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

Kryvyi Rih State Pedagogical University, 54 Gagarin Ave., Kryvyi Rih, 50086, Ukraine

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

https://orcid.org/0000-0002-0752-411X

https://orcid.org/0000-0002-8087-962X

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

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

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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 scientiﬁc sources;

• 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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