single
answers in the form of voice messages. It is also important to hold the attention of the audience
during the lesson.
Another unresolved issue is the results of scientific and methodological work. It is required
by the job responsibilities of educators. In the situation of excessive creation of electronic
educational resources it is extremely difficult to get good results. It is also important that
e-learning resources have no less functional teaching compared to planned, verified, proven
full-time learning.
Researches and statistics from mass open online courses have found that distance learning
is effective for 20-25% of students. This is the number of them who successfully complete the
distance course compared to the number of registered ones. There is another side – the specifics
of the selection of material for distance learning, which is determined by the professional
competence of the content curator. The search for educational material, its systematization,
processing in accordance with the level, goals and content of training forces to process a huge
amount of existing digital content.
Students are no less stressed. There are several problems in this category of participants in
the educational process:
• the construction of the procedure for evaluating the completed tasks, especially those of
a final nature, is not clear;
• learning at home relaxes rather than mobilizes and motivates learning activities, and
leaves visual control on the part of the teacher;
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• lack of own room for working remotely (presence of parents, younger or older siblings)
and therefore, the simplest solution that students come to is not to participate in online
classes;
• cases of lack of access to Internet resources due to lack of devices and lack of communica-
tion channels.
General secondary and higher education institutions make great efforts to organize learning
with the help of distance platforms. Seminars, webinars, trainings on forms, methods and means
of distance learning for teachers are held in an accelerated manner. Teachers communicate
with their students by any possible means, from e-mails, instant messaging, available distance
learning platforms to telephone communication. It should be noted that due to the different
activity of participants in the educational process there is a big discrepancy in the results. Thus,
it is extremely interesting for us to explore the issues of professional training of pre-service
teachers of mathematics for educational activities in the distance form of organization of the
educational process.
3. Review of the current state of the problem
The issue of application of information and communication technologies (ICT), and cloud
technologies in particular, in the process of professional training of pre-service mathematics
teachers is the subject of active research by Bobyliev and Vihrova [6], Clark-Wilson et al. [7],
Drijvers [8], Kiv et al. [9, 10], Kramarenko et al. [11, 12], Kumar and Bhardwaj [13], Lovianova
et al. [14], Merzlykin et al. [15], Mulenga and Marbán [16], Ndlovu et al. [17], Papadakis [18],
Perienen [19], Ponomareva [20], Popel [21], Purnomo and Jailani [22], Pyper [23], Semenikhina
et al. [24], Vlasenko et al. [25, 26, 27, 28, 29, 30, 31, 32, 33], Yang [34]. We will consider in more
detail some of them related to our study.
Professional training for the widespread use of ICT in the educational activities of pre-
service mathematics teachers begins long before entering higher education. During their
studies in a general secondary education institution, pre-service mathematics teachers can
already clearly observe the forms and methods of application of ICT. The study of the results
of the use of ICT during training in general secondary education was presented in a study by
Vakaliuk et al. [35]. Useful for our study is the answer to question #13 of their study: “Did any
information and communication technology tools (curricula, multimedia, simulators, games,
virtual laboratories, etc.) be used in the school / college by non-CS teachers?”. Unfortunately,
only 48.5% of respondents answered this question positively. The result suggests that every
second pre-service teacher while studying in a general secondary education institution has not
received the necessary experience of using ICT in educational activities. However, the variety
in answering question #14: ”If the answer to the previous question is ”Yes”, in what lessons
did the teachers use such tools?” (see figure 14, [35]) indicates that some subject teachers,
including teachers of language and literature, mathematics, physics, history, chemistry, biology
and geography have found not only the possibility of using ICT in learning activities, and this
application was successful, otherwise it would not be remembered by students. Thus, due to
the introduction of ICT in the secondary school education system, pre-service mathematics
teachers are occasionally familiar with the use of ICT in educational activities.
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Let’s consider the approaches used in e-learning based on the results of the study of Proskura
and Lytvynova [36] for bachelors of computer science. The conducted semantic analysis of
scientific achievements of colleagues and based on their own experience allowed the authors to
develop the model of Web-based learning of Computer Science Bachelors (see figure 1 in [36]).
Considering such structural components as learning environment, web-oriented environment,
control and evaluation unit, levels of student’s educational achievements, the authors determine
the content component of e-learning. Among the components of e-learning there are such as
cloud computing, working together classroom, web-automated knowledge validation systems
and others. These components are implemented through network technologies as means of
data transportation. Their appearance is caused by the availability of network technologies and
they belong to cloud services. Thus, the need to use cloud services to support the training of
pre-service mathematics teachers is one of the current educational trends.
A logical continuation of our study is to identify specific cloud tools to support the training
of pre-service mathematics teachers. The specifics of professional training is determined by
the specifics of the field of science. The specificity of mathematics lies in its abstractness. The
study by Vlasenko et al. [37] examines the requirements for modern web-based online training
courses for pre-service mathematics teachers. Researchers have analyzed the ways of presenting
mathematical text through to the specifics of its formation, and the creation of mathematical
content with a focus on network use.
Shyshkina and Marienko [38] determined the content of necessary general skills and specific
skills needed for pre-service mathematics teachers (see table 2 in [38]) based on professional
functions, typical tasks of mathematics teachers (see table 1 in [38]). Using the example of
Web-SCM CoCalc (formerly called SageMathCloud), the authors conducted an experimental
study that revealed the benefits of using the CoCalc cloud service in the training of pre-service
mathematics teachers.
Fedorenko et al. [39] studied the problem of studying free software using cloud services. The
results of this study had a positive result, for the training of pre-service mathematics teachers
in particular. Researchers have discovered the didactic capabilities of cloud services that allow
you to run a free mathematical software.
4. Research results
According to the Law of Ukraine “On Higher Education”, the educational process at the university
is carried out in the following forms: classes; individual work; practical training; control
measures [40]. The most common types of training are lectures. A lecture is a clear, systematic
presentation of a particular scientific problem or topic. Its additional purpose is to help students
with mastering the methods of independent work with textbooks, manuals, primary sources.
This is one of the most important factors in the organization of educational activities of students
and occupies a significant place in the training of pre-service professionals receiving higher
education.
The normative-directive documents, which determine the content and organization of the edu-
cational process in higher education institutions of Ukraine, substantiate the main requirements
for this type of classes. Their implementation allows to fully use the significant educational and
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upbringing opportunities of this form of education, to increase the impact of each lecture on the
consciousness and feelings of students [41]. However, the lecture to some extent accustoms the
student to the passive appropriation of other people’s thoughts, does not stimulate the desire
for independent learning, does not provide an individual, differentiated approach to learning.
The leading role of the lecture in the teaching of academic disciplines is related to their
content aspect, organizational principles and methodological features. The main content is
the central methodological, theoretical and practical problems. Not all issues of the topic are
revealed, but the most important, most significant ones that require scientific substantiation.
The pace of development of modern technologies has a significant impact on teaching
methods and learning models in general [42]. This allows to expand the ways of implementing
the paradigm of competence in order to improve the quality of education. The model of
blended learning has the greatest potential for optimizing the learning process [43]. This model
allows you to implement new technologies without abandoning conventional teaching methods.
Blended learning is a model of organization of the educational process, as “it allows to increase
the motivation of future teachers to learn, makes it transparent, interactive and manageable,
provides constant involvement of students in the educational process” [44].
A blended form of learning is the individualization of learning, the creation of a favorable
psychological climate, continuous training. The purpose of this form of learning is to combine
the benefits of face-to-face learning and electronic educational resources through a combination
of distance and traditional communication in integrated learning activities. The integration of
traditional and computer-based learning in the educational environment will lead to a purposeful
process of acquiring knowledge, skills and abilities in the classroom and extracurricular learning
activities of the subjects of the educational process through the use of ICT. The existence of this
form of learning is possible due to the effective combination of different ways of presenting
educational content, teaching models and styles. It is based on the interaction between all
participants of the educational process.
One of the forms of blended learning is realized through flipped learning (flipped classroom)
[45, 46]. There are different ways to implement the model of flipped learning and they are
all based on one basic principle: traditional learning is carried out outside the classroom, and
practical work and application of knowledge is classroom. In general, the essence of flipped
learning is to regroup the key components of the learning process. With the help of this model
of learning “the content of new educational material is independently mastered in the electronic
environment, and then the acquired knowledge is applied in practical classes or discussions”
[47].
Reduction of classroom hours (lectures, practices, seminars, laboratory classes) leads to a
violation of the traditional logic of the educational process. This fact leads to a loss of quality of
education. One of the ways to “restore the balance of the learning process is to use a mixed
learning model with Flipped Classroom technology” [48]. At the same time, the key components
of the learning process change places: the basic components of the new material are studied
independently at home, and in the classroom the studied material is consolidated and together
with the mentor more complex issues and practical application of the mastered information
are considered. Flipped classroom technology is characterized by the fact that the necessary
“theoretical knowledge is obtained outside the classroom, and in the classroom individual tasks
are performed or a group project is developed” [49].
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Flipped classroom technology was used by us in the study of mathematical disciplines
“Mathematical Logic and Theory of Algorithms” and “Elementary Mathematics” in the 3rd year
of the Faculty of Physics and Mathematics of Donbas State Pedagogical University. Taking into
account the fact that students majoring in “Secondary Education (Mathematics)” specializing
in “Computer Science” in the 3rd year have significant learning experience, and the level of
self-awareness is sufficient to use elements of Flipped classroom technology in not only logical
but also appropriate way. In addition, this model of study does not contradict the work program,
in which the main number of hours is set aside for independent work of students.
Based on the practical experience of use, the following structure of the approach to each
topic was formed:
1. Formulation of the theme and purpose.
2. Determining the place of this topic in the work program of the discipline.
3. Offering sources of information.
4. Definition of types and content of control.
5. Monitoring and evaluation.
While introducing the flipped classroom technology during teaching the course of “Mathe-
matical Logic and Theory of Algorithms” it is advisable to consider the following topics:
1. Boolean n-ary functions;
2. Zhegalkin polynom;
3. Complete systems of Boolean functions;
4. Mathematical theories of the first order.
For each of the proposed topics, the place in the work program and sources of information
are determined, the content of tasks for control and its types are selected.
For example, to study the topic “Complete systems of Boolean functions” students receive
the following information in table 1.
The main reasons for the introduction of a blended learning model with flipped classroom
technology in the educational process of the university are active cooperation between students
and teachers and, as a consequence, increasing students’ success and motivation. A feature of
this model is the possibility of using group classes where students can discuss key aspects of
lecture materials, test their knowledge and interact with each other. The task of the teacher is
to explain the problematic issues, to comment on the work of students.
Another example of supporting the training of pre-service math teachers is the use of computer
math systems in the form of cloud services. One such free service is the Math Partner computer
math system, which is available at http://mathpar.com. This service allows you to create your
own cloud mathematical “Notebook”, in which the user performs the necessary mathematical
calculations. To ensure quality and comfortable work, this service provides access to a large
amount of reference material with examples. The language of this service is the Mathpar
language, which is based on the widely used language of mathematicians and physicists TEX,
which is usually used for typing mathematical texts. It is possible to save both the problem
statement and its solution. You can save both text and images.
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Table 1
Tasks for studying the topic ”Complete systems of Boolean functions”
Theme Complete systems of Boolean functions
Meta Learn the concepts of classes of functions that store zero, store unity, self-dual
functions, monotonic and linear. Master the criterion of completeness.
Sources of
information • Bondarenko M.F., Belous N.V., Rutkas A.G. Computer discrete mathe-
(independent matics: textbook. – Kharkiv: SMITH Company, 2004. – 480 p.
selection of
• Khromoi J.V. Mathematical logic. – Kyiv: Higher School, 1983. – 208 p.
sources of
• Kaidan N.V., Pashchenko Z.D. Methodical instructions for practical
information is
classes of the course ”Mathematical logic and theory of algorithms.
encouraged)
Section ”Mathematical Logic” for the specialty 014 Secondary Educa-
tion (Mathematics). – Slovyansk: B.I. Motorin Publishing, 2019. – 92 p.
• Rosen K. H. Handbook of Discrete and Combinatorial Mathematics,
2000. – 1183 p.
• Discrete Math. Lecture: Criterion of completeness of the system of
Boolean functions (https://www.youtube.com/watch?v=CYL7o4Ru35c)
• Game simulator “Collect crystals” (http://www.ggpk.by/virt_cab/102/
Files/logic.zip)
• Exercise machine “Logical elements” (http://www.ggpk.by/virt_cab/
102/Files/log.rar)
• Quine – McClassky logic function minimization simulator (http://www.
ggpk.by/virt_cab/102/Files/KMK.rar)
• Construction of the truth table. SDNF. SCNF. Zhe-
galkin polynomial (https://programforyou.ru/calculators/
postroenie-tablitci-istinnosti-sknf-sdnf)
• Truth table (https://allcalc.ru/node/745)
Types of con- test for mastering the material (conducted remotely outside the classroom),
trol an individual task to determine the completeness of the system
Date of con- conducting a test for self-study of the material
trol
In particular, Math Partner allows you to effectively solve such common problems as finding
the smallest distances between all vertices of the graph and finding the shortest path between
the vertices. For the first task the command ∖𝑠𝑒𝑎𝑟𝑐ℎ𝐿𝑒𝑎𝑠𝑡𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑠(𝐴) is used, and as a
result the matrix of the shortest distances between vertices will be received. For the second task,
use the ∖𝑓 𝑖𝑛𝑑𝑇 ℎ𝑒𝑆ℎ𝑜𝑟𝑡𝑒𝑠𝑡𝑃 𝑎𝑡ℎ(𝐴, 𝑖, 𝑗) command, resulting in the shortest path between
the vertices 𝑖 and 𝑗. It should be noted that this service is convenient to use to check your
own solutions, because it provides the answer itself, without access to intermediate results of
calculations.
Another relatively new service is Graph Online, which is available at http://graphonline.ru.
This is a free cloud service designed to visualize the graph and find the shortest path on the
graph, finding the Euler cycle. Creating a graph is performed on the adjacency matrix or
incidence matrix. In addition to finding the shortest path, you can search for connectivity
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components. The service supports work with oriented (digraphs) and non-oriented graphs. The
result of the work, the constructed graph can be saved thus you can continue working with it
later.
In addition, the cloud service Graph Online provides the user with many auxiliary functions
to facilitate work. Available to save and load a graph with support for saving the visual
representation, fast conversion between all supported types, determining the appearance of
vertices, arcs, background, constructor mode, etc.
Let’s consider the example of the use of the presented services in solving the problem of
finding the shortest distances between the vertices of the graph, which are often found in
practice. It is clear that in order to be able to find the shortest distances, there must be at least
one path from vertex 0 to every other vertex, i.e. the graph must be connected. For this problem,
the most well-known solution algorithm is the Dijkstra algorithm. The idea of this algorithm is
that first for each vertex other than vertex 0, we set the distance equal to +∞, and then step by
step we reduce these distances until we find the minimum distance 𝑑(𝑣) and the shortest path
𝑝(𝑣) for each vertex 𝑣.
Condition: Suppose that in a weighted graph 𝐺 = (𝑉, 𝐸), the set of vertices 𝑉 = {0, 1, 2, 3, 4, 5},
and the set of edges 𝐸 is given by a matrix of weights:
− 8 7 − 10 12
⎛ ⎞
⎜ 8 − 5 1 4 − ⎟
⎜ ⎟
⎜ 7 5 − 3 − 4 ⎟
𝐸=⎜ ⎜ ⎟
⎜ − 1 3 − 2 1 ⎟
⎟
⎝ 10 4 − 2 − 3 ⎠
12 − 4 1 3 −
Using the Dijkstra algorithm, construct a skeleton tree of the shortest paths from vertex 0 to
all other vertices of the graph G and find the shortest distances.
Solution: The progress of the Dijkstra algorithm is shown in the table 2.
Table 2
The progress of the Dijkstra algorithm
1 2 3 4 5
8 7 10 10 12
9 11
10
0; 1 0; 2 0; 2; 3 0; 4 0; 5
0; 1; 3 0; 2; 5
0; 1; 3; 5
When performing the Dijkstra algorithm, the current vertices were in the following order:
2, 1, 3, 4, 5. Thus, the shortest distance to the vertex 1 is 8, 𝑑(2) = 7, 𝑑(3) = 9, 𝑑(4) = 10,
𝑑(5) = 10. The shortest to the top 1 is the path 0.1; 𝑝(2) = 0.2; 𝑝(3) = 0.1.3; 𝑝(4) = 0.4;
𝑝(5) = 0, 1, 3, 5.
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Using the Math Partner service we have the opportunity to check the correctness of the
results in figure 1.
Figure 1: The shortest distances from vertex 0 to all other vertices of graph 𝐺 in the Math Partner
service.
But graph visualization is better performed by Graph Online (figure 2).
Figure 2: Graph 𝐺 visualization and the shortest distance from vertex 0 to vertex 5 of graph 𝐺 in the
Graph Online service.
Among the students of 2-4 courses of the specialty ”Secondary education (Mathematics)” of
the Faculty of Physics and Mathematics of Donbass State Pedagogical University was conducted
a survey to find out which tools of computer training are used by pre-service teachers of
mathematics in professional training, including self-education. A total of 120 students were
involved in the survey. We asked the respondents the following questions:
1. Did you use e-learning resources while studying?
2. Did you use cloud services during your training?
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3. Have you used cloud services during self-education activities?
4. If the answer to 2 or 3 questions is yes, then which cloud services did you use?
5. If the answer to 2 and 3 questions is no, then what software did you use in the learning
process?
The following results were obtained:
• 100% positive result on the first question. This result suggests that pre-service mathemat-
ics teachers understand the concept of “electronic educational resources” despite their
diversity.
• 82% of respondents answered positively to the second question. The result of the answer
to the second question shows that not all respondents identify the concept of cloud
service. We came to this conclusion when discussing the results of the survey with the
respondents. After all, during the practical classes that we described in the study, all
students were involved in the use of cloud services.
• 46% of respondents answered positively to our third question. This percentage is a good
result of self-educational activities.
The answer to the fourth question is shown in figure 3.
Figure 3: Cloud services used by pre-service math teachers.
It is important to note the significant advancement of cloud communication services due
to quarantine measures caused by the COVID-19 pandemic and cloud file storage services. A
positive result of the survey is the availability of cloud services for mathematics.
The answers to our question 5 are presented in figure 4.
At the first glance, pre-service math teachers use a regular calculator and calculator on
mobile devices and make presentations and reports in a word processor. Note that the presented
list includes purely mathematical programs, which are extremely necessary in the training of
pre-service teachers of mathematics.
327
Figure 4: Software used by pre-service math teachers.
5. Conclusions
The learning process in higher education is implemented within a diverse integral system of
organizational forms and methods of teaching. Each form solves its specific task, but the set of
forms and methods of teaching creates a single didactic complex, the functioning of which is
subject to the objective psychological and pedagogical laws of the educational process.
The results of the study provide an opportunity to claim that cloud technologies are used
in the teaching of mathematics in high school. Pre-service mathematics teachers have the
opportunity to use cloud technology during their training. Available cloud technologies have a
wide range of applications in mathematics education.
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