The article briefly describes the possibilities of implementing cloud technologies into the professional-pedagogical training of future mathematics teachers. The results of implementing a specially developed methodically oriented system of teaching the disciplines of the mathematical and methodical cycle are presented. Based on the personal orientation in the process of training of future mathematics teachers, specifically used cloud-based learning technologies as an integral part of information and communication learning technologies. The experimental work was carried out after an ascertainable stage of the experiment, which was carried out to identify the level of readiness for the use of cloud technologies in professional activities. At this stage of the experiment working teachers of mathematics and teachers of mathematical disciplines, as well as students of the same specialty, were involved. An ascertainable stage of the experiment showed that in educational institutions of secondary, professional, and higher education, Yalta and Alushta, cloud technologies as a didactic tool are used only by 7.5% of respondents. At the same time, 86% of respondents consider it necessary to be specifically trained for the use of cloud technologies. In the article, one of the methods of forming the skills of using cloud technologies in the professional training of a future mathematics teacher was described. This is the application of cloud technology in the teaching of all disciplines of the mathematical and methodological-mathematical cycle based on the principles of personal orientation and professional-pedagogical orientation. The results of the experiment allowed to improve the quality of professional and pedagogical training of future mathematics teachers.
The process of making the education of students in the training direction 44.03.01
“Pedagogical education” (“Mathematics”) fundamental is provided by many conditions, one
of which is the refocusing of basic professional training to the ability to use rapidly
changing modern educational technologies based on the integration system of various
components of the formation of professional competencies of a future teacher [
The use of cloud technology by the teacher is a must and necessary condition in the modern learning process. The teacher must know not only the practical but also the theoretical foundations of their use as a didactic tool. The theoretical foundations of the use of cloud technologies in the professional and pedagogical training of a future teacher can be studied at various levels: from elementary to advanced.
Practical aspects of their application in the educational process should be formed at the level of special competence. For a teacher of mathematics and a teacher of mathematical disciplines, the ability to use cloud technology as an effective methodological tool is necessary. In-depth knowledge of cloud technology theory is also welcome.
In the context of a scientific research topic being developed at the Department of Mathematics, Theory, and Methods of Teaching Mathematics “Integration of the educational and research activities of future teachers of mathematics in the context of their personality-oriented professional training” (registration number R&D AAAA-A18118041190060-7 of 04/11/2018), the teaching of all disciplines assigned to the department is carried out using their methodological potential. The use of cloud technology as one of the methodological tools is also illustrated in the classes in these disciplines. 2
The work of many researchers is devoted to the problem of using cloud technologies in
the process of training future teachers. S. Zenkina, T. Suvorova, O. Pankratova, L.
Filimanyuk [
This way, the research examines [
Research performed by M. Ovchinnikova, L. Shilova, and E. Linnik describes a
methodology for teaching Discrete Mathematics to future mathematics teachers, which
is based on a combination of traditional and cloud (basic and additional) study guides.
Google Apps for Education, Wolf-ram / Alpha, Moodle Cloud were used as learning
tools in the cloud. Using this technique allowed future mathematics teachers to be
involved in professionally oriented educational and cognitive activities [
Various academic disciplines can be used to master the theoretical part of cloud
technology. For example, the curriculum provides for the study of the scientific foundations
of computer science. An important role is given to computer modeling and
computational experiment, which are the methodological basis of computer science and
teaching methods at the same time. Modern studies show that mathematical informatics is
one of the effective means of making the professional training of future teachers
fundamental [
In the considered training, mathematical informatics is included in theoretical computer science and it also studies the use of information systems and technologies for applied problem-solving. The basic models, methods, and algorithms for solving problems arising in the field of intellectualization of information systems are studied, and the problems of using information, including mathematical, models and information technologies to study them are considered. But, as the experience shows, the mastery of cloud technology just a didactic tool in the desired amount only when studying this discipline does not occur. 3
When developing the didactic foundations of using cloud technologies in teaching mathematics and implementing it into the educational process as one of the means of digitalization of learning, we used the standard scheme of psychological and pedagogical research: an ascertainable stage of the experiment, identifying theoretical and practical components, organizing and conducting a forming stage of the experiment, and summarizing.
To find out the possibilities of independent formation of competencies associated with the use of cloud technologies in professional activities, we analyzed the existing basic educational programs, both in pedagogical universities, and the proposed additional educational programs for teachers (a total of 25 programs of continuing education courses). At the same time, we took into account the availability of additional educational programs based on various parameters: content, course structure features, training form (full-time–distant), presentation style, price (paid –free-of-charge), etc.
Let’s consider just some of them, which the most accessible.
The all Russia educational portal “ICT for educators” (https://edu-ikt.ru) is a portal for modern teachers, the main purpose of which is to familiarize teachers with new information technologies, help in the development and formation of new competencies in the field of ICT. Out of the twelve six-hour training courses (“Audio-visual technologies in training”; “Use of modern information and communication technologies in the work of a teacher”; “Effective use of programs and Internet services to create educational interactive posters”; “Safe work on the Internet”; Online services to help educators; etc.), only two contain topics related to cloud technology. Moreover, these topics cover only the use of ten cloud storage services (Google Drive, Microsoft OneDrive, Dropbox, Mega, Cloud@mail.ru, Yandex.Disk, Amazon Web Services, pCloud, iCloud Drive, 4shared). The lecture analyzes the cost of services, advantages, and disadvantages, the level of data protection, and privacy). Which, in our opinion, is not sufficient. The form of training is distant/online. Education is free, with only a certificate being paid for.
The PEDAGOGI.ONLINE portal provides access to the online store of webinars for educators (http://www.web-school-detsad.ru/). Retraining courses on this portal are presented in the form of a webinar system. On average, each of the webinars costs about 300 rubles. From a large number of topics, the topic of our research covers a cycle of three webinars “Teacher and Information Technology. Easy about the complex”, in which the existing cloud services are not analyzed. And the webinar “Learning to Create Google Docs. Super help in planning and reporting! Accessible to all". As the names suggest, the topics mostly affect the use of Google features and do not consider other cloud services. The form of training is online.
We found the proposal for the project “Digit to the Regions” (http://digital.naukavregiony.ru/math) to be a very interesting one, which is carried out by ANZhT P.L. Kapitsa Physics-Technical Sciences Lyceum, with the support of the Ministry of Education and the Development Fund for Physics -Technical Sciences Schools. Further education courses for teachers in the subject areas “Mathematics”, “Computer Science” and “Technology” are conducted at the Moscow Institute of Physics and Technology and Physics-Technical Sciences Lyceum for teachers from regional schools. The main difficulty is that only 20 teachers in each subject area are selected for these free courses based on the test results. Training is funded by a grant from the Ministry of Education. Full-time form of education.
Within the framework of these courses, it is planned to hold seminars on the use of various services by a mathematics teacher to increase the efficiency of students learning the material and to improve their knowledge control, open lessons of teachers of the Physic-technical Lyceum for project participants, masterclasses from teachers of the ZFTSh for conducting circles and distance learning.
In the above-mentioned examples, as it had been planned, we analyzed publicly available refresher courses, with the help of which a mathematics teacher can use the skills of using cloud technologies. Almost all of them only in passing concern this aspect. This fact allowed us to conclude that it would be quite difficult for a mathematics teacher who does not own the skills of using cloud technologies in professional activities to independently form these skills.
Also at an ascertaining stage of the experiment, a questionnaire devoted to the relevance of organizing special training for the use of cloud technologies in the learning process and the future professional activities of future mathematics teachers was developed and offered to be completed (Table 1). Questionnaire Dear Colleagues! Please answer the following questions Question 1. Do you use cloud technology in teaching mathematics? - yes, if necessary - sometimes - not using If your answer is “Yes, if necessary,” please go to question 3.
If your answer is “Sometimes”, please go to question 2.
If your answer is “I don’t use”, please answer question 2, 3, 4 and send us a questionnaire Question 2. If you do not use cloud technology in the process of teaching mathematics or do it infrequently, please indicate the reason (you can choose several answer options or offer your option) - I think that this is not necessary at all (distracts students, interferes with studies, does not develop students' mathematical thinking, etc.) - preparation for classes using cloud technologies takes a lot of time from a teacher - I do not know enough about cloud technology - there is no appropriate methodological support to the use of cloud technologies in the teaching of mathematics - other: Question 3. Would you like to use cloud technology in your math teaching process? - Yes - no - I find it difficult to answer Question 4. Is the need for methodological support for the use of cloud technologies in the process of teaching mathematical disciplines relevant (in the form of methodological recommendations, an electronic training course, aids, etc.)? - Yes - no - I find it difficult to answer Question 5. What is the purpose of you using cloud technologies in the process of teaching mathematics? - required by the school authorities - I try to make the lesson as useful as possible - I find it difficult to answer - your option Question 6. What software and cloud services do you use in the process of teaching mathematics most often? Question 7. What difficulties do you encounter in the process of using cloud technologies (can you choose several answer options or offer your option)? - not sufficiently familiar with the software functionality - not all students or students have a sufficient level of digital competency - lack of appropriate software or hardware in the classrooms - the use of cloud technology in the class takes a lot of time - other Thank you for your help and we invite you to scientific cooperation! Sincerely, the staff of the Department of Mathematics, Theory, and Methods of Teaching Mathematics.
The questionnaire was conducted online using https://docs.google.com/forms. 132 teachers of mathematics and teachers of mathematical disciplines of colleges and universities of Yalta and Alushta took part in it. Here we provide the main results that allowed us to conclude that special training is necessary.
Out of all the respondents, only 10 people (7.58%) use cloud technology (sometimes if necessary), while the remaining 122 respondents (92.42%) do not. Out of these, 7 respondents (5.74%) do not see this as a necessary part of the class. As a reason, 18 respondents (14.75%) indicate that preparing for classes using cloud technology takes too much time. 23 respondents (18.85%) noted that they do not have sufficient knowledge and expertise about digital technology. 74 respondents (60.66%) complained about the lack of appropriate methodological support for using cloud technologies for teaching mathematics. Other reasons indicated is the lack of technical equipment in the institution 53 respondents (43.44%).
105 respondents (86.06%) confirmed the relevance of the need for methodological support for the use of cloud technologies in the process of teaching mathematical disciplines.
Questions 5–7 were answered only by 10 respondents (7.58%). All of them indicated that they use Mail.ru and Google services. The main difficulties in using cloud technologies were attributed to the lack of appropriate software or hardware in classrooms.
An analysis of the results of the ascertainable stage of the experiment showed the
insufficiency of the existing opportunities for independent formation of competencies
in mathematics teachers related to the use of cloud technologies. This has confirmed
the need to focus on special training in the use of cloud technologies in education. The
findings are also confirmed in a study on the development issue of Electronic Advanced
Training Courses for the Development of Information Competence of the Teacher [
In the methodological system for the use of cloud technologies in the professional
activities of future teachers of mathematics and teachers of mathematical disciplines, it
is necessary to identify the goals and content of teaching the basics of using cloud
technologies for distance (online) learning of future teachers of mathematics, as well as the
development of an appropriate teaching methodology aimed at implementing
interdisciplinary connections and integration as well as a systematic approach to the training
of future specialists. Since the considered system lives and develops in a didactic
environment, the environment-oriented approach becomes mandatory in training, in which
the learning tools are transferred to the cloud (a specially created environment that
covers all aspects of the use of cloud computing in the organization of education of
students of all categories in different forms and models of learning [
Methodologically sound use of network technologies in the process of teaching the basics of using cloud technologies of future mathematics teachers should help the organization of individual and collective educational activities of students in a cloud environment to actively, consciously use and master the relevant models and teaching methods. 5
The methodology of using cloud technologies in the education of future mathematics teachers is currently in the process of creation and intensive development. However, in the process of this system development, research for other pedagogical specialties cannot be ignored. Most often, this is the training of computer science teachers for whom cloud technologies are both the content of instruction, and the means of instruction, and forms of instruction.
T.P. Kobylnik [
Comparison of the content of computer science training for future teachers of
mathematics and computer science showed that for teachers of mathematics there is no study
of separate sections of artificial intelligence systems, and all other components of the
content of computer science training in pedagogical universities are included in the
content of the training. Besides, individual blocks of mathematical informatics are
studied by future teachers of mathematics in the form of separate disciplines: discrete
mathematics (set theory, graph theory), the theory of algorithms. In the training of the future
teacher of mathematics, the study of the theory of the use of cloud technologies implies
only an introductory level. The focus is on utilitarian issues. For example, the study of
cloud technology application models, which are initially considered as one of the
varieties of services. Future teachers get acquainted with the history of the subject. Without
this, students cannot get a holistic picture of the material being studied. Technological
changes on the Internet led to the emergence of the network (primarily social) Web 2.0
services, which began to provide opportunities for using open, free-of-charge, and free
electronic resources in the learning process, self-creation of online educational
materials, the formation of educational communities, etc. The evolution and convergence of
Web technologies have led to the emergence of the concept of cloud computing and
related technologies to support training and research, primarily cloud Web-SCM
(computer mathematics systems) [
Authors P. Mell, T. Grance [
b) Cloud Platform as a Service (PaaS), in which the consumer is provided with the opportunity to deploy on the cloud infrastructure user-created or acquired programs developed using the tools and programming languages supported by the service provider;
c) Cloud Infrastructure as a Service (IaaS), in which the consumer is provided with data processing, storage, network access, and other basic computing resources on which the consumer can deploy and execute arbitrary software, including operating systems and applications. The consumer does not control the cloud infrastructure itself, but it can control the operating systems, storage facilities, hosted programs and, possibly, have limited control over some network components.
O. Markova, S. Semerikov, and others [
– SaaS – “Higher Mathematics”, “Theory of Probability and Mathematical Statistics”, “Algorithms and Computing Methods”, “Discrete Mathematics”, “Ecology”, “Computer Logic”, “Database Organization”;
– PaaS – “Physics”, “Theory of Electric and Magnetic Circuits”, “Computer Electronics”, “Programming”, “Computer Circuitry”, “Parallel and Distributed Computing”, “Software Engineering”;
– IaaS – “Computer Architecture, “System Programming”, “System Software”,
“Technology of Computer System Design”, “Computer Systems”, “Computer
Networks”, “Computer Systems Information Security” [
In our opinion, the introduction of only the SaaS model is sufficient in the training of a mathematics teacher. Although the use of other models is also possible.
Let’s note the features of cloud access models that need to be considered by a future math teacher.
Cloud access is regulated by four deployment models: - a private cloud, in which the cloud infrastructure operates entirely to serve one organization. Infrastructure can be managed by the organization itself, a third party, or any combination of them and can exist both on the consumer side and at the external service provider;
- community cloud, in which the cloud infrastructure is used by a limited community of consumers from several organizations that have common principles (for example, mission, security requirements, rules, requirements). The infrastructure can be managed by the organizations themselves, by a third party, or any combination of them, and can exist both on the consumer side and at the external service provider;
- public cloud, in which the cloud infrastructure is created as public. Such infrastructure is deployed by a cloud service provider and may be owned and operated by firms, training or government organizations, or any combination thereof;
- a hybrid cloud, in which the cloud infrastructure is a composition of two or more clouds (private, public, or community clouds) that remain unique entities, but combined through standardized or proprietary technologies that transfer data and programs between the clouds.
Using the basics of using cloud technologies in the professional and pedagogical
training of future mathematics teachers helps to ensure making the process of training
fundamental and the methodological orientation of the training as well. At the same
time, future teachers are forming the corresponding competence for using cloud
technologies, which is closely related to “Information competence of a teacher – their
readiness and ability to independently use information and communication technologies in
his professional activity” [
To illustrate the possibilities of using cloud technologies in the teaching of mathematical and methodological-mathematical disciplines, we used the following didactic opportunities: expeditious delivery of educational materials without territorial binding of the user to the place of provision; the ability to create, share, use and comment on documents of various formats; organization of joint work in various formats; organization of interactive classes; organization of various forms of control; organization of independent work in conditions of both synchronous and asynchronous operation.
Some emphasis on the use of cloud technology is analyzed in the work of O. Bondarenko, O. Pakhomova, V. Zaselskiy, S. Mantulenko, А. Pikilnyak [18; 19]. The authors offer a selection of online services that can contribute to the effective acquisition of geographical knowledge in higher school. The publication describes such cloud technologies as Gapminder, DESA, Datawrapper.de, Time.Graphics, HP Reveal, MOZAIK education, Settera Online, Click-that-hood, Canva, Paint Instant. There is also made some theoretical generalization of their economic, technical, technological, didactic advantages and disadvantages. Visual examples of application are provided in the article. The authors make notice that in the long run, the technologies under study should become a valuable educational tool for creating virtual information and education environments connected into common national, and then global, educational space. Authors also share their experience with using Google Classroom as a tool of support of blended learning for geography students [18; 19].
We relied on the data of this study to familiarize ourselves with the possibilities of using cloud technologies in education. We oriented students to the analysis of didactic features of the use of these tools.
Besides, we asked students to analyze the experience of teaching mathematics at
various stages of training (from primary to higher). This is because the methods of
teaching mathematics are interpenetrated and interconnected. As an example, we give
the experience of significantly improving the quality of education in elementary school
using various environments and applications. This experience can be used in teaching
mathematics in grades 5-6. “Tools and apps feature the ability to provide real variability
of tasks, uniqueness of exercises, operative assessment of correctness in each task,
adjustment of task difficulty, ability to provide a shade of competitiveness and gaming to
the exercises». They use Microsoft Office package, GeoGebra
(http://www.geogebra.org), Learningapps.org (http://learningapps.org), Zondle (http://www.zondle.com),
Classtools.net (http://classtools.net), Studystack (https://www.studystack.com) and
others. “Tools and apps can be created by the universal software tools, such programs
that are part of an integrated Microsoft Office package or special designing
environments. The capabilities of the tools and apps are covered, which ensure successful
acquisition of knowledge, for developing young schoolchildren’s skills. Considered tool
kits enable a teacher-to-be to design independently author's apps that meet the needs of
a particular lesson, enable to achieve the lesson goal with the peculiarities of the
educational process in primary school” [
Then we introduce students to the experience of using the capabilities of web-based
software for teaching mathematics in a primary school. For example, in [
In high school practice, there are all the possibilities of organizing a special
cloudbased environment. Using reviewed tools and apps in the practice of Math education
must be based on some principles: developed apps should generate learners’ interest;
apps should be visually presented to create pleasant emotional background; problem
definition should involve learners into a critical analysis of input data as for their
adequacy, redundancy, actuality; apps should allow learners to operate free, for example,
to perform transformations of geometric solids (rotate, drag, resize them) [
Following the standard grading system adopted at CFU, such levels of cloud computing ownership as methodological tools by future mathematics teachers were considered (Table 2). 90-100 82-89 74-81 64-73 60-63 35-59 Levels research tall middle sufficient satisfactory low zero The experimental group included students who studied using cloud technologies according to the developed methodology (61 respondents), the control group included students who studied according to the traditional methodology without using cloud technologies (53 respondents). Comparative results of the forming experiment are shown in table 3. The analysis of experimental data showed that 4.92% and 9.32% of students in the experimental group of research and high level, respectively. And in the control group, they remained unchanged. Moreover, in the experimental group, there was also a transition from a satisfactory level to a sufficient level of 9.85%. 6
The study confirmed that the implementation of the following conditions makes it possible to increase the efficiency of the use of cloud technologies by mathematics teachers: 1. the use of cloud technologies to provide a methodological orientation for teaching future mathematics teachers; 2. the inclusion in the learning content of the basics of using cloud-based learning technologies; 3. selection of freely available cloud-based learning technologies; 4. development and implementation of the methodology for using cloud technologies as a means of teaching the basics of the methodology of teaching mathematics, aimed at increasing the level of their knowledge.
The first condition was realized in the process of designing the content component of the methodological training system for future mathematics teachers, the second condition was in the design of its technological subsystem.
The relevance of the study is confirmed by the fact that in the context of the digitalization of the economy, with the introduction of distance learning elements in schools and universities, school teachers and higher education teachers are faced with the fact that there is an urgent need to know the technologies of organizing education in these conditions.