=Paper=
{{Paper
|id=Vol-2433/paper32
|storemode=property
|title=Using the e-learning course "Analytic Geometry" in the process of training students majoring in Computer Science and Information Technology
|pdfUrl=https://ceur-ws.org/Vol-2433/paper32.pdf
|volume=Vol-2433
|authors=Oksana M. Hlushak,Volodymyr V. Proshkin,Oksana S. Lytvyn
|dblpUrl=https://dblp.org/rec/conf/cte/HlushakPL18
}}
==Using the e-learning course "Analytic Geometry" in the process of training students majoring in Computer Science and Information Technology==
https://ceur-ws.org/Vol-2433/paper32.pdf
472
Using the e-learning course “Analytic Geometry” in the
process of training students majoring in Computer
Science and Information Technology
Oksana M. Hlushak[0000-0001-9849-1140], Volodymyr V. Proshkin[0000-0002-9785-0612]
and Oksana S. Lytvyn[0000-0002-5118-1003]
Borys Grinchenko Kyiv University, 18/2, Bulvarno-Kudriavska Str., Kyiv, 04053, Ukraine
{o.hlushak, v.proshkin, o.lytvyn}@kubg.edu.ua
Abstract. As a result of literature analysis the expediency of free access of
bachelors majoring in Computer Sciences and Information Technologies to
modern information educational resources, in particular, e-learning courses in the
process of studying mathematical disciplines is substantiated. It was established
that the e-learning course is a complex of teaching materials and educational
services created for the organization of individual and group training using
information and communication technologies. Based on the outlined possibilities
of applying the e-learning course, as well as its didactic functions, the structure
of the certified e-learning course “Analytic Geometry” based on the Moodle
platform was developed and described. Features of application of cloud-oriented
resources are considered: Desmos, Geogebra, Wolfram|Alpha, Sage in the study
of the discipline “Analytic Geometry”.
The results of the pedagogical experiment on the basis of Borys Grinchenko
Kyiv University and A. S. Makarenko Sumy State Pedagogical University are
presented. The experiment was conducted to verify the effectiveness of the
implementation of the e-learning course “Analytic Geometry”. Using the Pearson
criterion it is proved that there are significant differences in the level of
mathematical preparation of experimental and control group of students.
The prospect of further scientific research is outlined through the effectiveness
of the use of e-learning courses for the improvement of additional professional
competences of students majoring in Computer Sciences and Information
Technologies (specialization “Programming”, “Internet of Things”).
Keywords: e-learning course, computer sciences, information technologies,
analytic geometry, professional training.
1 Introduction
In conditions of modernization of higher education in accordance with the requirements
of the information society development, an important problem remains the free access
of individuals of education to modern information educational resources. A number of
scientific studies which disclose the tendencies of the development and reformation of
modern professional education in the context of the building of an information society
___________________
Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0).
473
have been recently implemented [18; 20]. The influence of information and
communication technologies on the improvement of content, forms and methods of
teaching has been revealed (Yurii O. Doroshenko [3], Svitlana H. Lytvynova [7],
Oleksandr V. Merzlykin [8], Nataliia V. Morze [9], Zarema S. Seidametova [15],
Serhiy O. Semerikov [19], and etc.).
Mentioning the undeniable value of the research carried out, another important
problem of using electronic educational resources should be outlined, in particular, e-
learning courses in the process of studying mathematical disciplines at the university.
It should be noted that the issue of extremely low mathematical training of university
students worries not only the authors of this scientific work. In recent years, a series of
studies aimed at improving the mathematical training of students through ICT has been
implemented. Yurii V. Horoshko [5] has developed a system of information modeling
in training of future teachers of mathematics and informatics, Yurii S. Ramskyi [12]
has developed a methodical system for the information culture formation by future
teachers of mathematics. Besides the method of using mobile mathematical
environments (Kateryna I. Slovak [17]) and the system of computer mathematics Sage
during independent work of high school students (Svitlana V. Shokaliuk [16]), systems
of computer mathematics (Oksana I. Tiutiunnyk [21]) are developed. The implemented
studies are aimed at improving professional training, mainly students of Engineering
and Economic specialties. The problem of improving the professional training of
bachelors majoring in Computer Science and Information Technologies through ICT
requires further careful consideration.
2 The objective of research
The purpose of our research paper is to prove the effectiveness of using the e-learning
course “Analytic Geometry” in order to improve the mathematical training of bachelors
majoring in Computer Science and Information Technology.
3 Research methodology
The purpose of research has made us use the complex of the relevant methods: scientific
literature analysis in order to establish the state of the problem development, the
definition of the categorical and conceptual apparatus of investigation; synthesis,
generalization, systematization for theoretical substantiation and practical development
of e-learning course; empirical: diagnostic (conversation, content analysis, testing) for
monitoring the dynamics of the mathematical training level of students; a pedagogical
experiment in order to prove the effectiveness of using the e-learning course;
mathematical methods (Pearson criterion) to assess the significance of positive changes
in experimental work results.
The research was carried out within the framework of the complex scientific theme
of the Department of Computer Science and Mathematics of Borys Grinchenko Kyiv
University “Theoretical and practical aspects of the use of mathematical methods and
information technologies in education and science”, SR No 0116U004625.
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Experimental research base: Borys Grinchenko Kyiv University and A. S. Makarenko
Sumy State Pedagogical University.
4 Results and discussion
According to the provision on the certification of an e-learning course at the higher
education institution level the e-learning course (ELC) is a system of teaching materials
and educational services created for the organization of individual and group learning
using information and communication technologies [10].
Following the provisions of the ELC, the procedure for the creation, certification and
use in the e-learning system at Borys Grinchenko Kyiv University, we note that the
main difference between ELCs from the electronic version of the training manual is the
following: a clear structuring of educational and methodological materials; the system
of interaction between the teacher and the student, students among themselves,
organized using the resources of the ELC throughout the time of studying the discipline;
system for monitoring the implementation of various types of educational activities
[11].
The position of Nataliia V. Morze and Oleksandr V. Ihnatenko is very close to us.
They point out that by introducing in the educational process of an e-learning course
the educational institution has the opportunity:
─ to accumulate and analyse the statistics of students’ academic achievements – real-
time statistics can be passed on to the teacher, supervisor, and curator, which will
enable students majoring in Computer Science and Information Technology to
evaluate the results of their own activities;
─ to standardize educational content – one e-learning course can be accompanied by
several teachers while its content does not change, only the teaching method
changes;
─ promptly administer – the training administrator can promptly grant or cancel the
student’s access to the required content;
─ to provide interactive cooperation between the teacher and students, students with
each other at all stages of the educational process – during the study of theoretical
material, its consolidation in the process of performing practical tasks, discussing
problem situations and issues, joint implementation of educational projects and their
public defence, control the results of educational activities, reflection and self-
assessment of students’ academic achievements, etc. [9].
The literature analysis confirms that the study of mathematical disciplines by means of
ELC implements the following didactic functions:
1. Creation of favourable organizational and methodical conditions for training of
future specialists in Computer Sciences and Information Technologies:
implementation of the visibility principle: demonstration of the dynamics of the
studied processes, graphical interpretation of the studied patterns, conditional
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graphic means (tables, diagrams, flowcharts, charts, diagrams, organizational
charts, maps, etc.), modern multimedia (audio and video fragments, animation));
simulation and imitation of processes that are studied and researched, phenomena
with the transition to “reality-model” and vice versa;
providing access to educational materials;
creation of a stable cognitive motive aimed at the need for obtaining, processing
and transmitting information, the use of ICTs at the stage of training and future
professional activities;
the principle of differentiation and individualization of education.
2. Improvement of psychological and pedagogical conditions of educational activity:
creating interest;
ensuring an adequate emotional state of students.
3. Implementation of the education content in the conditions of informatization of
education.
4. Management of educational activity and formation of the structure of philosophical,
behavioural and creative qualities [3].
The teaching experience of the authors of the research paper shows that in order to
improve the quality of mathematical training for bachelors majoring in Computer
Science and Information Technologies it is worth using an e-learning course as a system
of electronic teaching materials designed for the organization of individual, frontal and
group training. E-learning courses are posted on the server of e-learning courses at
Borys Grinchenko Kyiv University at the address: http://elearning.kubg.edu.ua/. The
portal’s work is organized on the basis of the use of a Moodle platform.
The Moodle-based platform allows teacher to create and edit text, graphical,
animated, multimedia blocks in the body of the course using the built-in courseware,
create and edit test tasks, view course-tracking statistics by registered students, and
discuss topics in the forum.
Bachelors in Computer Science and Information Technology based on the Moodle
platform can study the material in a given teacher sequence, perform tasks, ask
questions at the forum for the teacher of the course, use the teaching materials posted
by the teacher. All course progress statistics are kept, accessible to both the student and
the teacher.
The structure of the certified e-learning course “Analytic Geometry” on the basis of
the Moodle platform consists of the following blocks:
1. General information about the course: a work program, a thematic plan, evaluation
criteria, printed sources and Internet sources, a glossary, a course guide (presentation
of the course, a course card, information about the authors, methodical
recommendations for the course work);
2. Each of the modules is represented by the following components:
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Module guide which includes methodological recommendations for the content
module, mental map of the module and a forum for discussing issues that arise
during the study;
Theoretical educational material in the form of structured lecture material, which
is provided by means of “book”, multimedia presentations, audio and video
teaching materials; practical work, which includes a list of main tasks;
Tasks for independent work which include a description and a list of individual
tasks for independent study; the deadlines for their implementation and the form
of submission, as well as the criteria for evaluation;
Modular control which includes a list of typical tasks for modular control work;
3. The final certification, which includes the list of questions for the exam on the
discipline “Analytic Geometry”, as well as the example of the examination card
(Fig. 1).
Fig. 1. Content module of ELC “Analytic Geometry”
In addition, the ELC has links to cloud-based resources for the study of higher
mathematics.
We have a deep conviction that this kind of ELC structure is convenient for students.
This contributes to the realization of their activity within the framework of educational
activities (lectures, consultations, practical and individual classes). As practice shows,
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students also use the developed ELC in the implementation of individual study and
research tasks, writing coursework and master’s work.
Our selected cloud-oriented technology application in the study of geometry is
related to the SaaS model [4]. We share the scientific views of Tatiana V. Batura, Fedor
A. Murzin and Dmitrii F. Semich that the main advantages of implementing such a
model are the reduction of capital stock in hardware and work resources; reducing the
risk of investment loss; a smooth update, and the lack displays as the need for reliable
safety features [1].
Let’s also turn to the scientific position of Svitlana H. Lytvynova, who points out
that cloud-oriented resources for educational institutions have significant advantages,
that is: inexpensive computers for users; increased productivity of computer users;
reduce costs and increase the efficiency of IT infrastructure; less maintenance
problems; less software costs; constant updating of programs; increasing available
computing power; unlimited amount of data storage; compatibility with most operating
systems; improved document format compatibility; ease of teamwork of user groups;
access to documents anywhere and anytime; always the latest version of services;
availability of different devices; ecologization and economical spending of natural
resources; the stability of the data to the loss or theft of equipment [7, p. 38].
Here are examples of cloud-oriented resources: Desmos, Geogebra, Wolfram|Alpha,
Sage, etc [6]. Let’s consider the peculiarities of the application of the indicated services
in the study of the discipline “Analytic Geometry”.
The Desmos Graphic Calculator is an online Internet service that is available at the
link https://www.desmos.com/calculator, which builds function graphs using the
formulas in the Cartesian and Polar coordinate systems, the graph of the function with
the parameters, binding inequalities and contains a set of mathematical patterns and etc.
In studying the discipline “Analytic Geometry” it is expedient, in our opinion, to apply
this resource within the topic “Analytical geometry on the plane”. The resource allows
students to demonstrate different types of equations of direct on the plane, as well as
equations of curves of the second order on the plane (ellipse, hyperbola, and parabola).
The Wolfram|Alpha [22] computer mathematics system is useful in solving tasks on
geometry: construct a vector on a plane and in space, find a vector module, angle with
axes, polar coordinates of a vector, calculate the sum and difference of vectors (on a
plane and in space), to calculate the scalar product of vectors (on a plane and in space),
calculate the vector product in space, find the angle between two vectors (in degrees,
radians), the point of intersection of two straight lines on a plane, find the point of a
symmetric given relative to the line, the coordinate of the middle of a segment, etc.
Let’s consider the use of computer mathematics systems on an example of
accomplishing a task: find a point on a plane symmetrical to a point (5, 7) relative to
the straight line
–x + y + 1 = 0.
To do this, you have to offer students the following algorithm:
1. Go to https://www.wolframalpha.com/.
2. Enter the command:
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reflect (5,7) across -x+y+1=0
3. Get the result (Fig. 2).
Fig. 2. An example of solving a task in wolframalpha.com
One of the powerful tool for learning mathematics is the GeoGebra Dynamic Geometry
System. We agree with the scholars that the functionality of the program and the web-
support of GeoGebra users provide an opportunity to use it effectively when studying
the vast majority of the topics of the mathematics course. It is important that the
program has a wide set of tools for creating dynamic computer models of mathematical
479
objects, which makes it possible to use it not only for solving mathematical problems,
but also for organizing heuristic learning, forming skills and abilities of research
activity, development of creative abilities of students, creation of dynamic visual
manuals, etc. [13].
Let’s look at software for algebraic and geometric studies Sage (Software for algebra
and geometry experiments). It is an open source distributed mathematical computing
environment for performing numerical calculations and symbolic transformations as
well as visualization of data [1]. In particular, in the course of geometry it is expedient
to use a graphical environment for the demonstration of the operation on vectors, a
vector, vector length determination, vector construction, arithmetic operations on
vectors, calculations of scalar product vectors, etc.
During 2017-2018 an experimental study was carried out to verify the effectiveness
of the implementation of e-learning course “Analytic Geometry”. Its goal was to
determine the level of mathematical training for students majoring in Computer Science
and Information Technology. The experimental research base was Borys Grinchenko
Kyiv University (experimental group (EG) in the number of 37 students),
A. S Makarenko Sumy State Pedagogical University (control group (CG) in the number
of 28 students). An analysis was made of the academic discipline “Analytic Geometry”
which is compulsory for students to study both in experimental and control groups.
Students of the experimental group were offered an e-learning course. Students in the
control group studied higher mathematics traditionally, using a teaching methodology
that does not involve the use of e-learning courses and digital resources.
The volume of the educational material of the disciplines “Analytic Geometry” is
defined as an independent variable of this study. Assessment of the academic
achievements of the experimental and control group students was carried out according
to the modular rating system, which is based on the principle of operational reporting,
compulsory modular control, accumulation system for assessing the level of
knowledge, skills and abilities, expanding the number of final scores to 100.
Calculation of rating points by types of current control of load: 18 hours of lectures, 24
hours of practical work and 6 hours of modular control were carried out according to
the table 1. The main methods of pedagogical diagnostics which were enabled: methods
of verbal verifying of theoretical knowledge, methods of written verification of the
learning curve, skills and assumptions – an independent work performed on each
practical lesson, and a test work which is given in the form of modular test. Since in the
educational process of higher education institutions students receive an official
assessment of their academic achievements, which are recorded in the academic class
register, the records of the success studies depending on the form of control, therefore
the method of studying the products of the activity was used for the study of these data.
Analysis of the results of independent work and modular tests allowed to find out the
significance of qualitative assessment of academic achievements of students (table 2).
It should be noted that Borys Grinchenko Kyiv University has a unified system for
assessing academic achievements of students. The transfer of the final rating grade to
the ranking indicators of success in European ECTS assessments is carried out using
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the algorithm: the transfer coefficient is calculated: k 0, 2597 ; received during
231
480
the semester the final rating point of each student is multiplied by the coefficient k.
Table 1. Calculation of rating points by types of current (modular) control
Max points number per
Module 1 Module 2 Module 3
Number of units to
Number of units to
Number of units to
number per type
number per type
number per type
be calculated
be calculated
be calculated
Max points
Max points
Max points
unit
No Type of students activity
1 Visiting lectures 1 3 3 4 4 2 2
2 Visiting practical classes 1 4 4 4 4 4 4
3 Performing tasks for independent work 5 1 5 1 5 1 5
4 Work on practical (seminar) classes 10 4 40 4 40 4 40
5 Performing of modular tests 25 1 25 1 25 1 25
Laboratory classes (admission, performing,
6 10 – – – – – –
protection)
Max number of points by type of current
– – 77 – 78 – 76
control
Table 2. Methodology of calculations of module and semester assessments of the student
Max
No Student’s grade M1 М2 М3
grade
1 Maximum final semester modular grade (МS) 60 – – –
2 Maximum totals for content modules (ММ) 20 20 20
The actual number of points received by the student by type of
3 70 70 70
current control (example) (AP)
Final student’s actual grades for content modules
4 18 18 18
М = AP*ММ/МS (example)
Final semester modular student grade
5 54
S = М1+М2+М3 (example)
6 Examination rating grade of students, (Е) (example) 40 40
Final Semester rating student’s grade
7 94 / А
A = S + Е (example)
Thus, during a semester the student can score a maximum of 60 points according to
the ECTS system. Other 40 points can be scored on the exam (the theoretical part of
the test is presented in the form of tests).
Educational results of the students are recorded in the ELC evaluation register
“Analytic Geometry”. In the e-register assessments the teacher sets the categories for
the assessment of all types of educational activities and their extent (in percentages)
relative to the final assessment from the discipline is determined. Each student has a
personal register, which shows all categories of evaluation and the results of their own
educational achievements (Fig. 3). Within each evaluation module, a 100-point scale is
performed. Moodle provides the automatic transfer of points in accordance with the
volume of the module in the final assessment of the discipline and representation of the
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letter mark. In our opinion, such a tool contributes to tracking their own educational
activities by each student and analyzing the results of the student’s progress with a
teacher.
Fig. 3. User report
The experiment was conducted in two stages: the recording and forming. At the
recording stage (May 2017 – September 2017), a set of diagnostic procedures
(questionnaires, knowledge sections and conversations of students with teachers) was
developed to identify the level of knowledge, skills and abilities of students in
discipline. Matching levels are defined for the level of success: the initial level – the
grade on the ECTS scale E and D, the average – C, the sufficient – B, and the high – A.
The experimental group was the object of scientific research. During the forming
stage of the experiment (October 2017 – July 2018) a complex of methodological
materials was offered at the Moodle system on the basis of the e-learning course. At the
end of the discipline the educational results were checked in the form of final control.
As a result of the experiment the obtained results indicate the effectiveness of using
the e-learning course. Thus, the number of students with a high level of knowledge,
skills and abilities in the EG – 26.67%, in the CG – 11.11%; 39.33% for the students
of the EG and 42.74% for CG on the sufficient level; 17.3% of EG of respondents and
21.37% of CG is on average level; the initial level is 16.67% of students of EG and
24.79% of CG.
To verify the truth of the hypothesis Н0, Н1 the Pearson statistical criterion χ2 was
used:
Н0 – argues that there are no significant differences in the level of mathematical
training of experimental and control students’ groups;
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Н1 – argues that there are significant differences in the level of mathematical training
of experimental and control students’ groups.
Determination of criteria statistics χ2 is carried out according to the formula:
1 k ( n1Q1i n1Q2i ) 2 ,
2 Q Q
n1 n2 i 1 1i 2i
n1, n2 – volume of samples; Q1i, Q2i – the number of elements of the corresponding
samples related to the i-th level; k – number of levels.
The substitution of the values for the formula made it possible to obtain the size of
the criteria statistics for the levels of success of the students of the EG and CG groups
χ2 = 10.9.
At the level of significance =0.05 the critical value for the four levels is 9.49.
Determined statistic data χ2 = 10.9 exceeds the critical value of 9.49. Consequently, in
accordance with the rules of decision making the values obtained refute the hypothesis
Н0 and give reasons for the hypothesis Н1.
Comparison of the generalized results of the students’ success levels before and after
the formative stage of the experiment is presented in the table 3.
Table 3. Results of evaluation of students' level of success before and after the formative stage
of the experiment
Levels ЕG1, % ЕG2, % CG1, % CG2, %
Initial 20.67 16.7 25.64 24.79
Average 17.33 17.3 28.21 21.37
Sufficient 43.33 39.3 34.19 42.74
High 18.67 26.7 11.97 11.11
50
40
ЕG1, %
30
ЕG2, %
20
CG1, %
10
CG2, %
0
Initial Average Sufficient High
Fig. 4. Comparative data of success styles levels before and after the formative stage of the
experiment
Table 3 shows the designation: ЕG1 – experimental group (before experiment),
ЕG2 – experimental group (after experiment), CG1 – control group (before experiment),
CG2 – control group (after experiment). As can be seen from Table 3 the number of
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students with a high level of knowledge in discipline in the experimental group
increased by 8.03%, in CG – decreased by 0.86%; at a sufficient level the indicator
dropped by 4.03% in the EG, but increased by 8.55% in CG; on average, the indicators
decreased in both the EG and the CG, respectively, by 0.03% and 6.84% and at the
initial level, the indicators decreased by 3.97% in the EG and by only 0.85% in the CG.
The graphic representation of the results is reproduced in Fig. 4.
5 Conclusions
1. The importance of free access of bachelors majoring in Computer Science and
Information Technologies to modern information educational resources, in
particular e-learning courses, in the process of studying mathematical disciplines is
substantiated. It was found out that the e-learning course is a complex of teaching
materials and educational services created for the organization of individual and
group training using information and communication technologies. The possibilities
of applying the e-learning course, its didactic functions (creation of favourable
organizational and methodical conditions for educational activity, improvement of
psychological and pedagogical conditions of educational activity, implementation of
the content of education in the conditions of informatization, the management of
educational activities and the formation of the structure of ideological, behavioural
and creative qualities) are outlined.
2. The structure of the certified e-learning course “Analytic Geometry” based on the
Moodle platform has been developed and described. Features of application of
cloud-oriented resources are considered: Desmos, Geogebra, Wolfram|Alpha, Sage
in the study of the discipline “Analytic Geometry”.
3. In order to verify the effectiveness of the implementation of the e-learning course
“Analytic Geometry” on the basis of Borys Grinchenko Kyiv University and
A. S. Makarenko Sumy State Pedagogical University an experimental study was
carried out. Using Pearson’s criterion, it was found that there are significant
differences in the level of mathematical training of experimental and control groups
of students.
The prospect of further research is to demonstrate the effectiveness of using e-learning
courses in order to improve the additional professional competences of students
majoring in Computer Science and Information Technologies (specialization
“Programming”, “Internet of Things”).
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