=Paper=
{{Paper
|id=Vol-2914/Paper19.pdf
|storemode=property
|title=The Application of Open Education Resources as a Tool and Object of Study in the Professional Training of a Mathematics Teacher
|pdfUrl=https://ceur-ws.org/Vol-2914/paper19.pdf
|volume=Vol-2914
|authors=Marina V. Ovchinnikova,Elena P. Linnik,Irina N. Zinenko,Lyubov I. Shilova
}}
==The Application of Open Education Resources as a Tool and Object of Study in the Professional Training of a Mathematics Teacher==
https://ceur-ws.org/Vol-2914/paper19.pdf
224
The Application of Open Education Resources as a Tool
and Object of Study in the Professional Training of a
Mathematics Teacher*
Marina V. Ovchinnikova 1[0000-0002-5070-8061], Elena P. Linnik 2[0000-0002-1742-5940],
Irina N. Zinenko 3[0000-0001-5878-9380], Lyubov I.Shilova 4[0000-0003-4817-132X]
1,2,3,4V.I.VernadskyCrimeanFederalUniversity, Simferopol, Russia
m_ovchinnikova@ukr.net,
aplinnik@mail.ruir,
iwe4ka.86@mail.ru,
lshilova07@gmail.com,
Abstract. The article analyzes and describes the basic concepts associated with
the organization of open education: open education (OE), open educational re-
sources (OER), Massive open online courses (MOOC). The experience of organ-
izing the study of history and methods of using open educational resources in the
professional and pedagogical training of future Mathematics teachers is de-
scribed. It also analyzes some of the open education platforms offered by Russian
universities. The methodological possibilities of using the resources of open ed-
ucation as an object of study for obtaining professionally significant information
in the professional and pedagogical training of future Mathematics teachers are
illustrated.
Keywords: Distant Learning System, Open Teacher Education, Professional
Training of a Mathematics Teacher.
1 Introduction
In a concept note by UN Secretary-General AntónioGuterres, together with the
#SaveOurFuture campaign “Education in the era of the COVID-19 pandemic and be-
yond” [1-3], very large disruptions in the global education system have been noticed.
It has been caused by a pandemic. This situation can cause a loss of skills and
knowledge for many generations of students. In his opinion, it is necessary to combine
the efforts of international and national actors to restore education.
According to UNESCO, about 1.6 billion students (94%) in the world are now af-
fected by the closure of educational institutions. It is predicted that 24 million students
(from preschoolers to university students) may not return to school in 2020 after the
* Copyright 2021 for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0).
225
closure of institutions due to the COVID-19 pandemic. UNESCO assumes a high drop-
out rate and predicts a 3.5% reduction in the number of university students (approxi-
mately 7,900,000 people).
According to “The Concept of Development of Mathematical Education in the Rus-
sian Federation“Educational institutions of higher education and research centers
should ensure the advanced level of fundamental and applied research in the field of
mathematics and their use in mathematics education. It is necessary to strengthen the
integration of Russian mathematical research into world science, to ensure that the
mathematical faculties of leading Russian universities achieve high positions in world
rankings, as well as an increase in the quality, quantity, and citation of works of Russian
mathematicians, the attractiveness of Russian mathematical education for the best for-
eign students and professors. The mobility of students, graduate students, and young
candidates of sciences should increase, cooperation between educational institutions of
higher education and research institutes should develop” [4].
The above-mentioned factors made the pedagogical community look for new as well
as modernize old forms of education in all educational institutions. This also affected
higher education. In this situation, the phenomenon of open education acquires partic-
ular relevance.
In this article, we plan to share the experience of studying the topic “Possibilities of
using open education resources in the work of a Mathematics teacher” and the actual
use of open education resources in the professional and pedagogical training of future
Mathematics teachers.
2 Task Setting
Following the recommendations of the UN and UNESCO for mitigating the conse-
quences of the pandemic in education, the fourth item is highlighted; “Reimagine edu-
cation and accelerate positive change in teaching and learning: The scale of innovations
made in a short time to ensure learning continuity proves that change can happen
quickly. They have set the ground to reimagine education and build systems that are
more forward-looking, inclusive, flexible, and resilient. Solutions must address learn-
ing losses, preventing dropouts, particularly of the most marginalized, and ensuring the
social and emotional welfare of students, teachers, and staff. Other priorities include
better support to the teaching profession, removing barriers to connectivity, investing
in digital technologies, and flexible learning pathways”[5].
In our opinion, one of the ways to achieve this task is to use the open education
system at all levels of education.
Open education in these conditions is becoming a powerful tool for the implemen-
tation of the task. The use of open education resources makes it possible to obtain high-
quality education for various groups of students.
Under the new conditions, the faculty of the Department of Mathematics, Theory,
and Methods of Teaching Mathematics required an urgent correction of the forms of
organization of education. Work in the social network “Vkontakte”, which they
226
switched to at the CrimeanFederalUniversity, made it possible to implement basic ed-
ucational programs, but at the same time implied greater independence of students. Not
all students were ready for this. Therefore, there was a need for non-standard selection
and structuring of the content of the subjects taught.
For students studying the program 44.03.01 “Pedagogical education”, the focus
“Mathematics” and 44.04.01 “Pedagogical education”, the Master's program “Mathe-
matics in professional education” there was an urgent need to strengthen the methodo-
logical and practical orientation of teaching of all studied disciplines. The peculiarity
of teaching all disciplines of the department in the professional training of a Mathemat-
ics teacher is that the organization of training (forms, methods, means) is aimed not
only at the formation of competencies corresponding to the discipline, but also is a
model of the teacher's methodological activity, which will then (or will not) be used by
future teachers. One of the aspects of providing a methodological orientation is the
work within the framework of open education.
3 Method Development
Let's analyze the main theoretical aspects related to the concept of open education.
According to Wikipedia's definition, “Open education is education without academic
admission requirements and is usually assumed to be online. “Open” education expands
access to learning offered in schools and universities. The term “open” refers to the
removal of barriers that can impede both opportunity and acceptance of participation in
learning-based learning. One of the aspects of the openness of education is the devel-
opment and implementation of open educational resources”[6].
In this definition, the concept of open education is narrowed down to online educa-
tion with open access. It can be obtained by any person who has a desire, and, at the
same time, there are no requirements for his educational level, profession, age, and
other subjective factors. The absence (availability) of payment is not noted in any way,
i.e. the subject can access the resources either free of charge or for a small fee.
In modern pedagogical science, the following definition is used as the main one:
“Open education is an integrated and holistic learning system based on the interaction
of educational institutions, centers, and virtual offices that provide educational services
to various groups of the population” [7]. The integrity of the system under consideration
is ensured by its goal –“the creation of optimal conditions for the development of the
personality of each person through continuous education and increasing his profes-
sional growth in the information society” [7].
The difference between the previous definition and the last one is that the second is
based on a systematic approach, relies on the need to ensure the development of the
individual, its professional qualities through the continuity of education, and the first
may have other motives. Unfortunately, this definition uses the term “educational ser-
vice”, and also does not indicate whether the services are paid or free.
Open education is directly implemented through Open Educational Resources
(OER). According to Cable Green, Director of Open Education at Creative Commons,
227
this term means “freely available materials that can be legally downloaded, edited, and
shared to better serve all students” [8].
The next concept related to open educational space is a Massive open online course
(MOOC). “This is a training course with massive interactive participation using e-learn-
ing technologies. This is a form of distance education available to anyone with an In-
ternet connection. In addition to traditional actions with the materials of the training
course (reading, watching videos, completing assignments), the MEP has the oppor-
tunity to use interactive forums that are created and supported by students and teach-
ers”[9].
One of the first works devoted to the introduction of the MEP into the practice of
teaching in the transition to the digital economy, which became the benchmark for fur-
ther research [10].
The ideological inspirers of the creation of an open educational space do not equate
to free and free access to educational sources. At the same time, it is noted that for
MOOCs to become OER, free licensing is necessary (for example, in Creative Com-
mons). So, the following meaning is put into the concept of OER: the resource exists
in digital form (created with the help of electronic technologies, maybe in digital or
paper form), it is freely stored, copied, and distributed; using the Internet, its general
availability is ensured; open licenses keep copyrights [8].
In our research, we also relied on the results of such works on the professional train-
ing of future mathematics teachers [11-15].
4 Results
We found out the state of the use of open education sources in the methodological
activity of a mathematics teacher using various means (observation, analysis of lessons,
electronic journals, conversations, questionnaires). To clarify the attitude of mathemat-
ics teachers to the use of open education tools, we conducted an online survey us-
inghttps://docs.google.com/forms(Table 1). Respectfully yours, the staff of the Depart-
ment of Mathematics, Theory, and Methods of Teaching Mathematics.
It was attended by 198 respondents (teachers of Mathematics and teachers of math-
ematical disciplines of colleges and universities in Yalta and Alushta, students - future
teachers of Mathematics). Here are the main results that made it possible to roughly
assess the state of use of open education sources by teachers and teachers of mathemat-
ics on the southern coast of Crimea.
takes a lot of time (you cannot offer students unverified information). 22 respondents
(11.11%) noted that they do not have enough knowledge of digital technologies. 112
respondents (56.57%) complained about the lack of appropriate methodological sup-
port.
228
Table 1. Application form.
№ Dear Colleagues! Please answer the questions posed.
Question 1. Do you know what open education is?
- Yes
- I heard, but I'm not sure I understand the meaning
- no, but I would like to know
- no
Question 2. Is there a need to study the theory and methods of using the sources of
open education in the professional training of a future mathematics teacher?
- Yes
- no
Question 3. Do you use sources of open education in your professional activities?
- yes, if necessary
- sometimes
- not using
If your answer is “Yes, if necessary” or “Sometimes”, please go to ques-
tion 5
If your answer is “I don’t use”, please go to question 4 and send us a ques-
tionnaire
Question 4. If you do not use sources of open education in your professional activities
or do it infrequently, please indicate the reason (you can choose several an-
swers or suggest your version)
- I think that this is not necessary at all (distracting, interfering with learn-
ing, I can cope myself, etc.)
- preparing for classes using open education sources takes a lot of time for
the teacher
- I do not know enough IT technologies
- there is no appropriate methodological support for organizing the use of
open education in teaching mathematics
- harmful content
- other
Question 5. Is the need for methodological support for the use of open education
sources in the process of teaching mathematical disciplines urgent for you (in
the form of guidelines, an electronic training course, manuals, etc.)?
- Yes
- no
- I find it difficult to answer
Question 6. For what purpose do you use the sources of open education in the process
of teaching mathematics?
Question 7. What sources of open education do you most often use in the process of
teaching mathematics?
Question 8. What difficulties do you face in the process of using the sources of open
education (you can choose several answers or offer your version)?
- insufficiently familiar with the list of open education sources recom-
mended by the ministry
- not all students have a sufficient level of digital competence formation
- there is no corresponding software or hardware in classrooms
- use in class distracts from the main purpose of the lesson
- other
229
Of all the respondents, only 30 people (7.7%) do not know what open education is
and do not use its sources. Out of the remaining 168 respondents (92.3%), they have an
idea of this phenomenon or know what it is. They would like to study the historical,
theoretical, and methodological foundations of using open education in their activities.
Only 7 respondents (4.04%) believe that the use of open education sources harms the
educational process. More than 90% of respondents want to know the scientific and
practical foundations of using open education. And the desire to improve the quality of
their teaching is indicated as the main reason. However, 40 respondents (20.20%) note
that in preparation for lessons, you need to carefully review the proposed content, which
Thank you for your help and invite you to scientific cooperation!
Poor equipment of the school with technical means was noted by 63 respondents
(31.81%). 134 respondents (67.68%) confirmed the urgency of the need for methodo-
logical support of open education sources.
Of the resources that teachers and teachers of mathematics use, in the survey, they
indicated Foxford, Info-lesson. And the technical component complicates the work.
The analysis of the results of the questionnaire showed that open education and its
resources are of interest to the majority of Mathematics teachers, and they are ready to
use them in their professional activities to improve the quality of teaching.
5 Discussion
Founded in 2002, ISKME (a global nonprofit organization that inspires educators
and brings them together in a collaborative and sharing learning ecosystem, is at the
forefront of open education. It is characterized by the research in the social sciences,
the development and the scientific justification of innovation for knowledge exchange
in education) (https://www.iskme.org/).
In our activities, we try to use open educational resources that provide free access to
our courses. At the same time, we use some platforms as samples (fictitious), and Rus-
sian resources also as training ones.
One of the platforms that we introduce to our students - future Math teachers - is the
open education platform OER Commons (https://www.oercommons.org/), which is de-
veloped and maintained with the participation of ISKME. This platform is considered
to be the oldest of its kind. From a methodological point of view, the interface and the
possibilities of working with this platform are of high interest. The platform allows you
to navigate to 38 hubs (a customizable resource center in the OER Commons where
teams can create and share collections related to a project or organization). Projects,
institutions, states, and initiatives use the hubs to bring groups of educators together to
create, organize, and share collections that align with their common goals
(https://www.oercommons.org/hubs/ ). For example, one of the hubs - Open Educa-
tional Practice and Professional Training (https://www.oercommons.org/hubs/open-
educational-practice/) offers a series of interesting webinars on creating your open ed-
ucational resources. Using the Google Chrome browser allows you to overcome the
language barrier. Russian translation for non-English speaking students is of very good
quality.
230
The materials posted on this platform are mainly developed by teachers from the
United States. For our students on the site https://www.oercommons.org/, the following
subjects presented some interest: education and mathematics. Of course, we did not
limit our work to other subjects either. For each of the subjects, there is an opportunity
to choose an educational level (from preschool to higher). Working with the "Educa-
tional Standards" menu item gave our students a unique opportunity to analyze the US
state math education standards and the math education standards of various states.
The use of free resources based on the principles of open education in the profes-
sional and pedagogical training of future Mathematics teachers has proven itself well
during remote work and has good prospects.
One of the most interesting platforms providing access to domestic open educational
resources is the National Open Education Platform (https://openedu.ru/ ).
This platform is organized by the leading universities of our country: Moscow, St.
Petersburg, Tomsk, and other cities (MoscowStateUniversity, MIPT, NRU HSE,
SPbPU, St. PetersburgStateUniversity, NUST MISIS, UrFU and ITMO University, and
other universities. All courses hosted on this platform, free of charge, built following
the requirements of the Federal State Educational Standard of Higher Education, read
by the leading professors of these universities, a total of 616 courses are presented on
the platform.
For future Mathematics teachers, many sections of the courses offered on the plat-
form are interesting: mathematical (“Various sections of mathematical analy-
sis”https://openedu.ru/course/msu/CALCSV/,
https://openedu.ru/course/msu/MATHAN/; “Analytic geome-
try”https://openedu.ru/course/msu/ANGEOM/, “Higher alge-
bra”https://openedu.ru/course/spbu/MATGR/,etc.), linguistic (mathematical Eng-
lishhttps://openedu.ru/course/hse/MATHENG/), pedagogical (“Modern educational
technologies” (https://openedu.ru/course/spbu/EDU_TECH/)), etc.
For students of the master's program, we also offered, in addition to the discipline of
the same name, which is taught by our teachers, an open course “Pedagogy and Psy-
chology of Higher Education” (https://openedu.ru/course/tgu/PEDPSY/), sections of
which are read by the leading teachers of Tomsk. Master students note that communi-
cation with our teachers and video lectures of professors and associate professors was
very useful not only in terms of professionally significant information but also interest-
ing in terms of communication with new people, authors of current textbooks.
Another platform that opens up opportunities for free access to educational resources
National Open University “Intuit” (https://intuit.ru). While studying the topic “Control
and assessment of knowledge in mathematics”, our students became interested in the
course “Introduction to practical testing” (by V. Kaziev, Kabardino-BalkarianStateUni-
versity) (https://intuit.ru/studies/courses/1023/300/info).
The author in an accessible format accessible level sets out the basics of creating
tasks for tests, their high-quality connection into tests, and the specifics of testing. It
also provides practical guidelines for testing in some programs.
However, almost all the courses offered on this resource relate to the application of
information technology in various industries (education, business, science, program-
ming, etc.).
231
Project “Universarium”, which is offered by LLC “Assessment of the quality of ed-
ucation” (https://universarium.org/), is a network interuniversity platform. The goal of
the project is to develop the electronic part of the Russian educational space by leading
Russian universities. On this platform, pre-profile training, targeted profile training are
organized for the formation and retention of domestic personnel for the Russian indus-
try and economy.
We would especially like to note such social functions of the “Universarium” as
preserving the national identity of the Russian educational space, strengthening the po-
sition of the Russian language in the Russian Federation, and promoting the Russian
language abroad as one of the leading languages of communication
(https://universarium.org/docs/o-proekte).
Many courses at “Universarium” that are of interest to future Mathematics teachers
are presented by MoscowStatePedagogicalUniversity. This is one of the leading peda-
gogical universities in the country, which trains Mathematics teachers. We will list just
a few of them: “Modern lesson as a space for the formation of meta subject learning
outcomes”, “Modern psychological and pedagogical technologies in education”, “Ge-
ometric methods for solving algebraic problems”, “Geometry: an analytical method for
solving a problem”. All of these courses allow us to provide a methodological focus in
teaching methodological and mathematical disciplines.
From a methodological and cognitive point of view, our students were attracted by
the course “Course on the Unified State Exam or Unified State Exam for Teachers”,
the purpose of which is to improve the level of training of Mathematics teachers.
Of the Russian-language platforms of open education, I would like to note the “Lec-
torium” project (https://www.lektorium.tv/). This resource also offers both paid and
free courses.
From a methodological point of view, our students are interested in a selection of
courses “Mathematics with Georgy Wolfson” by one of the best young teachers in St.
Petersburg and Russia. These are courses “Not boring Algebra”, “Not boring Geome-
try”, “Gambling theory of probability”, and others. The audience includes pupils, par-
ents, students, and teachers.
When studying the topic “Methods for studying ordinary fractions”, by the way, I
got a free course for schoolchildren of grades 4-6 “Crrrrush everything” (Crush every-
thing). It presents a practice-oriented approach to learning fractions. Some of the classes
take place in a pizzeria, where the whole is visually divided into equal parts (usually
8), but less or more is possible). The concept of a fraction is formed in action, which is
very important for this age group of students. The course consists of 15 full lessons
(colorfully illustrated), 7 interesting homework assignments, and tests.
Also “Lectorium” together with the Autonomous non-profit organization “Center for
Continuing Professional Education” ALFA-DIALOG (http://www.alfa-dialog.ru/)
within the framework of the program “Personal digital certificates” from the state of
the project “Personnel for the digital economy” offers free advanced training courses
“Modern course building”, “Artificial intelligence in creative industries”, “Design of
Crypto economic Mechanisms”.
Our undergraduates who already have higher education (bachelor's level) chose the
first one. The course program analyzes existing online educational products and teaches
232
you to design and produce your online courses. The authors emphasize that blended
learning forms the future of education (a combination of full-time and digital (online)
forms). Therefore, the future teacher needs knowledge of the principles of creating and
using digital content.
Students receive knowledge in computer graphics, which is necessary for the work
of a modern teacher, media manager, producer, or leader in online education, modern-
ization of educational programs. The stages of creating a MOOC are considered, the
features of the production processes of online courses are revealed. In the practical
module, users develop and submit their projects of online courses for examination
(goals, visual solution, work plan following global educational trends, application of
the acquired skills in graphic editors and website builders). To complete the project
assignment, users are encouraged to master Tilda site builder tools for project presen-
tations.
Our students also use free materials, which are kindly offered during the pandemic
by famous platforms: Urait (https://urait.ru/), Netology-group (Foxford project
(https://foxford.ru/) and Edmarket (https://edmarket.ru/)), GK “Prosvesh-
cheniye”(https://prosv.ru/), Russian teachers (http://school-detsad.ru/)and many others.
Edmarket (https://edmarket.ru/) offers free webinars. For example:
“How do different types of online activities affect the motivation of children?” (what
is important to consider when teaching children online, the peculiarities of motivating
children of different ages, how to involve parents in online learning).
“How does game design work?” and others.
Other forms of work are also offered. For example, an online camp for creating
courses, (5 days, live broadcasts) (topic and niche for an online school, drafting a course
strategy, project launch budget, creating a popular online course).
In working with such materials, the opportunity to organize “observation lessons”
that are included in the program of introductory training practices is especially valuable
for us. During the quarantine period, working online in real-time at Foxford, MIPT free
courses have become an indispensable help.
6 Conclusion
The use of resources of open education in the professional and pedagogical training
of future Mathematics teachers during the period of distance learning made it possible
not only to increase the level of professional competencies but also contributes to the
methodological orientation of the training in question and an increase in interest in the
profession.
References
1. Concept Note by the Secretary-General on Education and COVID-19, available upon re-
quest from the UNESCO Press Office, Roni Amelan, r.amelan@unesco.org (link sends e-
mail)
233
2. UNESCO COVID-19 Briefing Paper: How many students are in danger of not returning to
school? https://en.unesco.org/news/new-academic-year-begins-unesco-warns-only-one-
third-students-will-return-school
3. Campaign#SaveOurFuture:– Access mode : www.saveourfuture.world
4. The Concept of Development of Mathematical Education in the Russian Federation (ap-
proved by the order of the Government of the Russian Federation of December 24, 2013,
No. 2506-p). Moscow (2013).
5. UN Secretary-General warns of education catastrophe, pointing to UNESCO estimate of 24
million learners at risk of dropping outa Press release – Access mode:
https://en.unesco.org/news/secretary-general-warns-education-catastrophe-pointing-
unesco-estimate-24-million-learners-0
6. Open education – Access mode : https://ru.wikipedia.org/wiki/Открытое_образование
7. Lupanov V.N. Open education – Access mode : https://w.histrf.ru/articles/article/show/ot-
krytoie_obrazovaniie
8. Cable Green Sharing legally and freely for better learning – Access mode:
https://en.unesco.org/courier/julio-septiembre-2017/sharing-legally-and-freely-better-
learning
9. What is МООС? – Access mode: https://www.facebook.com/URAITpublishing/pho-
tos/a.1111396068882898/3537079386314542
10. McAuley A., Stewart B., Siemens G. and Cormier D. The MOOC Model for Digital Prac-
tice: – Access mode: http://amp.gs/Lowj.
11. Zenkina, S., Suvorova, T., Pankratova, O., Filimanyuk, L.: The Method of Design of Elec-
tronic Advanced Training Courses for the Development of Information Competence of the
Teacher. Proceedings of SLET-2019 - International Scientific Conference Innovative Ap-
proaches to the Application of Digital Technologies in Education and Research, Stavropol -
Dombay, Russia, 20-23 May 2019. pp. 366 - 375. http://ceur-ws.org/Vol-2494/paper_35.pdf
12. Konopko, E., Pankratova, O., Nersesyan, E., Abdullaev, J.: Training of Teachers for Pro-
fessional Activity in the Digital Environment of the Educational Space. Proceedings of
SLET-2019 International Scientific Conference Innovative Approaches to the Application
of Digital Technologies in Education and Research, Stavropol - Dombay, Russia, 20-23 May
2019, pp. 205-212. http://ceur-ws.org/Vol-2494/paper_18.pdf.
13. Taran, V. Use of Elements of Augmented Reality in the Educational Process in Higher Ed-
ucational Institutions. CEUR Workshop Proceedings. In 2019 International Conference on
Innovative approaches to the application of digital technologies in education and research
SLET-2019 http://ceur-ws.org/Vol-2494/paper_28.pdf
14. Astafieva, M., Bodnenko, D., Proshkin, V. Cloud-oriented training technologies as a means
of forming the XXI century skills of future mathematics teachers. ICT in Education, Re-
search, and Industrial Applications. Integration, Harmonization and Knowledge Transfer
Proceedings of the 15th International Conference on ICT in Education, Research and Indus-
trial Applications. Integration, Harmonization, and Knowledge Transfer. Volume I: Main
Conference Kherson, Ukraine, June 12-15, 2019. http://ceur-ws.org/Vol-
2387/20190507.pdf
15. Ovchinnikova M., Shilova L., Linnik E.Using Means of Cloud Technologies of Training in
the Study of Discipline "Discrete Mathematics" in the Professional-Pedagogical Training of
Math Teachers. Information Systems and Technologies in Modeling and Control 2019: Se-
lected Papers of the IV All-Russian scientific and practical conference with international
participation "Information Systems and Technologies in Modeling and Control"
(ISTMC’2019) Yalta, Crimea, May 21-23, 2019. http://ceur-ws.org/Vol-2522/paper15.pdf