=Paper=
{{Paper
|id=Vol-2740/20200278
|storemode=property
|title=Development of an Online-Course Syllabus "Operations Research
Oriented to Cloud Computing in the CoCalc System"
|pdfUrl=https://ceur-ws.org/Vol-2740/20200278.pdf
|volume=Vol-2740
|authors=Kateryna Vlasenko,Olena Chumak,Dmytro Bobyliev,Iryna Lovianova,Iryna Sitak
|dblpUrl=https://dblp.org/rec/conf/icteri/VlasenkoCBLS20
}}
==Development of an Online-Course Syllabus "Operations Research
Oriented to Cloud Computing in the CoCalc System"==
https://ceur-ws.org/Vol-2740/20200278.pdf
Development of an Online-Course Syllabus “Operations
Research Oriented to Cloud Computing in the CoCalc
System”
Kateryna Vlasenko 1[0000-0002-8920-5680], Olena Chumak 2[0000-0002-3722-6826], Dmytro Boby-
liev3[0000-0003-1807-4844], Iryna Lovianova4[0000-0003-3186-2837], Iryna Sitak5[0000-0003-2593-1293]
1Donbass State Engineering Academy, Kramatorsk, Ukraine
2
Donbas National Academy of Civil Engineering and Architecture, Kramatorsk, Ukraine
3Kryvyi Rih State Pedagogical University, Kryvyi Rih, Ukraine
4Kryvyi Rih State Pedagogical University, Kryvyi Rih, Ukraine
5 The Institute of Chemical Technologies (the town of Rubizhne) of the East Ukrainian
Volodymyr Dahl National University, Rubizhne, Ukraine
vlasenkokv@ukr.net, chumakelena17@gmail.com,
dmytrobobyliev@gmail.com, lirihka22@gmail.com,
sitakirina@gmail.com
Abstract. This discussion paper provides an insight into the issue of develop-
ing a course syllabus for mastering Operations Research. The study focuses on
implementing cloud computing while solving optimization problems. The re-
search analyzes practical experience of using mathematical modeling in plan-
ning technological, biological and vital processes. This analysis confirms the
relevance of using cloud environment CoCalc while teaching students how to
solve Operations Research tasks. The discussion paper describes the study of
the specific features of online-courses on Operations Research with the help of
the Deductive Approach to Content Analysis guidelines that give recommenda-
tions on developing syllabus for on-line courses. The study presents the devel-
opment of the course syllabus for students who study the Operations Research
course, or those who want to study Operations Research methods independent-
ly. The study shows the analysis of the survey results that allowed reviewing
students’ and teachers’ opinions on improving the course with the use of com-
puter mathematics systems. This study also discusses the course annotation and
aim, requirements to course users, learning organization of course modules tar-
geted at acquiring certain competencies. There was ground to make a conclu-
sion concerning the importance and relevance of developing Operations Re-
search Oriented to Cloud Computing in the CoCalc System online course on the
Higher School Mathematics Teachers platform.
Keywords: online-course, syllabus, Operations Research, cloud computing in
the CoCalc system.
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
1 Introduction
1.1 Problem Statement and Its Topicality Substantiation
The standards for training Mathematics teachers, developed by the Association of
Mathematics Teacher Educators [1], brought out the problem of training mathematics
teachers for technical and economical higher schools as the most relevant one. Among
the ways of solving the issue connected with students’ mobility support, the Associa-
tion highlighted the development of online courses with interdisciplinary integrated
content. On the one hand, such courses help students to see more closely into the per-
spectives of their studies on the chosen specialities. On the other hand, they meet
educational requirements set by students of technical and economic specialities. But
as the research by K. Vlasenko et al. [2] showed, the insignificant number of respond-
ents, including students of mathematics departments from pedagogical universities of
Ukraine, noted the skill of developing mathematical models on which the majority of
interdisciplinary courses are based. Operations Research refers to the disciplines that
study the system approach to the stated issue. The essence of the approach is that any
task should be considered with the regard for its influence on the criteria of function-
ing the system as a whole. It is typical for Operations Research that while solving any
problem new tasks may occur. An important feature of Operations Research is its
focus on searching the optimal solution for the task (the principle of “optimality”).
However, it is impossible to find such a solution in actual practice: the absence of
methods that enable to find a globally optimal solution for the task and the lack of
existing resources that make it impossible to implement exact methods of optimiza-
tion.
Moreover, the emphasis in learning modern courses on Operations Research is
made on routine computing procedures but not on the process of creating mathemati-
cal models that are interrelated with designing technical and technological processes,
with the distribution of limited resources and planning the work of enterprises and,
finally, with solving problems that occur in a person’s everyday life. Therefore, Oper-
ations Research training requires an informed choice of computer mathematic system
to support the course. After analyzing the articles on selecting CMS [3, 4, 5], we can
make a conclusion that researchers pay attention mainly to commercial aids for teach-
ing and organizing calculations (MathCAD, MATLAB and Maple). At the same time,
the powerful capabilities of the non-commercial CoCalc system [6] are not taken into
account. Among the advantages of CoCalc are its being a cloud-orientated and open
source software. In addition, due to a number of components of this CMS, we can
make the Operations Research course more efficient: the LaTeX editor provides the
ability to prepare high-quality teaching materials, and the IPython interpreter can be
used to develop dynamic models. Consequently, the necessity to develop a course,
which will consider the issues of implementing cloud computing for solving optimiza-
tion tasks with approximation to reality, is timely and relevant.
The objective of this paper is to perform a theoretical analysis of the features of
resources that offer teaching Operations Research and focus on the use of cloud com-
puting, in particular CoCalc. In addition, we present the development of the syllabus
for the online-course “Operations Research Oriented to Cloud Computing in the Co-
Calc System” [7].
The condition for achieving the objective lies in solving the following research
tasks:
• the analysis of existing Operations Research courses and the needs of the target
audience;
• the definition of the objective, tasks, educational content for Operations Re-
search;
• the choice of aids for organizing the teaching of the course.
1.2 Analysis of the Latest Researches and Publications
While searching for research papers dedicated to teaching Operations Research, we
analyzed the studies [8, 9] in which the researchers put emphasis on the importance of
learning this discipline through solving practical tasks. The scientists believed that the
teacher has to focus more on mathematical modeling of various processes and phe-
nomena. We studied the experience of the scientists who considered the practice of
using mathematical modeling in designing technological [10, 11] and biological pro-
cesses [12]. While analyzing the researchers’ works we concluded that learning Oper-
ations Research exclusively through practical tasks has its disadvantages. The built
models have a considerable number of variables, and it complicates the process of
finding a solution with its further analysis. Taking it into consideration the fact that
the majority of the Operations Research courses are overloaded with theoretical mate-
rial that does not encourage the formation of students’ coherent insight into solving
practical tasks.
The development of computer technologies and current computer mathematics sys-
tems allowed removing this disadvantage. Several scientists used efficiently different
systems of computer mathematics in the process of learning Operations Research [13,
14, 15]. However, the analysis showed an insignificant number of scientific papers
dedicated to the use of CoCalc cloud environment. I. Lovianova et al. [16] offer to use
CoCalc during optional classes “Optimization classes” but the level of offered learn-
ing tasks and technologies is oriented at pupils of the 10th-11th grades of specialized
schools and doesn’t include distance education. It is more interesting to study the
experience by O. Markova et al. [17] about the use of CoCalc while teaching Mathe-
matical Basics of Information Technology to the students of technical specialities, but
the authors rely on the fact that students can code at an adequate level. In the opinion
provided by M. Shyshkina [18] the usage of cloud computing systems will allow im-
plementing innovative technologies in the university learning environment and will
stimulate the creation of a coherent educational infrastructure and provide access to
the best examples of electronic resources, in particular, environment design, applica-
tion virtualization, infrastructure unification, service integration, extension of elec-
tronic resource use, extension of cooperation forms. Following scientists' conclusions,
we see that the use of such an approach for developing an online course on Operations
Research will be efficient during training higher school mathematics teachers.
2 Method
The authors the paper used the Deductive Approach to Content Analysis manuals
[19, 20, 21, 22], which provide recommendations for developing syllabuses for online
courses. The analysis of the recommendations, developed by the experts (Table 1),
made a contribution to the development of the syllabus sections: Summary of the
Course, Course Objective, Requirements to the Course Users, and Arrangement of the
Learning Process.
Table 1. Recommendations for developing syllabuses for online courses
The syllabus sections The recommendations
Summary of the Course Analyze the content of existing courses, identi-
fying their features, shortcomings
Determine what are the expectations of future
course users
Course Objective Determine the essence of the problems that arise
during the study of the discipline, identify what
skills students want to acquire
Requirements to the Course When choosing learning tools, including cloud
Users environments, determine and indicate the mini-
mum requirements for their engagement in the
course
Arrangement of the Learning Indicate the topic list of the course, by getting to
Process know the other teachers’ opinion of this list, speci-
fy the rules, assessment principles, remembering
about the incentives
To be able to take into account the recommendations of the above-mentioned
guidelines, the authors of this study analyzed online resources [23-32] that share the
experience of teaching Operations Research. The content of these resources helps to
practically train how to set problems and solve them with the help of computers, but
does not give enough attention to the mathematical methods themselves. The tutor of
these courses note that it is the job of the specialist to set the task correctly, choose the
right computer mathematics system, enter data into the computer and correctly inter-
pret the results. We can also add that some of the resources [27] partly replace the
content of the Operations Research course with the content of the Mathematical Pro-
gramming course. That can be explained by the fact that most Operations Research
topics require the methods studied in the Mathematical Programming course. But in
this case, students acquire only some idea of the range of issues that should be studied
in detail during the Operations Research course. In addition, the analysis of the fo-
rums of these resources demonstrates a low level of students’ interest in such educa-
tional material.
Following expert recommendations concerning the need to communicate with fu-
ture users of the course, the authors of this paper also developed a questionnaire for
the students (the qualification code of the program “014.04. Secondary Education.
Mathematics”) and mathematical disciplines teachers working at higher educational
institutions. In this way, the course developers determined the essence of the prob-
lems that arise when teaching topics related to optimization tasks, and identified
methods by which these problems can be solved. 112 respondents participated in the
survey on the Higher School Mathematics Teachers platform [33].
The analysis of the survey results helped to discover that while learning Operations
Research, in particular, Linear Optimization, there are certain difficulties connected
with the complexity of mathematical tools which are used and the necessity to have
skills of computer work using modern systems of computer mathematics, in particu-
lar, CoCalc.
As students’ survey showed, for the purpose of getting them interested in the disci-
pline, the resources should cite examples of using Operations Research methods, in
particular, linear optimization, for specific processes and in the activities of really
existing enterprises. Surveyed mathematics teachers recommended using the general
modeling methodology so that the content corresponds to the students’ expectations.
Moreover, respondents indicated the relevance of considering the following topics:
• place of mathematical modeling in different situations;
• special features of using models in different situations;
• types of mathematical models;
• computer mathematics systems that can be used;
• means of analyzing the situation that requires optimization and problem formula-
tion;
• modeling process organization;
• relevant modeling method selection and mathematical model building;
• ways of getting data for modeling and requirements that are needed from them;
• verification of the built model adequacy to the real situation and the trust level to
this model;
• modeling results interpretation (as the model is a simplified abstract image of the
reality and a lot of things are not taken into consideration);
• determining the ways of the most efficient use of modeling results after their inter-
pretation.
All the respondents also pointed out that the class should be given using computer
mathematics systems. The respondents ask to pay special attention not only to the task
setting but to their mathematical formulation (which is the most complicated and
creative part of modeling). So, while forming an online-course syllabus, we took into
account the respondents’ ideas expressed in the survey and the carried out analysis of
resource characteristics that offer to learn Operations Research.
The online course that will be posted on the platform “Higher School Mathematics
Teachers” [33], got the name “Operations Research Oriented to Cloud Computing in
the CoCalc System” [7]. The course is designed for students who study the course
Operations Research, or those who want to learn the methods of Operations Research
independently. The course learning, consulting will be carried out by platform tutors.
While preparing the syllabus we followed the recommendations developed by Eberly
Center in Carnegie Mellon University [32].
Online-Course Syllabus “Operations Research Oriented to Cloud Computing in
the System CoCalc”
Summary of the Course. Operations Research refers to the disciplines that provide
insight into the systematic approach to the problem raised. The essence of the ap-
proach is that any task should be considered in terms of its influence on the criteria of
system functioning as a whole. An important feature of Operations Research is its
focus on seeking an optimal solution to the raised task (principle of “optimality”).
During the course learning the emphasis is put not on routine calculating procedures
but on the process of building mathematical models that are connected with designing
technical and technological processes, distribution of limited resources and planning
enterprise work, the solution to the problems that arise in a person’s everyday life.
Solving a range of various relative optimization problems with the help of a cloud
environment CoCalc is included in the course.
Objective of the course. The students have an opportunity to acquire the following
competencies:
• readiness to use the knowledge on Information technology, fundamental and ap-
plied Mathematics for the analysis and synthesis of the systems and processes;
• capability to use mathematical tools, programming methodology and modern com-
puter technologies for the optimization of practical tasks for information getting,
storing, processing and transferring;
• possession of modern formalized mathematical, information and logical – semantic
models and methods of information providing, collecting and processing;
• readiness to provide computer and technological process support to solve the tasks
of Operations Research in computer mathematics system of CoCalc;
• capability to use modern information and communication technologies to create,
form and represent the received modeling results.
Requirements to course users. Students need to have an account in the environ-
ment CoCalc [6] (previous name SageMathCloud). Since the environment supports
the technology of web-cloud computing (SaaS), it is necessary to set up a random
browser on the computer. For convenient group work while doing the course, it could
be recommended to arrange a prepayment (prices start from $14 per month). This will
provide more resources to store, calculate and increase the quotes on one project
which is used for several accounts.
The organization of learning course modules is directed at students’ acquiring cer-
tain competencies.
During the course, students review models of operations research, methods of their
construction and analysis and learn to work in the CoCalc environment. When master-
ing the elements of the resource allocation and inventory management theory, course
users apply the concept of a definite integral. When studying waiting-line problems,
students use Markov chains with discrete and continuous time to solve systems of
equations, find their exact and stationary solutions. Performing such activities con-
tributes to the development of students’ readiness to apply knowledge of computer
science, fundamental and applied mathematics for the analysis and synthesis of sys-
tems and processes.
The ability to use mathematical tools, programming methods and modern computer
technology to optimize the practical tasks of obtaining, storing, processing and trans-
mitting information is improved when working with ready-made templates in CoCalc.
The participants in the course have to modify the given templates according to the
model they have built. They should save the template to their folder in the system and
then work with it. Also for each fragment they are given a brief theoretical infor-
mation on the functions included in the templates and algorithms for working in the
system. Such activities contribute to forming the course users’ readiness to provide
computer and technological support for the process of solving the operations research
tasks in the CoCalc computer mathematics system.
At the end of each course module, its participants have to perform a certain part of
a comprehensive research work on stock planning for the chosen enterprise. The stu-
dents will need to determine for themselves what data they need and then collect it.
Execution of projects by students helps to increase their mastery level of modern for-
malized mathematical, informational and logical-semantic models and methods of
presentation, collection and processing of information. Upon completion of the
course, the students are to perform research work and present the results. The imple-
mentation of such activities contributes to the formation of the ability to use modern
information and communication technologies to create, form and present the results of
modeling.
The student can choose his/her own learning pace while doing the modules. Check-
ing the level of acquired competencies is planned to be carried out through expert
assessment of the projects completed by students. We also plan to use peer assess-
ment with results discussion on the platform forum “Higher School Mathematics
Teachers” [33]. Students will be offered the evaluation criteria in order to implement
this part of the task. When the course is finished the students get a certificate about
their results.
3 Results
While creating the online-course syllabus “Operations Research Oriented on Cloud
Computing in the system CoCalc” [7], we followed the concept that using computer
mathematics systems allows focusing teachers’ attention on the modeling process
during teaching a course. Thus, while designing a survey for teachers and students the
authors of this paper aimed at studying the views on improving the course through
engaging computer mathematics systems. Respondents’ answers to the survey ques-
tions helped us to get a sense of it. The survey for Operations Research course teach-
ers included 10 questions and for students – 8 questions and it was designed using an
open online service Google Forms, posted on the platform “Higher School Mathemat-
ics Teacher” [33].
We got the responses of 71 higher school mathematics teachers, among them
57,3% teach Operations Research course in higher schools, and 15,4% – use methods
of Operations Research in practice. This demonstrates that the answers to survey
questions also include practitioners’ opinions. Also, 41 students joined the problem
research, among them, 62,5% studied/study Operations Research course in higher
schools and 37,5% – studied/study Operations Research course independently. Thus,
the majority of students (53, 5%) studied most course topics at a sufficient or deep
level. At the same time, there are some topics (Markov chains with continuous-time,
Johnson’s issues, etc.), that in students’ opinions are important, but they were not
considered during the course. Also, teachers (34,3%) marked an insufficient methodi-
cal development of these topics. Regarding the offered themes most respondents (stu-
dents and teachers) agreed that the course should consist of:
Module 1. Methods of economic-mathematical modeling – 82,3%;
Module 2. Tasks and models of the optimal resources distribution and stock man-
agement – 71,7%;
Module 3. Mass service tasks – 69,1%;
Module 4. Ordering and coordination tasks – 54,3%.
Respondents-teachers’ idea regarding the use of computer mathematics systems
during teaching Operations Research is more conservative. Only 13,5% believe that
CMS should be used and 51,3% – that it is rather relevant. These results are con-
firmed by students’ responses, the majority of whom point out that while learning
Operations Research course they were not offered the tasks that required the use of
computer mathematics systems and their use in the course is very insignificant
(82,3%), but all the respondents-students noted that there is need to use such systems
in the course.
Meanwhile, most respondents-teachers marked organizational and psychological-
pedagogical advantages of implementing computer mathematics systems in Opera-
tions Research (see Fig. 1 and Fig. 2). A significant number of respondents (57.9%)
note that the advantage of using CMS is the increase in students' interest in learning.
A smaller number of respondents (21.1%) bring out as an advantage the development
of students’ intellectual abilities. The authors of this paper believe that this view is
caused by the stereotype about using CMS and want to show the course participants
that the removal of a big number of routine calculations will enable them to spend
more time in the modeling process, which will undoubtedly contribute to their intel-
lectual abilities. Moreover, 52.6% of respondents chose the possibility of mathemati-
cal modeling among the organizational advantages of the course.
Fig. 1. Organizational advantages of using computer mathematics systems
Fig. 2.Psychological-pedagogical advantages of using computer mathematics systems
82.3% of respondents demonstrated that they have a sufficient level of awareness
about the capabilities of cloud CMS. At the same time, few teachers and students
pointed out that they have a sufficient awareness level concerning the CoCalc system
of learning management. 57, 9% of teachers explained it as the lack of scientific-
methodical recommendations of using this CMS and the lack of mathematics courses
with the orientation on cloud computing in the system. Also, teachers pointed out the
necessity to devote additional time to programming while solving tasks. All the re-
spondents stated that they are willing to improve their knowledge in Operations Re-
search and get an experience of implementing CoCalc while solving tasks.
4 Discussion
Numerous examples provided by N. Finlay and M. King [34], prove that optimal
solutions increase the efficiency of processes by 10-40% under the condition that the
operations research method is applied to the model. The researchers rely on these
statistics and conclude that professionals make more effective decisions when using
operations research compared to their colleagues who are unaware of this science.
C. Keller and J. Kros [35] cover the problem of training Operations Research within
Master of Business Administration (MBA) program. The scientists believe that the
course is an important part of a training program that concentrates on strong interdis-
ciplinary connections. U. Kohut [14] studies employers’ opinion regarding the practi-
cal training of graduates. He mentions that their level of readiness for the application
of research methods does not meet modern requirements and is not sufficient. Accord-
ing to the scientist, the reason for this is the lack of communication between students
and the lack of projects that are related to actual practice. C. Keller and J. Kros [35],
U. Kohut [14], N. Ahuja [36] analyze the causes of these problems. The researchers
also say that insufficient use of computer mathematics systems in teaching Operations
Research is the cause of the shortcomings. The authors of this paper took into account
the works of the following scientists: I. Lovianova et al. [16], O. Markova et al. [17],
V.N. Kozhukhova et al. [37] and selected the virtual online computer lab CoCalc to
be used while teaching Operations Research. The choice of this learning management
system is based on its advantages, including the ability to write and compile program
code inside, with support for different programming languages. The authors of this
study also took into account the opinion of A.M. Geoffrion [38], who pointed at the
theorizing of this course in most universities and noted that advances in computer
technology would greatly simplify the process of solving the developed mathematical
model.
While searching for factors that influence the effectiveness and satisfaction with
learning mathematical modeling, the authors of this paper analyzed the study of
H. Kauffman [39], K. Vlasenko et al. [40], L. Panchenko [41], K. Vlasenko et al. [42],
I. Lovyanova [43]. The researchers singled out online learning as one of the effective
ways of non-formal education. The authors of this study share the opinion of
H.A. Henson et al. [44], who called Syllabi as a coursemap of any online course. To
prepare the complete syllabus for Operations Research Oriented to Cloud Computing
in the System CoCalc, the course developers collected and evaluated all the infor-
mation (results, assessments, actions and content).
While pointing out the learning outcomes, the course tutors relied on the conclu-
sions made by C. Campbell et al. [45]. According to these scientists, checking learn-
ing efficiency through the level competencies formation is the most adequate strategy
of lifelong learning. To prepare learning material for presenting a short description of
the modules the authors of this research oriented at the recommendations given by
M. King [46], K. Vlasenko et al. [47] and selected such course tasks that do not re-
quire formalization in the form of mathematical symbolism. The course developers
believe that students will only need to select and correctly interpret the data to enter
them into the CoCalc system. This approach, according to W.J. Erikson and
E. Turban [48], should lead to a significant increase in interest in the operations re-
search, reduce fear of mathematics and computers, and improve problem-solving
ability. In order to show the course participants the details of using the CoCalc system
and the correct interpretation of the results, the course developers focus on where
exactly the necessary information is in the results of the system work and how to use
them in practice.
The discussion of Syllabus and course materials on the platform [33] will help the
course developers to improve it in accordance with the participants’ needs. Students’
engagement in course development through discussions at the forum will encourage
their desire to work in the course.
5 Conclusions and Future Studies
The survey of the resources and scientific research confirmed the conclusion about
the necessity of developing a course in which the issues of implementing cloud com-
puting for solving optimization tasks will be considered. The review of the features of
the Operations Research course showed that it contributes to the formation of stu-
dents' ability to develop mathematical models on which most interdisciplinary math-
ematics courses are built. This explains the choice of subject for course development.
The analysis of the capabilities of cloud-based environments confirmed the feasibility
of using the CoCalc system, the components of which will help the course developers
to prepare quality teaching materials and dynamic models. It is substantiated that the
placement of the “Operations Research Oriented to Cloud Computing in the CoCalc
system” [7] online course on the Higher School Mathematics Teachers platform [33]
should begin with the creation of the syllabus.
The analysis of the recommendations, developed by the experts on working out
online courses, contributed to working out the syllabus sections: Summary of the
Course, Course Objective, Requirements to the Course Users, and Arrangement of the
Learning Process. A review of online resources sharing the experience of teaching
Operations Research helped to identify a methodology for providing the content for
these sections. While developing the summary of the course and the course objective,
its developers clarified the expectations of future course users, who consisted of both
mathematics students and teachers. In selecting the topic for the course, its authors
took into account the desire of the respondents to master the models of operations
research, their construction and analysis methods, as well as gain experience in en-
gaging CoCalc in solving optimization problems. In formulating the requirements to
the course users, the developers of the online syllabus found out the minimum re-
quirements for engaging the CoCalc system for the convenient organization of stu-
dents’ independent and group work during the course. Arrangement of the Learning
Process aims to attract students to the learning environment, which promotes positive
motivation through a clear message of high expectations and confidence in the im-
plementation of projects that will be encountered during hard work.
Uploading materials of the Operations Research Orientated to Cloud Computing in
the CoCalc System on-line course [7] to the Higher School Mathematics Teacher on-
line educational platform [33] is our focus of further research. The direction for fur-
ther research implies describing the implementation of the on-line course into practi-
cal training of the students majoring in Mathematics in teacher training universities.
6 Acknowledgments
We are grateful to the teachers and students who took part in the survey that help to
define the essence of the issues that arise during learning the topics connected with
optimization tasks and define the methods of solving these issues.
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