=Paper=
{{Paper
|id=Vol-1844/10000396
|storemode=property
|title=The Systems of Computer Mathematics in the Cloud-Based Learning
Environment of the Educational Institutions
|pdfUrl=https://ceur-ws.org/Vol-1844/10000396.pdf
|volume=Vol-1844
|authors=Mariya Shyshkina,Ulyana Kohut,Maya Popel
|dblpUrl=https://dblp.org/rec/conf/icteri/ShyshkinaKP17
}}
==The Systems of Computer Mathematics in the Cloud-Based Learning
Environment of the Educational Institutions==
https://ceur-ws.org/Vol-1844/10000396.pdf
The Systems of Computer Mathematics in the Cloud-
Based Learning Environment of Educational Institutions
Mariya Shyshkina1, Ulyana Kohut2, Maya Popel1
1Institute of Information Technologies and Learning Tools of NAES of Ukraine,
9 M.Berlynskoho St., Kyiv, Ukraine
{shyshkina, popel}@iitlt.gov.ua
2Drohobych Ivan Franko State Pedagogical University, 24 I.Franko Str., Drogobych
(ulyana_kogut@mail.ru)
Abstract. The article highlights the promising ways of providing access to the
mathematical software in higher educational institutions. It is emphasized that
the cloud computing services implementation is the actual trend of modern ICT
pedagogical systems development. The analysis and evaluation of existing ex-
perience and educational research of different types of mathematical software
packages use are proposed. The methodological guidance on the organization of
the cloud-based learning environment in higher educational institutions using
the systems of computer mathematics (SCM) is outlined. The advantages and
disadvantages of different cloud service models of access to SCM are de-
scribed. The cloud-based learning component with the use of Maxima system is
described and evaluated. .
Keywords: Cloud computing, learning tools, mathematical disciplines, learning
environment, educational university.
Key Terms. Methodology, InformationCommunicationTechnology, ICTTool,
Educational Process.
1 Introduction
1.1 Research Objectives
Nowadays, the cloud computing is among the leading technological trends in the for-
mation of information society. This is the core of the innovative concepts of learning
and their implementations make significant impact on the content and forms of educa-
tion [2; 13; 16].
Cloud computing (CC) technology is used to enhance multiple access and joint use of
educational resources at different levels and domains, combining the corporate re-
sources of the university and other learning resources within a united framework.
Progress in the area has provided new insights into the problems of educational elec-
tronic resources provision and configuration within the learning environment, bring-
ing new models and approaches. These tools make the great impact of the data pro-
cessing changing the content, methods and organizational forms of learning, lifting
the restrictions or significantly improving the access for all participants.
A separate set of problems concerns to the application of software packages for the
implementation of various mathematical operations, actions and calculations, these
are the so-called Systems of Computer Mathematics (SCM), including Maple Net,
MATLAB web-server, WebMathematica, Calculation Laboratory and others [13; 19;
8]. This is one of the most common types of mathematical software, which is a part of
the modern educational environment of educational institutions [2]. The problems
emerge when searching for promising ways and models to use this type of cloud-
based tools being an essential factor of engineering and mathematics disciplines train-
ing quality improving.
The aim of the article is to analyze the state of the art of mathematical software use
and design within the cloud-based settings and evaluation of the cloud-based learning
component with the use of Maxima system.
1.2 The Problem Statement
According to recent studies [2; 10; 16; 3] the challenges of making the ICT-based
learning components of the university environment fit the needs of its users, have led
to the search for the most reasonable ways for their design and delivery within the
cloud-based settings. The cloud-based components possess many progressive features
including better adaptability and mobility, as well as full-scale interactivity, free net-
work access, a unified structure among others [2, 10, 12]. So, the modeling and analy-
sis of their design and deployment in view of the current tendencies of modern ad-
vance of the cloud-based mathematical software and available learning experience
have come to the fore.
Among the priority issues there are those concerning the existing approaches and
models for electronic educational resources delivery within the different cloud-based
service models; the cloud-based learning components elaboration, assessment and
testing; research indicators substantiation.
1.3 The Research Methods
The research method involved analysing the current research (including the domes-
tic and foreign experience of the cloud-based learning services and mathematical
software use in educational institutions in Ukraine and abroad), evaluation of existing
approaches to software delivery, their advantages and disadvantages; comparison of
promising ways of popular mathematical software implementation "in the cloud",
examining of models and approaches, technological solutions and psychological and
pedagogical assumptions about better ways of introducing innovative technology into
the learning process. The cloud-based component with the use of Maxima system
was designed and elaborated within the study undertaken in 2012-2014 in the Institute
of Information Technologies and Learning Tools of NAES of Ukraine devoted to the
use of the SCM for informatics bachelors training (U.Kohut). The special indicators
to reveal ICT competence of educational personnel trained within the cloud-based
learning environment and also the learning components quality evaluation indicators
were elaborated within the research work devoted to the university cloud-based learn-
ing and research environment formation and development held in 2012-2014 in the
Institute of Information Technologies and Learning Tools of NAES of Ukraine
(M.Shyshkina). To measure the efficiency of the proposed approach the pedagogical
experiment was undertaken in Drohobych Ivan Franko State Pedagogical University.
The expert quality evaluation of the CC-based components elaborated in the study
was implemented. The approach and methodology were grounded within the research
work “Methodology of the cloud-based learning environment of educational institu-
tion formation” that was held in the Institute of Information Technologies and Learn-
ing Tools of NAES of Ukraine in 2015-2017, Registration number 0115U002231
(coordinated by M.Shyshkina).
2 The State of the Art
According to the recent research [2; 5; 7; 15; 11; 14], the problems of cloud technolo-
gies implementing in educational institutions so as to provide software access, support
collaborative learning, research and educational activities, exchange experience and
also project development are especially challenging. The formation of the cloud-based
learning environment is recognized as a priority by the international educational
community [9], and is now being intensively developed in different areas of educa-
tion, including mathematics and engineering [1; 4; 16; 18].
The transformation of the modern educational environment of the university by the
use of the cloud-based services and cloud computing delivery platforms is an im-
portant trend in research. The topics of software virtualization and unified university
ICT infrastructure formation on the basis of CC have become increasingly popular
lines of investigation [8, 21]. The problems with the use of private and public cloud
services, their advantages and disadvantages, perspectives on their application, and
targets and implementation strategies are within the spectrum of this research [3; 4;
16].
There is a gradual shift towards the outsourcing of ICT services that are likely to
provide more flexible, powerful and high-quality educational services and resources
[2]. There is a tendency towards the increasing use of the software-as-a-service (SaaS)
tool. Along with SaaS the network design and operation, security operations, desktop
computing support, datacentre provision and other services are increasingly being
outsourced as well. Indeed, the use of the outsourcing mechanism for a non-core ac-
tivity of any organization, as the recent surveys have observed happening in business,
is now being extended into the education sector [5]. So, the study of the best practices
in the use of cloud services in an educational environment, the analysis and evaluation
of possible ways of development, and service quality estimation in this context have
to be considered.
The valuable experience of the Massachusetts institute of technology (MIT) should
be noted in concern to the cloud based learning environment formation in particular as
for access to mathematical software. The Math software is available in the corporate
cloud of the University for the most popular packages such as Mathematica, Mathlab,
Maple, R, Maxima [19]. This software is delivered in the distributed mode on-line
through the corporate access point. This is to save on license pay and also on compu-
ting facilities. The mathematics applications require powerful processing so it is ad-
visable to use it in the cloud. On the other case the market need in such tools inspires
its supply by the SaaS model. This is evidenced by the emergence of the cloud ver-
sions for such products as SageMathCloud, Maple Net, MATLAB web-server, Web-
Mathematica, Calculation Laboratory and others [1; 4]. Really there is a shift toward
the cloud-based models as from the side of educational and scientific community, and
also from the side of product suppliers. The learning software actually becomes a
service in any case; let it be a public or a corporate cloud [12].
An essential feature of the cloud computing conception is dynamic supply of com-
puting resources, software and hardware its flexible configuration according to user
needs. So comparison of different approaches and cloud models of software access is
the current subject matter of educational research [3; 4; 11; 17]. Despite of the fact
that the sphere of CC is rather emerging there is a need of some comparison of the
achieved experience to consider future prospects [17]. Also the problems of software
choice in the learning complexes to be implemented in a cloud arise. This leads to the
problems of cloud-based learning resources evaluation techniques and research indi-
cators substantiation.
The special attention is to be paid to the system Maxima, because it is easy to mas-
ter, it is comparable to such systems as Maple and Mahtematisa as for solving prob-
lems (for example in the field of operations research) and it is free accessed. It is
equipped with a menu system that enables characters conversion, solve equations,
compute derivatives, integrals, etc., avoiding some additional efforts as for learning
the special language tools to implement these actions. In view of that the Maxima
system can be used to study Math and Computer Science disciplines even on the first
year of study at the pedagogical university [13]. The use of Maxima will not cause
any difficulties for the students as for solving problems of mathematical analysis and
linear algebra – the students are required only to choose a menu item and enter the
expression. However, programming within Maxima requires knowledge of certain
language and syntax, as well as some commands.
Thus, in view of the current tendencies, the research questions are: how can we
take maximum advantage of modern network technologies and compose the tools and
services of the learning environment to achieve better results? What are the best ways
to access electronic resources and mathematical software if the environment is de-
signed mainly and essentially on the basis of CC? What are the most reasonable ap-
proaches to evaluate the results? This brings the problem of the cloud-based learning
components modelling, evaluation and design to the forefront.
3 The Research Results
With the development of cloud-based network tools and technologies new kinds of
services and applications emerge that may be used to support math and engineering
disciplines learning. There is a shift towards greater use of on-line network tools in
educational universities, among them there are such as:
- platforms of distance learning support (Moodle, LearningSpace, Sakai, Blackboard,
etc.), including online resources (Competentum.ONLINE, Google Open Class, Can-
vas) [10];
- mathematical software for special purposes - for example, Maple Net, MATLAB
web-server, WebMathematica, Calculation Laboratory and others [13; 17; 19].
An The use of these technologies adds and provides an opportunity to explore and
develop new approaches to learning, which in turn leads to the development of new
strategies and methodology of teaching of mathematics disciplines in educational
universities [13].
A separate set of problems relates to the use of mathematical software tools within
the cloud-based learning environment. This raises the possibility of computer capaci-
ties, software and hardware dynamic delivery and its flexible configuration due to the
user needs. With this approach, the organized access to various types of electronic
educational resources may be arranged being specially installed on a cloud server and
provided as a public service. [2]
"On this basis the subject-technological organization of information learning space,
organized processes of accumulation and storage of various domain collections of
electronic educational resources ensures equal access to them for learners, significant-
ly improving ICT support of learning, research and educational management " [2,
with. 11].
By means of the cloud services the applications may become available to users, as
well as storage space and also computer capacities [2]. The main types of cloud ser-
vice models reflect the possible ways of ICT outsourcing use in educational environ-
ment of the university in particular there are SaaS (Software-as a Service) - "software
as a service", PaaS (Platform as a Service) - "platform as a service", IaaS (Infrastruc-
ture as a Service) [2, 3, 4, 9].
Recently many software applications and packages of mathematical destination
started the cloud versions supplied by SaaS model, which can be used in the learning
process and research as specialized software [12]. In this case, organized access to
ready-made software is supported on the vendor server.
For example, the Sage mathematical software is supplied by this model. The sys-
tem is designed to operate Sage and support experimentation with algebraic and geo-
metric objects. As open source software, that can be used to take advantage of a varie-
ty of packages for operations on mathematical analysis, algebra, group theory, graph
theory, and others. Currently, the cloud versions of SageMatCloud can do it directly
from the browser. Now this is a freely available service supported by the server of the
University of Washington. There is a cluster for supporting SageMathCloud, contain-
ing 288 cores, 1.2TB RAM and 50TB of storage.
In turn, the IaaS model is designed to run any application on the cloud hardware of
the provider configured and selected by the user. The IaaS composition may include
hardware (servers, storage, client systems and equipment); operating systems and
software (virtualization, resource management); software communication tools (net-
work integration, resource management, equipment management) provided over the
Internet [12].
Using this technology there is no need to maintain complex infrastructures, data
processing, network applications and client server organization, but yet renting them
as a service. Specifically, users can get, at their disposal, a completely prepared virtu-
alized workplace. This raises the possibility to provide significant amount of educa-
tional content by means of quite cheap hardware (this may be a laptop, a netbook or
even a smartphone) [2].
Recently there has been a trend towards convergence and integration of various
mathematical packages. For example, the latest versions of Mathematica and Maple
are supplied by powerful tools for visual programming; MathCAD can work together
with MatLab etc. So, for the aim of practical training any of the above packages may
be used with regard to specific traditions and support opportunities of educational
institutions [13]. These factors significantly influence the choice of software that can
be installed "in the cloud".
Given the factors of the license application and other features the Maxima system
may be advised to be used, because:
─ the system is distributed under the license GNU / GPL;
─ it is equipped with a system of menu that has a Ukrainian-language interface;
─ it is one of the best on the implementation of symbolic computation (in fact, the
only one that can compete with commercial Maple and Mathematica) [13].
Recently Given the existence of different models of cloud services use the special
attention to a balanced selection of the most appropriate solutions that fit each case
for a particular organization, both collective and individual user should be made. The
SaaS model choice in this respect could be justified by the fact that these services are
the most affordable to use, even though they need a thorough analysis of the market
and educationally prudent selection of software application, to achieve the desired
educational or research purposes. These tools can be involved in the learning process
by individual teacher, on the level of a department, for individual or collective users.
At the same time, the construction of the ICT infrastructure of an institution as a
whole needs to select and analyze the appropriate cloud platform that can be orga-
nized by the models of PaaS or IaaS. This requires the solution of a number of organi-
zational issues, such as the formation of a special ICT unit of employees that are to be
qualified to configure and deploy that infrastructure, the construction of the necessary
hardware and software, the determining the plan and design phases, the designing and
test of information and educational environment, filling it with the necessary re-
sources to implement and monitor their quality, training teaching staff etc. [2]. In this
case, given the results of foreign experience and current trends of the IT sector devel-
opment, we can conclude that the most appropriate is the use of hybrid service models
that can be incorporated by means of public and corporate clouds, not excluding the
means of the model of "software as a service" if necessary. [2]
Due to the possibilities of resources sharing, the cloud services provide a base for
easy access to educational services, in line with the principles of open education,
combining of science and practice, integrating the processes of training and scientific
research.
3.1 The Design of the Cloud-based Learning Component with the Use of the
Maxima System
To research the hybrid service model of learning software access, especially for the
mathematical software delivery a joint investigation was undertaken in 2013–2014 at
the Institute of Information Technologies and Learning Tools of the NAES of Ukraine
and Drohobych State Pedagogical University named after I.Franko. At the pedagogi-
cal experiment the cloud-based learning component with Maxima system was de-
signed and used for the operations research study.
In this case, the implementation of software access due to the hybrid cloud de-
ployment was organised.
The configuration of the virtual hybrid cloud used in the pedagogical experiment
was described in [12]. The model contains a virtual corporate (private) subnet and a
public subnet. The public subnet can be accessed by a user through the remote desk-
top protocol (RDP). In this case, a user (student) refers to certain electronic resources
and a computing capacity set on a virtual machine of the cloud server from any de-
vice, anywhere and at any time, using the Internet connection.
The advantage of the proposed model is that, in a learning process, it is necessary
to use both corporate and public learning resources for special purposes. In particular,
the corporate cloud contains limited access software; this may be due to the copyright
being owned by an author, or the use of licensed software products, personal data and
other information of corporate use. In addition, there is a considerable saving of com-
putational resources, as the software used in the distributed mode does not require
direct Internet access for each student. At the same time, there is a possibility of plac-
ing some public resources on a virtual server so the learner can access them via the
Internet and use the server with the powerful processing capabilities in any place and
at any time. These resources are in the public cloud and can be supplied as needed
[12].
Within the experimental study the Maxima system installed on a virtual server run-
ning Ubuntu 10.04 (Lucid Lynks), was implemented. In the repository of this opera-
tional system is a version of Maxima based on the editor Emacs, which was installed
on a student’s virtual desktop [13].
To create a session (to insert an item Maxima) you should choose the menu option
Insert - Session - Maxima. There is an active input line to input Maxima commands.
An example of successful use of the Maxima cloud-based component is Graph
Theory learning. Maxima has a rich set of features on the design and elaboration of
relevant objects of this theory. Some examples of its use are presented at [12].
3.2 The Cloud-based Component Implementation and Evaluation
In the research experiment held at Drohobych State Pedagogical University named
after I.Franko, 240 students participated. The aim was to test the specially designed
learning environment for training the operations research skills on the basis of Maxi-
ma system. During the study, the formation of students’ professional competence by
means of a special training method was examined. The experiment confirmed the rise
of the student competence, which was shown using the χ 2 –Pearson criterion [13].
This result was achieved through a deepening of the research component of training.
The experiment was designed using a local version of the Maxima system installed on
a student’s desktop.
The special aspect of the study was the expansion of these results using the cloud
version of the Maxima system that was posted on a virtual desktop. In the first case
study (with the local version), this tool was applied only in special training situations.
In the second case study (the cloud version), the students’ research activity with the
system extended beyond the classroom time. This, in turn, was used to improve the
learning outcomes.
At the next stage of the experiment (2014-2015) the aim was to test the use of the
cloud-based component in the learning process. 48 students participated in this exper-
iment. There was the experimental group of 24 students who used the cloud-based
component with Maxima system. It showed increase of the students’ percentage with
the high level of ICT competence from 16% to 75%. It was significantly different
from the level of ICT competence of those students who did not used this component
(from 14% to 20%), which was justified by the Fisher criterion.
The cloud-based learning component used in the experiment has undergone a qual-
ity estimation. The method of learning resources quality estimation developed in the
joint laboratory of educational quality management with the use of ICT [6] was used
and adapted for this study. The 20 experts were specially selected as having experi-
ence in teaching professional disciplines focused on the use of ICT and being in-
volved in the evaluation process. The experts evaluated the electronic resource by two
groups of parameters. The first group has contained 7 technological parameters: ease
of access; the clarity of the interface; sustainability; support of collaborative work,
ease of integration; mobility; and usefulness. The second group has contained 9 psy-
chological and pedagogical parameters: the scientific clarity; accessibility; fostering
the intellectual development; problem orientation; personalization; adaptability; me-
thodical usefulness; professional orientation; and feedback connection.
The problem was: is it reasonable and feasible to arrange the environment in a pro-
posed way? For this purpose there were two questionnaires proposed to expert con-
cerning two groups of parameters. The 20 experts estimated 16 parameters (there
were 7 technological and 9 psychological and pedagogical among them). A four-point
scale (0 (no), 1 (low), 2 (good), 3 (excellent)) was used for the questions.
The resulting average value was calculated for every parameter among the technolog-
ical ones : “Ease of access” = 2.1, “Interface clarity” = 2.4, “Responsiveness” = 2.1,
“Sustainability” = 2.56, “Support of Collaborative work” = 2.0, “Ease of Integration”
= 2.0, “Usefulness” = 2.8, the total value was 2.3.
The resulting average values for every psychological and pedagogical parameter
was calculated as: “Scientific clarity” = 2.6, “Accessibility” = 2.7, “Fostering the
intellectual development” = 2.5, “Problem orientation” = 2.8, “Personalization” = 2.8,
“Adaptability” = 2.6, “Methodical usefulness” = 2.81, “Professional orientation” =
2,75, “Feedback connection” = 2,75. The total value was 2.71.
The resulted average criterion of EER quality K=2,59. This characterises the re-
source quality as sufficient for further implementation and use.
The advantage of the approach is the possibility to compare the different ways to
implement resources with regard to the learning infrastructure. Future research in this
area should consider different types of resources and environments.
4 Conclusions and Prospects for Further Research
The results of the study indicate certain movement in the development of new ways to
create and use the software for educational purposes based on the concept of cloud
computing.
The methodological guidelines on the organization of a cloud-based learning envi-
ronment of computer science and mathematics disciplines cover a range of delivery
services and software applications to be available for use. Choosing the SaaS model
in this respect could be justified by the fact that these services are the most affordable
to use, regarding the restriction in the choice of software application to those offered
by a supplier. When choosing a PaaS or IaaS model one must take into account a
number of technological and organizational factors forming the environment, and
quality characteristics of software selection which need to be installed in the cloud.
The introduction and design of the cloud-based learning components into the pro-
cess of math and computer science study contributes to the growth of access to the
best examples of electronic resources and services, ICT tools modernization, better
learning outcomes. The cloud-based learning component on the basis of Maxima
system was successfully developed and justified within these settings. Its use is prom-
ising regarding learning design that can account for the advances and tendencies of
CC progress.
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