=Paper=
{{Paper
|id=Vol-1844/10000327
|storemode=property
|title=The Learning Technique of the SageMathCloud Use for Students
Collaboration Support
|pdfUrl=https://ceur-ws.org/Vol-1844/10000327.pdf
|volume=Vol-1844
|authors=Maya Popel,Svitlana Shokalyuk,Mariya Shyshkina
|dblpUrl=https://dblp.org/rec/conf/icteri/PopelSS17
}}
==The Learning Technique of the SageMathCloud Use for Students
Collaboration Support==
https://ceur-ws.org/Vol-1844/10000327.pdf
The Learning Technique of the SageMathCloud Use for
Students Collaboration Support
Maya Popel1, Svitlana Shokalyuk2, Mariya Shyshkina1
1Institute of Information Technologies and Learning Tools of NAES of Ukraine,
9 M.Berlynskoho St., Kyiv, Ukraine
{popel, shyshkina}@iitlt.gov.ua
2Kryvyi Rih State Pedagogical University
54 Gagarina Ave., Kryvyi Rih, Ukraine
ksv_ipm@mail.ru
Abstract. The article describes the advisable ways of the cloud-based systems
use to support students’ collaboration in the process of math disciplines learn-
ing. The SageMathCloud-based component that aggregates electronic resources
for several math disciplines training is introduced. The learning technique of the
SageMathCloud use in the process of educational staff training is proposed. The
expediency of this technique implementation for more active take up of innova-
tive approaches, forms and methods of math training with the use of the cloud-
based tools is substantiated. The experimental results of the SageMathCloud
learning component introduction research along with the methods of its use that
were elaborated in the course of the study are presented. The use of the evi-
dence-based technique as improving the educational environment of the univer-
sity, empowering access to electronic learning resources in the course of math
training and engaging with this the educational community and also rising their
ICT competence is grounded.
Keywords: cloud computing, ICT-based tools, learning environment,
teamwork, learning collaboration.
Key Terms: Methodology, InformationCommunicationTechnology, ICTTool
1 Introduction
1.1 The Problem Statement
Application of the cloud computing (CC) technology in education is to provide the
comprehensive development of learner’s personality and competencies according to
the individual needs and requirements of a society. Its implementation is associated
with the objective need to create an open learning environment where students
become the active subjects of purposeful search and creation of knowledge. In this
concern, the research and implementation of essentially new forms of learning and
educational activity are necessary. The learner-centered approach and adaptive
learning technologies empowering students and teachers collaboration and increasing
the share of knowledge become the central point.
With the use of the cloud technology the better results of learning may be achieved,
providing each student with his own educational trajectory using adequate technologi-
cal solutions. There are new opportunities for differentiation and individualization of
the learning process, its flexible adaptation to the needs and individual characteristics
of the students [2].
The cloud technology emergence alters our understanding of the hardware and
software use and also the data storage and access in the learning process.
Really, the use of the cloud services enables the individuals to acquire and process
their data, perform the calculations, make certain adjustments referring to them via the
Internet. The user has no need to worry about software installing and updating,
memory limits, the use of data-storage devices and processing.
And also there is no need to use super-power devices for training. It's enough to
have access to regular notebook, Smartphone or any other device linked to the Inter-
net, having free space to store data. The learning content and tools may be delivered at
any time to any place due to the user demands. There is a problem to bring cloud
computing technologies to educational practice considering the better ways of learn-
ing tools selection and pedagogical personnel training. There is a need to develop the
learning techniques oriented to the most powerful and open accessed tools.
In this regard, the prospects of the SageMathCloud service implementation being
quite powerful and yet free accessed is an actual problem of theory and methods of
using ICT in teaching mathematical disciplines.
1.2 The State of the Art
In the recent years the wider use of the cloud-based tools and services became the
central point, forming an ICT platform of modern educational systems and learning
environment [1; 5; 13; 15; 16].
For example, M. A. Kislova considers the mobile learning environment for mathe-
matics learning in the university that includes the tools for various mathematical ac-
tivities support, mobile learning communication, enhancing the interaction between
students and a teacher [4].
The several cloud-based tools are considered by M. A. Kislova and K. I. Slovak [3]
who offered to use them in combination with other learning tools. Among them there
are such as: Google Apps for Education, Office 365, ThinkFree Online. The benefits
of their use for teaching mathematical disciplines are outlined.
In the current research of Systems of Computer Mathematics (SCM) the recent ten-
dency was determined that the popular mathematical software tools appear at cloud
versions, for example such as Maple Net, MATLAB web-server, WebMathematica
and others. The main differences between SCM and web-based SCM and also the
cloud-based SCM are highlighted in more detail in [9]. The SageMathCloud is an
example of such kind of software as the cloud-based version of Web-SCM Sage [9].
Some experience of using the cloud services in educational in Volodymyr Gnatiuk
National Pedagogical University of Ternopil is reported in [6]. The cloud-based infra-
structure with the Google Apps cloud services integrated into the learning environ-
ment of physics and mathematics faculty were described [6].
The most studies of Ukrainian researchers on the matter of research in the resent
years were focused on the principles, approaches and models design of the environ-
ments of higher education, which included the cloud services [9; 10; 12].
The experience of using the SageMathCloud in teaching the optional course in Tu-
tek Željka Croatia's University of Zagreb in the period of 2015-2016 years presented
in [14] shows that the primarily attention is necessary to focus on:
─ acquiring the skills of using the mathematical software for numerical and symbolic
computation;
─ supporting mathematical concepts teaching (including courses in Analytic Geome-
try, Linear Algebra and Calculus).
Usually the cloud services can be used for data visualization and calculation,
particularly for solving problems within the certain discipline and organization of
individual and collective work, the student learning monitoring.
So the advisable ways of the SageMathCloud use in pre-service math teachers
training need more careful research. The important topics are the following:
1. Organization of educational communication;
2. Keeping individual and group forms of learning activities (class and extracurricu-
lar);
3. Keeping a learning management;
4. Providing visibility by constructing different interpretations of mathematical mod-
els, visualizing mathematical abstractions etc.;
5. Ensuring availability and research opportunity by using a common interface of
learning environment objects access and reliable software with open source;
6. Increasing the temporal and spatial mobility;
7. Forming a unified learning environment with content developed in learning.
1.3 The Purpose of the Article
The main purpose of the paper is the analysis of the most appropriate ways of the
SageMathCloud learning component use to support collaborative work in the pro-
cess of mathematical disciplines learning and justification of the technique of its
application for training lecturers and academic staff in the pedagogical university.
2 Presenting the Main Material
The use of ICT affects the content, methods and organizational forms of teaching
and managing educational and cognitive activity that requires new approaches to
educational process arrangement. Therefore, the formation of modern cloud-based
systems for supporting teaching and research activities and students’ collaboration on
the learning projects should be based on appropriate innovative models and method-
ology that can ensure a harmonious combination and embedding of various network-
ing tools into the information-educational environment of higher education. The mod-
el of the SageMathCloud use to support various forms of collaboration in the process
of training of pre-service teachers of mathematics (Fig. 1) consists of the following
components: the organizational, the content and the technological ones. The model
includes teachers’ and students’ individual or collective spaces consisting of some
structural elements. The combination of certain elements provides different types of
interaction organization (between students and a teacher and between students with
each other) among them such as individual and group work of students, students and
teachers cooperation and active communication.
Lecturer
Monitoring and evaluation of assignments
Learning synopses inc. math texts processing
The learning activity planning
Individual Step by step instruction for tasks performing
work of The system of tasks access Group work
students The use of resources for tasks performing (fo- of students
cused on mathematics)
Files storage Coopera-
Active tion be-
The use the resources for communication tween
communi- (inc. Math. symbolic) teachers
cation and stu-
Collaborative creation of the resource (s) inc. dents
Math. texts
Student
Result
- the level of pre-service teachers of mathematics training increases;
- the access to educational resources expands and tasks performing at a conven-
ient time and in a convenient location is available;
- the learning system supporting better collaboration and communication of stu-
dents in the process of study is provided.
Fig. 1. The model of the SageMathCloud use to support various forms of collaboration in the
process of training of pre-service mathematics teachers
In this connection, in 2014-2016 in the Institute of Information Technologies and
Learning Tools of NAES of Ukraine the research study devoted to the use of the
SageMathCloud in pre-service teachers of mathematics training was carried out
(M.Popel) [11]. The main idea of the study was the provisions that purposeful,
scientifically grounded system of training using the cloud-based environment tools
and technologies integrated into the process of educational staff training at the
university is the precondition for improving the research process, widening access to
electronic resources and services, rising the ICT competence and learning outcomes
of students and teachers.
In the course of research the cloud-based learning component of the information
and educational environment included the SageMathCloud was elaborated and meth-
ods of its use were designed. It was introduced through the workshops, webinars,
seminars and other scientific and methodical and learning events conducted by the
Institute [11].
2.1 The Technique of the SageMathCloud Use
The Target
The aim of the SageMathCloud learning component use is to provide the
organizational and technological support for students’ collaboration in the process
of study, expanding access to qualitative electronic educational resources (EER),
increasing professional and ICT competencies.
The target group: educational and pedagogical and research personal.
The Learning Content
The learning content to be provided so as to incorporate the learning technique of
the SageMathCloud use occupies the topics aimed at formation of ICT competence
of research and educational staff, ICT departments employees and also students on
the use of the cloud-based systems and services in the research and educational
process. Some learning modules of such kind may be the elements of training, re-
training of academic and lecturers staff content.
The Technological Aspect of Use
The advisory teaching methods are: explanatory learning; partly research learning;
problem learning; research learning.
The organizational forms of learning are: lectures; individual, practical, laboratory
work; training sessions; seminars, webinars, web conferences; individual consulta-
tions.
Among the innovative forms of learning that can be realized only in the cloud-
based environment the combined training is appropriate. This kind of learning inte-
grates internal and remote forms of work. In the process of training the situational e-
learning network is designed and its members are motivated to maintain the collective
activity by a common scenario. The organizer gives the examples of successful train-
ing activities (as the previous material templates of training tasks and also interactive-
ly as using the visual and auditory tools for submitting worksheets and tasks monitor-
ing and organizing ICT-mediated learning management). The activity increase occurs
due to the involvement of the training experts.
The main important learning tools elaborated with the use of the SageMathCloud
are:
─ The working sheets on which students perform their activity with the construction
and study of mathematical models;
─ The chat room used for discussions of the simulation process and results;
─ The tools to support learning activities (resources such as course, tasks);
─ The tools for creating mathematical texts (tex) and hypertext (html);
─ The mobile tools for other mathematical activities access.
The Ways of Implementation
The implementation of the proposed method in the learning process may occur in
two ways:
1. 1. Through the introduction of the special learning course "Cloud Computing
Technologies in Educational Activity", as an element of the content of training, re-
training of academic and lecturers staff [5].
2. Through the introduction of a system of training (see Table 1) such as seminars,
webinars, individual consultations that can be carried out during the pilot experi-
mental study (project) on the deployment of a cloud-based information and educa-
tional environment at the university.
Table 1. Plan of trainings
№ Topic Title Number of hours
Introduction. The advisable ways to use the SageMa-
1. 2
thCloud in learning mathematical disciplines
2. Organization of collaboration in the SageMathCloud 2
3. Construction of lecture demonstrations 2
4. Creating of dynamic models and animations 2
Examples of SageMathCloud use in teaching of certain
5 2
math disciplines
Total: 10
The use of the SageMathCloud in teaching mathematical disciplines should be pri-
marily targeted to:
─ The acquisition of skills of individual use of the mathematical software for numeri-
cal and symbolic computation;
─ Supporting of mathematical concepts learning (including courses in Analytic Ge-
ometry, Linear Algebra and Calculus).
The Tools of Collaboration Support in the SageMathCloud
The main activity type in the SageMathCloud is going on with the project. The
user can create any number of independent projects or personal workspaces, to save
resources of various types, including:
─ SageWorksheet (*.sagews);
─ LaTeX Document (*.tex);
─ Manage a Course (*.course);
─ Chatroom (*.sage-chat);
─ Folder; etc.
Collaboration with the use of the SageMathCloud-project resources can be organized
in of two possible ways:
─ at the level of a single resource, including worksheets;
─ at the level of a project as a whole.
Sharing access at the level of a single resource is nothing more than a webpromulga-
tion of resource content. Moreover resource is made public for all Internet users who
have a link to it and they can operate with it in the mode "read only". The main disad-
vantage of this publication is that on the one hand a user as a "reader" is not able to
manage calculations on the worksheet (even if it contains standard elements of man-
agement) on the other hand this worksheet can be copied or downloaded along with
its full source code that does not guarantee security and protection of user copyrights.
Organization of collaboration at the level of the whole project is possible the other
way using a courses manager (Fig. 2), or without it.
Fig. 2. Overall view of the joint project
In case of collaboration without the course manager all participants have the oppor-
tunity to:
─ collaborate using existing (offered by a teacher) educational resources of a project;
─ add new training resources;
─ invite other members to collaborate on the project (Fig. 3);
─ communicate to each other and a lecturer by means of text chat or video chat.
While working with a learning resource in real time the users are able to see cursor
positions of each other and the icons of those project participants who addressed to a
file at this moment, as like as it happens if working collaboratively with a Google
document.
The contribution of each project participant in the tasks can be viewed at the pro-
ject backup (Fig. 3) or in the pages of history of the project or a worksheet.
Fig. 3. Page of the backup versions of the «Backups» project
Backups of a project ( «Backups») are saved every 5 minutes and can not be com-
pletely removed by the user.
Contribution of each member of the joint project into the tasks solving may be re-
viewed on the history pages of the project «Log» (Fig. 4): creating files, folders, delet-
ing, moving, copying, opening, renaming and more.
To review the whole history of changes of the worksheet content the page that
opens after clicking «TimeTravel» may be used (Fig. 5). In the history file the records
of all changes made by the author of a project or by any other participant are saved.
Moving the slider, you can view all the changes that were made on the worksheet.
Initial position of the slider corresponds to the file creation.
Fig. 4. Page of project history «Log»
If the file was not changed nor edited, it is indicated «Revision 0". For each change
the date and time are shown. The last position of a slider reflects the recent changes
that were made when editing the file.
Fig. 5. The page of worksheet history «Time Travel»
Communication between the project participants in real time is possible by means of
traditional "rooms" of text chat (Fig. 6), video chat or on the pages of the sage-chat
resource type. Text messages can be formatted with HTML tags and commands of
Markdown. The message with mathematical content may be performed in usual math-
ematical notation using commands of LaTeX. In addition, for a resource type sage-
chat the function of history viewing is available.
Fig. 6. The traditional "room" of a text chat
For the organization of individual collaboration with each student, the teacher creates
a separate project and fills it with educational resources and gives access only to a
specific user (the student). As a result, the number of projects created by the students
is determined by the number of academic groups. In this case the teacher is forced to
spend a lot of time to do the same actions dozens of times (as it is not possible to copy
the whole SageMathCloud). The process may be automated by using the special
SageMathCloud-resource namely the course Manager.
This method of training with the use of the SageMathCloud provides opportunities
for teachers to control the process of tasks performing by the students and also the
evaluation. The page of the training course Manager is shown in Fig. 7.
Fig. 7. The page of the training course manager
There are the next control elements on this page:
─ the page label «Students» (for management of students actions);
─ the page label «Assignments» (for management of educational activities within the
course);
─ the page label «Handouts» (for management of educational materials that are in
folders);
─ the page label «Settings» (to adjust the settings of the training course);
─ the page label «Shared Project» (to create a project common for all students).
A typical sequence of actions that envisages the teachers work using training
courses manager is as follows:
1. Inclusion of each student to the course (footprint refer to the page «Students»).
When a user is included into the course as a student, a personal project is automati-
cally created, with access to be opened to teachers and students.
2. Filling the training course with materials (hereinafter - management) is at «As-
signments».
3. Copy the educational materials for all students to their projects is made simultane-
ously by clicking the button «Assign ...».
4. When copying educational materials at least to one student above the list of stu-
dents in the box of general settings of folders the buttons appear that allow to as-
sign tasks to all students of the course simultaneously, collect the data about tasks
performing ( «Collect») and make the resulting assessment report ( «Enter grade»).
5. Educational materials that have been copied, you can update as needed.
6. On the page «Settings» of the general settings of a resource a teacher may be inter-
ested in the following blocks:
─ «Export grades» - clicking on the button «CSV file ...» or «Python file ...», in the
project structure will be created a file with indication of assessments of all students;
─ «Customize email invitation» makes the text message concerning inclusion of a
user into the course, which will go to the user mailbox, if he is not registered in the
system (the text message can be changed by clicking on the button «Edit»).
On the page «SharedProject» a shared project can be created for all students of the
training course, in which each student automatically becomes a member.
Organization, Conduct and Results of Experimental Work
The aim of pedagogical experiment was to justify empirically the theoretical assump-
tion that the proposed pedagogical approach was really effective.
At the ascertaining stage of experimental research the analysis of existing equip-
ment and logistics was made for it to be sufficient for the research; the current state of
teaching staff readiness to use the cloud services in their professional work was esti-
mated, appropriate tools were chosen. It was presupposed that the mastery of peda-
gogical staff in using the cloud services to support mathematical activity, including
the SageMathCloud service, was a prerequisite for improving the quality of learning
results.
At the ascertaining stage of the experiment some problems of specific professional
competencies formation, in particular ICT competence were found.
Teachers would liked to improve their knowledge through greater use of cloud-
based ICT in their professional activities.
Based on the data presented in Table 2, we may check the reliability of the hypoth-
esis of no statistically significant differences between the levels of formation of ICT
competencies of teaching staff in experimental and control groups. The chi-squared
test was used. As the critical value of chi-square as 5.99 was chosen.
Table 2. Average percentage levels of ICT competence in the control groups (CG) and experi-
mental groups (EG), the results of initial and final measurement
Percentages
CG EG
Equal
primary final primary final
measurement measurement measurement measurement
High 10 5 11 15
Average 41 42 51 63
Low 49 56 38 22
Defining empirical value of 2.53, we can see that it is in the area of insignifi-
cance and the hypothesis that the proportion of teaching staff with the appropriate
level of ICT competence is the same in experimental and control groups by the
results of entrance control is accepted.
After checking the authenticity of the hypothesis of statistically significant differ-
ences between the levels of ICT competencies of teaching staff in control and experi-
mental groups at the end of the experiment the following results were obtained:
23.98> 5.99, where 23.98 is the empirical significance for hypothesis testing. That
hypothesis is accepted that the proportion of teaching staff of the experimental group
with high and medium level of ICT competence is higher than that in the control
group.
Comparing the levels of ICT competence in the early formative stage and at the end
of the experiment (Fig. 8) shows the increase of the proportion of teaching staff with
the high and medium levels of ICT competence.
Fig. 8. Percentage distribution of ICT competency levels in the control and experimental
groups, the results of initial and final measurement
Analysis of the formative stage of pedagogical experiment showed that the distri-
bution of the levels of ICT competences in the experimental and control groups of
teaching staff have statistically significant differences due to the introduction of the
developed technique, which confirms the hypothesis of the study.
3 Conclusions
The introduction of the cloud-based tools and components into the learning pro-
cess contributes to the improving of the educational environment of the university,
increasing access to electronic resources and services, wider use of network tech-
nologies and tools in pedagogical practice. This is possible due to the application of
experimentally grounded methods of the design and use of the cloud-based learning
components on the basis of the SageMathCloud to support students collaboration in
the process of training.
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