CoCalc Tools as a Means of Open Science and Its Didactic Potential in
the Educational Process
Pavlo V. Merzlykin
1 a
, Maiia V. Marienko
2 b
and Svitlana V. Shokaliuk
1 c
1
Kryvyi Rih State Pedagogical University, 54 Gagarin Ave., Kryvyi Rih, 50086, Ukraine
2
Institute for Digitalisation of Education of the National Academy of Educational Sciences of Ukraine, 9 M. Berlynskoho
St., Kyiv, 04060, Ukraine
Keywords:
CoCalc, Cloud Oriented Environment, Informatics Disciplines, Mathematical Disciplines.
Abstract:
The article covers the questions of expedient CoCalc environment use as an integrator of services that can
be used during different kinds of learning activities. Research goal is to identify the structural elements of
the CoCalc environment, which are suitable for informatics and mathematical disciplines learning within the
context of open science. Research objectives: a) consider the structure of the CoCalc environment kernel; b)
highlight the structural elements that may be used in informatics and mathematical disciplines learning, and
c) explore the prospects of their use. The object of research is the computer-oriented study of informatics and
mathematical disciplines. The subject of research is the use structural elements of the CoCalc environment
in informatics and mathematical disciplines learning. Research methods used: CoCalc environment analy-
sis, comparison of its structural elements and their generalization according to informatics and mathematical
disciplines. In the work analyzed, generalization and systematization of the major structural elements of the
cluster CoCalc, reviewed the characteristics of items that can be used in the informatics and mathematical
disciplines study. Results of the research will be used to improve methods of computer-based informatics and
mathematical disciplines learning.
1 INTRODUCTION
Even before Computer Science disciplines studying,
the programming basics may be taught directly within
other courses. This is particularly true in the case
of practically used methods and concepts. It may
be considered as one of the ways to integrate prac-
tical programming exercises into other courses. We
mean focused on the conceptual level rather than pure
programming exercises, so that students learn more
about speciﬁc computational methods and concepts.
It is desirable that in the process of computer sci-
ence learning one of the leading places was given to
students’ cooperative problem solving that will allow
students to learn from each other and all together. As
for collective structure, universal access is a key prin-
ciple for learning in a modern higher education insti-
tution (HEI). After all, universal access is one of the
principles of open education and open science, which
is now being widely implemented in higher education
a
https://orcid.org/0000-0002-0752-411X
b
https://orcid.org/0000-0002-8087-962X
c
https://orcid.org/0000-0003-3774-1729
in Ukraine. Solving together the same problem cre-
ates an atmosphere in which joint learning is an inte-
gral part of everyday practice in the learning environ-
ment.
Also, students, researchers, and teachers are sub-
jects of the same information environment; they are
equal community members (users) without a certain
hierarchical structure. However, in reality there is a
strict formal hierarchy in modern universities. There-
fore, the question of the relationship between infor-
mation environment users is quite topical. Because
the difference between teachers and students is in fact
quite clear, management in the digital environment is
related to a structural hierarchy. Lecturers have not
only to teach the content of their courses. Their task
is also to maintain the existing conﬁguration of the
information environment (at least in terms of content)
as well as to advise students in case of technical prob-
lems. However, it should be noted that in the digital
environment, relationships unite all users: students,
teachers, and researchers (Klaßmann et al., 2020).
There are another two problems in interdisci-
plinary relationships. First, social sciences and nat-
Merzlykin, P., Marienko, M. and Shokaliuk, S.
CoCalc Tools as a Means of Open Science and Its Didactic Potential in the Educational Process.
DOI: 10.5220/0010921000003364
In Proceedings of the 1st Symposium on Advances in Educational Technology (AET 2020) - Volume 1, pages 109-118
ISBN: 978-989-758-558-6
c
2022 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
109
ural sciences students have to put in a great deal
of effort while perceiving information literacy ma-
terial and have some difﬁculties in performing com-
putational tasks. Humanities students often demon-
strate a certain distance in the perception of compu-
tational approaches in general. Second, the variety
of computing systems, methods, and concepts com-
plicates the transparency, comparison, reproducibil-
ity, and transmission of results. Moreover, taking into
account such a variety of calculation services, it is
almost impossible to develop uniform methodologi-
cal teaching standards. Therefore, not only informa-
tion and communication technologies (ICT) courses
are needed, but also it is necessary to integrate edu-
cational computer systems and research support sys-
tems (specialized, for scientists). This approach will
help to strengthen the scientiﬁc component of stu-
dents training not only in the humanities but also in
technical specialties. In addition, such an integra-
tive mechanism should promote the development of
the students and researchers community within a sin-
gle information space. The single digital environment
meets the objectives and offers such integrating tools.
Science is a joint activity by deﬁnition. Research
is usually conducted by several scientists working to-
gether, and this idea has been constantly conﬁrmed
in recent years. Moreover, experiments are increas-
ingly being conducted in cloud services or with the
use of cloud platforms, which involves the use of
appropriate tools to support experimental activities.
Workﬂow management systems and scenario-based
tools are popular ways to conduct experiments, but
these tools do not always support the idea of col-
laboration between a group of scientists. Even so-
lutions aimed at collaborative experiments do not al-
ways meet the needs of users. Cloud service tools
often focus on computing, but collaborating within a
single environment is usually underestimated. Even if
a certain cloud-oriented environment supports a work
or learning management function, the group work is
not considered enough in the framework of solving a
speciﬁc pedagogical problem. Our research therefore
was aimed primarily at the study of available tools for
students’ group tasks performing, joint research, and
open access to research results. An experimental re-
search carried out by a group of students, scientists
and teachers is rather a challenge of today. There is
an urgent need to identify every aspect of the collab-
oration between a group of students, faculty, and re-
searchers. The analysis should be based on the study
of current problems in the area from this aspect. In
particular, the evidence in the following paragraphs
suggests that the solution to some outlined problems
is possible through the use of cloud service tools as a
means of open science.
SageMath is an open-source computer algebra
system. It has been used in most research on issues re-
lated to algebra and geometry. However, open-source
cloud service has improved in recent years, and now it
supports collaboration, the use of Python, R, Jupyter,
LaTeX etc. Moreover, the CoCalc cloud service al-
lows teachers to customize the LMS environment.
Programming, the use of LaTeX, simulation these
are new skills in mathematics, and such environments
contribute to their development (Martines, 2020).
2 ANALYSIS OF RECENT
RESEARCH AND
PUBLICATIONS
Klaßmann et al. (Klaßmann et al., 2020) presents
a separate case study on the evolution of the digi-
tal learning environment and research at the Depart-
ment of Musicology, University of Cologne. It cov-
ers 14 seminars from 2016 to 2020. In particular,
the study examines the development of technological
conﬁguration as a digital environment and a curricu-
lum development, which consists of educational prac-
tice in digital literacy and contains interdisciplinary
links (Klaßmann et al., 2020).
de Assis Zampirolli et al. (de Assis Zampirolli
et al., 2019) studied MEGUA (Mathematics Exercise
Generator, Universidadede Aveiro) 2 open source
software that allows one to create data banks of pa-
rameterized questions with their corresponding an-
swers in LaTeX. It works with the mathematical soft-
ware CoCalc, which uses the Python programming
language (de Assis Zampirolli et al., 2019). Data
banks of questions are called “Books” and are built
with PDFLatex (for printing) or HTML and MathJAX
(for web publications) (de Assis Zampirolli et al.,
2019). The development of the issue, in fact, takes
place directly using the CoCalc toolkit. This process
consists of three steps:
1) on a new sheet, a cell is created to import the en-
tire MEGUA library and open / create a database
to store questions;
2) the question code is being typed into another cell,
which consists of LaTeX text and Python code.
The LaTeX block is divided into sections (cata-
loging and description of the exercise), “% of the
problem” (name and question) and “% of the an-
swer” (its solution);
3) CoCalc complements the part of the computation
that contains two functions: it generates random
AET 2020 - Symposium on Advances in Educational Technology
110
values for the operator, calculates the correct so-
lution and generates other multiple choices.
This cell yields two ﬁles: one in PDF format and
another in text format (de Assis Zampirolli et al.,
2019; Jandre et al., 2020).
There is also a resource for adding parameterized
graphs to tasks, but MEGUA is not equipped with au-
tomatic correction of printable copies of questions, a
function for rating hundreds of users.
The problem of developing a curriculum for
courses in the study of operations has been carried
out by Vlasenko et al. (Vlasenko et al., 2020). The
research focuses on the implementation of cloud com-
puting for solving optimization problems. The study
(Vlasenko et al., 2020) conﬁrms the appropriateness
of using the CoCalc cloud environment in student
teaching.
Bobyliev and Vihrova (Bobyliev and Vihrova,
2021) analyzed the experience of implementing
courses in Calculus and History of Mathematics for
future mathematics teachers in the learning manage-
ment system of Kryvyi Rih State Pedagogical Uni-
versity. There is a block-modular approach to cre-
ating courses, which allows not only to structure the
process of online fundamental mathematical subjects
studying, but also to control the students’ speed of
content mastering and the depth of knowledge. There
are examples of laboratory classes on the Calculus
taken by by students independently in the CoCalc sys-
tem of computer mathematics.
Gavrilyuk (Gavrilyuk, 2020) outlines the prob-
lems of using cloud services under the quarantine
conditions. The scientist considered the possibilities
of using cloud technologies for distance learning un-
der precautionary measures, in particular, a key place
among cloud services is occupied by CoCalc. An
overview of cloud services that may be used to study
Mathematics and Statistics related disciplines as well
as their brief characteristics is offered.
The aim of the study is to identify the structural
elements of the CoCalc environment, that it is appro-
priate to use in the educational process in the context
of open science.
3 RESULTS
CoCalc (Collaborative Calculation and Data Sci-
ence; cocalc.com) is a virtual online workspace
(cloud-based environment) for calculations, research,
authoring documents in collaboration mode.
The learning and scientiﬁc activities in the CoCalc
environment involve working on a project. The el-
ements of a project are folders and ﬁles in different
formats.
It is through the project ﬁles that the student
and/or scientist accesses the main components of Co-
Calc explicitly (ﬁgure 1) or through an “intermediary”
(ﬁle type “X11 desktop”, ﬁgure 2).
According to CoCalc’s statistics over the last
month, the most popular environment instrumental
and applied components are Jupyter Notebooks, Sage
Worksheets, LaTeX Documents and R Markdown
Documents.
The popularity of Jupyter Notebooks is obvious.
Because it is on Jupyter Notebooks that you can mod-
eling (calculate, programming, etc.), with the func-
tionality of SageMath or Python or R or Julia.
Before talking about the already popular tools
(SageMath, Python, R, LaTeX), let’s focus on the lat-
ter mentioned, Julia.
Julia is a high-level, high-performance program-
ming language with dynamic typing for mathematical
calculations. The syntax is similar to the matlab fam-
ily, the language is written in C, C++ and Scheme, it
is possible to call C libraries.
Julia was designed from the beginning for high
performance. Julia programs compile for efﬁcient na-
tive code for multiple platforms via LLVM.
Julia plays dynamically, is a scripting language
and has good support for interactive use.
Playable environments make it possible to play the
same Julia environment every time, on different plat-
forms, with pre-built binaries.
Julia uses multiple sending as a paradigm that fa-
cilitates the expression of many object-oriented and
functional programming patterns. Provides asyn-
chronous I/O, metaprogramming, debugging, log-
ging, proﬁling, package manager, and more. You can
create entire programs and microservices in Julia.
Julia is an open source project with more than
1,000 authors. It is provided under MIT.
But ﬁrst of the stages in the development of the
CoCalc is a web Computer Mathematical System
(web-CMS) SageMath.
SageMath is a free open-source mathematics soft-
ware system based on many existing open-source
mathematical packages FLINT, GAP, Matplotlib,
Maxima, NLTK, Numpy, Pandas, Scikit Learn, Scipy,
Statsmodels, SymPy, and many others. They can
be accessed using a generalised language based on
Python, or directly through interfaces or shells.
The available web-CMS tools of SageMath ver-
sion 4.6 (the latest version before the advent of Co-
Calc, even earlier than SageMathCloud) were not suf-
ﬁcient to organize all types of learning activities un-
der distance learning or its elements. It was neces-
sary either to organize training or with the involve-
CoCalc Tools as a Means of Open Science and Its Didactic Potential in the Educational Process
111
Figure 1: Page to create a new project ﬁle.
ment of two systems web-CMS SageMath and any
system to support distance learning, such as Moodle,
or to integrate them. The ﬁrst method proved to be in-
convenient for neither teachers nor students, the sec-
ond method – continues to be widely used (Shokaliuk
et al., 2020), but it, with the advent and improvement
of CoCalc, may lose relevance.
Since 2014, more than 80 students have com-
pleted the courses “Computer Technologies in Re-
search” and “Computer Mathematics” for future com-
puter science teachers with the additional qualiﬁca-
tion “applied programmer”. The SageMath toolkit in
CoCalc became especially popular with the advent of
the ability to work on interactive Jupyter Notebooks
instead of Sage Worksheets (Markova et al., 2018).
While the latter has the advantage of being able to
work simultaneously (within one sheet) with different
mathematical applications.
In addition, future teachers of mathematics and
computer science were offered to master the tools
of SageMath in CoCalc within the optional course
“Using SageMathCloud in learning mathematics” (by
Maiia V. Marienko), the course “Numerical Meth-
ods / Methods of Computing / Computational Math-
ematics”, “Discrete Mathematics”, “Operations Re-
search”, “Mathematical Programming”, as well as to
perform independent work on the courses “Linear Al-
gebra and Numerical Systems”, Analytical and Dif-
ferential Geometry”, “Calculus”, “Probability Theory
and Mathematical Statistics”.
The mathematical packages FLINT, GAP, Mat-
plotlib, Maxima, NLTK, Numpy, Pandas, Scikit
Learn, R, Scipy, Statsmodels, SymPy, TensorFlow are
known as members of the Python Scientiﬁc Comput-
ing Ecosystem or more simply Scientiﬁc Python be-
cause they provides data processing (modeling, exper-
iment control) and visualize results for quick analysis
with high-quality metrics for reports or publications.
Among the tools mentioned, the packages Tensor-
Flow and R are of particular note.
TensorFlow is a comprehensive open source plat-
form for machine learning. It has a comprehensive
ﬂexible ecosystem of community tools, libraries, and
resources that allows researchers to advance the lat-
est advances in machine learning, and developers can
easily create and deploy machine-based applications.
R is an integrated suite of software facilities for
data manipulation, calculation and graphical display.
Among other things it has
an effective data handling and storage facility;
a suite of operators for calculations on arrays, in
particular matrices;
a large, coherent, integrated collection of interme-
diate tools for data analysis;
graphical facilities for data analysis and display
either directly at the computer or on hardcopy;
a well developed, simple and effective program-
ming language (called ‘S’) which includes con-
ditionals, loops, user deﬁned recursive functions
and input and output facilities. (Indeed most
AET 2020 - Symposium on Advances in Educational Technology
112
Figure 2: Page of a new ﬁle of type “X11 desktop”.
Table 1: The main components (components, software) CoCalc: System software.
Type of software Name of the software
Request and process user account information accountsservice
FTP client CFTP
VNC server X11vnc
Archiver 7-ZIP, gzip, tar
Free command line utility for data compression bzip2
Garbage collector The Boehm-Demers-Weiser
Shell for GNU Screen and Tmux (application) Byobu
Shell for Python GD library gdmodule
Program for displaying a list of running processes htop, ps
SageMath Notebook Server SageMathNB
Operating System Debian GNU/Linux
of the system supplied functions are themselves
written in the S language.)
R is very powerful tool for newly developing
methods of interactive data analysis. It has developed
rapidly, and has been extended by a large collection
of packages.
Since September 2018, almost 50 PhD candidates
have been involved with the R toolkit in CoCalc and
have successfully completed the Modern Information
and Communication Technology in Research course.
To support cumbersome scientiﬁc calculations,
there is a need to reduce the computational delay.
Edge computations adopt a decentralized model that
brings cloud computing capabilities closer to the user
equipment to reduce computational latency. There are
two types of projects in CoCalc: “trial (free) projects”
and “participating projects”. Trial projects run on
computers that share the same node with many other
projects and system tasks. These nodes may also stop
at any time, causing the current project to interrupt
and restart.
Projects accepted by members are transferred to
less loaded machines, which are reserved only for
users who have purchased one of the proposed li-
censes (tariff plans). Those servers are not being
restarted daily. The cluster is dynamically scaled to
accommodate different numbers of member projects.
Work on members projects is much smoother be-
cause commands are executed faster with less delay,
and heavy operations of the processor, memory and
I/O work faster.
By default, free projects stop working after about
CoCalc Tools as a Means of Open Science and Its Didactic Potential in the Educational Process
113
30 minutes of inactivity. This makes the calculations
quite time-consuming.
There is an advanced license option to completely
prevent downtime. Processes can still stop if they use
too much memory, crash due to an exception, or or
being restarted by the server on which they are run-
ning.
That is, for users who have purchased one of the
proposed tariff plans, there are more opportunities to
use edge calculations.
Also, it is possible to change the free tariff plan
(default) Hub server by clicking “Reconnect” (ﬁg-
ure 3). To some extent, this setting may also be con-
sidered as a practical use of edge computing (Chen
et al., 2016).
Figure 3: Pop-up settings “Connection”.
In addition, we should mention Big Data. The
complexity arises from several aspects of the Big Data
lifecycle, such as data collection, storage on cloud
servers, data cleaning and integration. But edge com-
puting solves this problem, which is an essential point
for working with CoCalc.
CoCalc offers a wide collection of software envi-
ronments and libraries (see tables 1-4).
A complete list of the current versions of Co-
Calc (1267 Python packages, 4472 R packages, 447
Julia libraries and more than 243sd ﬁles have been
installed) can be obtained by using the command
$sudo dpkg --get-selections. Detailed information on the speciﬁed in tables 1-4 and other CoCalc components (at the time of publication) can be obtained by direct link https:// cocalc.com/help on the ofﬁcial website of the CoCalc project. Implementation of research projects, term papers with the use of CoCalc involves two ways: 1. Using the individual tools presented in CoCalc. 2. Execution, writing and registration of results of educational and research work in CoCalc without involvement of auxiliary software. At the same time, teachers and a group of students can be involved in the research project. The IPython interpreter in the process of train- ing future mathematics teachers can be used to de- velop dynamic models with semi-automatic / auto- matic demonstration modes. The ﬁrst way involves creating a model (models) of the phenomenon under study on a worksheet using standard controls, HTML tags, LaTeX commands and using CSS. The disadvantages of this use are that in the pro- cess of registration of the obtained results have to in- volve other software: text editor, software for creating presentations, video editor (if necessary). As a result, only a certain point of the research work was per- formed using the CoCalc toolkit. In addition, in the process of presenting scientiﬁc ﬁndings, the student will have to demonstrate to their colleagues in addi- tion to the presentation of the developed model using a browser (or video editor). This can be avoided by using CoCalc tools not only to perform the research part of a particular job. Therefore, it is better to use the built-in LaTeX editor as a CoCalc tool. LaTeX is a high-quality text document program. LaTeX is a TeX-based macrosystem that aims to simplify its use and automate many common format- ting tasks. This is the de facto standard for academic journals and books, and it offers one of the best free typography programs it has to offer. Performing a term paper or a thesis in the LaTeX editor, the student has the opportunity to print it, pre- formed on the basis of a resource such as tex PDF- document. That is, at the same time there is a process of reg- istration of the obtained results, calculations, presen- tation and presentation of the main provisions of the study (using the presentation developed in the LaTeX editor) and demonstration of the created model. The student does not need to include additional software to perform, design or present the results, because all the work is completely uniﬁed within one cloud ser- vice – CoCalc. \documentclass{article} \usepackage[a5paper]{geometry} \usepackage[utf8]{inputenc} \usepackage[ukrainian]{babel} \usepackage{sagetex} \title{Sharing Sage and LaTeX} \author{M. V. Popel} \date {13 January 2015 year} \begin{document} \maketitle The easiest way to embed the results of Sage commands in the tutorials created in LaTeX is to use the sage and sageplot tags:" a) finding the derivative:$(xˆ3)’=\sage{diff(xˆ3,x)}\$
b) plotting:
\sageplot{plot(sin(x),-pi,pi)}
\end{document}
AET 2020 - Symposium on Advances in Educational Technology
114
Table 2: CoCalc main components: General purpose application software.
Type of software Name of the software
Analog screen for graphics programs Xpra
Database of combinatorial graphs Graphs
Library for rasterization of fonts and operations on them FreeType
Library for working with raster graphics in PNG format Libpng
GNOME tooltip browser Yelp
File management and collaboration system Mercurial
Electronic dictionary (thesaurus) WordNet
Image viewer GPicView
Interactive editor and macro support Prerex
Programs for comparing the contents of text ﬁles and directories Meld, diff
Services for reading e-books Calibre, Evince
Document processing system in HTML, LaTeX or XML document formats Docutils
Database management systems RethinkDB, sqlite3
Text editors GNU Emacs, Vim,
nano, mcedit, AbiWord
Utility for ﬁnding differences between ﬁles GNU patch
Cloud ﬁle storage Dropbox
You can of course offer an alternative to CoCalc –
Jupyterhub and Zoom. However, they do not in-
clude the ability to synchronize with other commu-
nity members in a text ﬁle, although Zoom has a basic
real-time chat feature. Of course, you can offer to in-
tegrate the Markdown hypertext into the conﬁguration
by using the Jupyter Notebook, which seemed to be
the ideal solution to enable collaboration in a browser-
based text document in real time using Zoom, for ex-
ample in workshops. In addition, HackMD Mark-
down ﬁles will be available to students at any time
and will be used for notes during the workshop. In
this way, you can create joint documents that imple-
ment synchronous and asynchronous discussions. In
addition, HackMD will provide tools for document-
ing group work sessions so that it is easy to share with
other users. In this way, you can create templates for
courses that will be used later for notes, discussion
of seminar topics outside the classroom. Currently,
Jupyterlab does not allow real-time collaboration on
real-time collaboration due to technical limitations.
CoCalc offers shared computing capabilities to
small groups of users. It also includes basic chat and
video conferencing features. CoCalc toolkit supports
student projects and group assignments that require
synchronous collaboration in computer science and
math. Because CoCalc is also based on the Jupyter
Notebook, integration with individual workspaces
will be seamless, as users in the same group can eas-
ily transfer individual ﬁles between CoCalc to both
the shared workspace and their own, private instance
of Jupyterlab. Using the advanced conﬁguration with
Zoom, HackMD and CoCalc, seminars can be orga-
nized completely remotely (Klaßmann et al., 2020).
Overall, this conﬁguration is a good starting point
for the further evolution of the digital environment
and the management of a group of students to increase
digital literacy in interdisciplinary research and the
teaching of computer science and mathematics. To
assess the cloud environment, it is necessary to take
into account both the student’s opportunities and in-
teraction with them, as well as the success in achiev-
ing interdisciplinary learning goals and the level of
discussion of the content achieved in seminars. Co-
Calc cloud service can be recommended to groups of
students of all academic levels, from bachelor to doc-
toral and teachers of various ﬁelds of science. The
use of a single cloud platform has certain advantages:
it will help to form and hold regular meetings to dis-
cuss modern computational approaches in interdisci-
plinary research. This creates a digital environment
for developing students and researchers that goes be-
yond weekly seminars. From the point of view of
teaching, seminars conducted in one case study will
conﬁrm the potential of a common information envi-
ronment for teaching computational interdisciplinary
research. Thus, students with limited programming
experience or no previous programming experience
during distance learning workshops will be able to
fully learn the basics of Python programming and
gain skills in discussing and implementing high-level
computational models (Klaßmann et al., 2020).
The evolution of the conﬁguration of the digital
environment demonstrates clear progress, which is
closely linked to the requirements of pedagogical and
methodological practices within the developing free
CoCalc Tools as a Means of Open Science and Its Didactic Potential in the Educational Process
115
Table 3: CoCalc main components: Special purpose application software.
Type of software Name of the software
Automatic grid generator for geometric constructions Gmsh
Software package for algebraic, geometric and 4ti2
combinatorial problems on linear spaces
Library for performing problems in number theory FLINT
Library for dynamic work with images GD Graphics Library (GD)
Library for processing video and audio ﬁles Ffmpeg
Library for working with graphs and other network structures NetworkX
Library for solving linear programming problems GLPK
Library for solving convex programming problems CVXOPT
Library designed for applied and scientiﬁc mathematical GNU Scientiﬁc Library (GSL)
calculations
Libraries for determining and calculating elliptic curves eclib
deﬁned over a ﬁeld of rational numbers
Vector graphic editor Inkscape
Sage versions Sage.7, Sage.8, Sage.9, Sage.10
Client for Git repository SparkleShare
Mathematical library Cephes
Mathematical library for performing actions on complex numbers GNU MPC
A set of libraries that extend the functionality of C++ Boost
SageTeX package extension SageMathTeX
Software package for generating three-dimensional models GenModel
Software package for scientiﬁc calculations Scilab
Software packages for building phylogenetic trees Phylip
System for mathematical calculations GNU Octave
Computer algebra systems Gias/Xcas, Axiom, GAP
Computer mathematics system Maxima
economic system, students and researchers. Thus, the
resulting conﬁguration for the introduction of com-
putational thinking and digital literacy consists of the
following tools that support the necessary functions in
a single digital environment:
Jupyter Notebook, which is serviced through
Jupyterhub, will provide a basic environment for
notes, programming and working with computa-
tional methods and concepts without the need for
local installation and maintenance.
GitHub, GitHub Pages, and GitHub Classroom
will be used to track ﬁle versions, create a course
website as an alternative communication channel,
and support the logistics of issuing and submitting
course assignments.
Zoom will provide a tool for interactive syn-
chronous social communication in distance and
face-to-face learning.
HackMD is used for synchronous co-writing of
hypertext documents.
CoCalc provides collaborative real-time program-
ming based on the Jupyter Notebook.
4 DISCUSSION
The roadmap for Ukraine’s integration into the Euro-
pean Research Area (ERA-UA) has been approved by
the decision of the Ministry of Education and Science
of Ukraine No. 3/1-7 on March 22, 2018. Priority 5
contains a sub-item, which indicates the further direc-
tions of open science development in Ukraine. Open
science means revealing a research process by pub-
lishing all its results as well as details on how they
have been achieved and making them publicly avail-
able on the Internet.
The practical use of the open science paradigm is
(Shyshkina, 2018): presentation of educational mate-
rials in open access (data, program of the event, ab-
stracts, minutes of meetings, didactic materials, data
analysis ﬁles); open access materials publication; free
distribution and dissemination of educational and sci-
entiﬁc materials and data (for example, uploading
content to an open repository).
If we consider the principles of open science, then,
according to Shyshkina (Shyshkina, 2018), it means
(Shokaliuk et al., 2020):
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Table 4: CoCalc main components: Software tools.
Type of software Name of the software
Interactive shell for programming Jupyter Notebook
Python programming language Python 2.x, Python 3.x,
interpreters Python (Anaconda)
C ++ programming language compilers C++
Interpreters CPython, Java, Perl, bash
Compilers Mono, Embeddable Common Lisp
Functional programming environments DrRacket, MIT/GNU Scheme
Environment for statistical calculations, R
analysis and presentation of data in graphical form
open access to electronic resources used during
the study;
free access to data arrays obtained during a peda-
gogical experiment;
open e-infrastructures.
A common example of open source is the large
number of open source virtual learning environments
used in the academic environment. The most striking
example is Moodle due to its widespread use in edu-
cational institutions (Mintii et al., 2019; Polhun et al.,
2021).
As a consequence, the introduction of open sci-
ence norms in Ukraine should lead to greater ex-
change, accountability, reproducibility and reliability
of scientiﬁc materials and affect the learning process
as a whole. In the process of studying domestic and
foreign experience, the following advantages of using
cloud services for mathematical purposes were iden-
tiﬁed: resource savings; access mobility; ﬂexibility.
Cloud platforms and services engaging with the
educational process leads to the emergence and devel-
opment of education and research organization forms
focused on joint educational activities, creating more
opportunities for educational and research projects
(Merzlykin et al., 2017; Popel et al., 2017; Lovianova
et al., 2019). Methods and approaches of open science
have a signiﬁcant impact on the educational process.
Given the above advantages of cloud-based tools in
the mathematical disciplines teaching, as well as the
prospects of the CoCalc cloud service implementa-
tion in the educational process, the study considers
this service to be a potential cloud component of open
science.
CoCalc is a cloud service, a virtual workspace for
computing, research, collaboration and document cre-
ation (Jandre et al., 2020), which contains a cloud
storage where scientists may share ﬁles with their col-
leagues. These include Jupyter sheets, where multiple
scientists may edit scripts in real time.
CoCalc (Jandre et al., 2020) supports query, de-
tection and visualization subphases. This allows sci-
entists to query the results of the experiment and its
history, among other data. Users may also visualize
results using Jupyter sheets and libraries, such as mat-
plotlib. They may also use chats to discuss an experi-
ment and its stages.
In this cloud service (Jandre et al., 2020) the
whole experimental environment is based on the prin-
ciple of cloud operation. All changes are made di-
rectly in the cloud and synchronized with the user’s
browser via the Internet, that is to say, no blocking
occurs.
CoCalc (Jandre et al., 2020) allows one to share
a wide variety of ﬁles, including scripts in different
programming languages. The cloud service toolkit al-
lows you to share documentation that can help scien-
tists understand what has been done in the experiment
and help them make better use of shared data and sce-
narios.
The cloud service (Jandre et al., 2020) makes it
possible to store performed by scientists interaction
in a journal (chronology), but it resembles more un-
structured information that is difﬁcult to reproduce.
Although the cloud service is absolutely ready
for use in research (Jandre et al., 2020), it requires
a stable Internet connection to work. Working with
the service is possible directly through the browser,
which may cause some difﬁculties when replacing
the workspace, tools and development environments
to which the scientist is accustomed. You may run
code from the CoCalc environment, but this method is
different from running ﬁles from a scientist’s device.
There are some restrictions on using a free cloud ser-
vice account. Another problem worth mentioning is
that CoCalc does not properly capture all stages of the
experiment. It provides features such as “time travel”
and “log” that allow users to see the history of ﬁle
changes and activity of project participants. But these
data cannot be fully detailed so will be insufﬁcient to
guarantee the reproducibility of the experiment.
It may be concluded that CoCalc meets all the
CoCalc Tools as a Means of Open Science and Its Didactic Potential in the Educational Process
117
principles of open science. And CoCalc tools may be
considered to be open science tools that have didactic
potential in the learning process.
5 CONCLUSIONS
The given chronology clearly demonstrates creation
and adaptation of the digital environment on the ba-
sis of particular needs and practical tasks of group of
students, teachers and researchers in interdisciplinary
researches and educational process. As the digital en-
vironment is constantly evolving, research cannot be
considered exhaustive. We intend to integrate the con-
ﬁguration of CoCalc and the curricula of individual
disciplines for a deeper training material understand-
ing and to expand the means of professional compe-
tencies forming of future specialists in various ﬁelds
of education and science. CoCalc tools enhance stu-
dents’ ability to organize and perform teamwork by
implementing a joint project task. Thus, if the cloud
service is used, the indicators of scientiﬁc research
improve, the educational process becomes more open,
appropriate to human needs and content relevant.
Given the growing popularity of free software and
a wide range of CoCalc applications and services, it
should be noted that there is need to develop teaching
materials for Computer Science and Mathematics.
The use of cloud services leads to the emergence
and development of learning forms, focused on joint
learning activities on the Internet. Cloud services
should be used in Mathematics teachers training as a
means of: communication; cooperation; data storage
and processing, which should be the subject of fur-
ther research. It is advisable to focus further research
on the dissemination of open science approaches to
Mathematics teachers training process.
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