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Model of increasing the efficiency of the differential equations
section in higher educational institutions
Suyunjon KHALIKOV 1
Navoi State Pedagogical Institute
ARTICLE INFO ABSTRACT
Article history: This article presents a model for increasing the effectiveness
Received February 2021 of teaching the department of differential equations in
Received in revised form higher education institutions and offers suggestions and
20 February 2021 recommendations for its use.
Accepted 15 March 2021
Available online
15 April 2021
Keywords:
differential equation,
case study,
information technology,
practical guide,
maple,
blitz survey,
brain-ring.
2181-1415/© 2021 in Science LLC.
This is an open access article under the Attribution 4.0 International
(CC BY 4.0) license (https: //creativecommons.org/licenses/by/4.0/deed.ru)
Oliy o’quv yurtlarda differensial tenglamalar bo'limining
samaradorligini oshirish modeli
ANNOTATSIYA
Kalit so Zlar: Ushbu magolada oliy ta’lim muassasalarida differensial
cifferensal tenglama, tenglamalar bo‘limini o‘qitish samaradorligini oshirish modeli
case-study,
axborot texnologiyalari,
amaliy dastur,
maple,
blits so‘rov,
breyn-ring.
keltirilgan va undan foydalanishga oid taklif va tavsiyalar berib
o‘tilgan.
1 Basic doctoral student of Navoi State Pedagogical Institute, Navoi, Uzbekistan.
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Модель повышения эффективности раздела
дифференциальных уравнений в ВУЗах
АННОТАЦИЯ
Ключевые слова: В данной статье представлена модель
дифференциальное повышения эффективности преподавания на кафедре
case-study, дифференциальных уравнений в высших учебных заведениях
информационные и даны предложения и рекомендации по ее использованию.
технологии,
приложение,
maple,
блиц-опросник,
brain-ring.
INTRODUCTION
Improving the methods of teaching mathematics in higher education today,
increasing the effectiveness of teaching on the basis of modern innovative technologies,
using the potential of didactic materials on the subject. Therefore, in order to form
students’ mathematical thinking and develop their creative thinking in higher education
institutions, it is necessary to use a variety of methods to prove theorems in a variety of
ways, non-standard, logical, practical examples and problems.
LITERATURE REVIEW
Improving the effectiveness of teaching the subject through the study of information
and communication technologies in the teaching of mathematics in higher education
institutions. Researches can be mentioned by scientists such as D.N. Ashurova,
J.B. Ergashev, D. Mahmudova, G.A. Artikova, I.Sh. Laktaeva, N.M. Mukhitdinova, M. Tojiev,
р. Уипизоуа, G.N.Goibnazarov, M.S. Berdibayev, A.J.Khurramov, 7Z.Kh. Siddikov,
Г.Р. Martirosya, F.K.Matsur, 0O.A.Aryukova, J.M. Nurmukhamedova, _I.I. Bondarenko,
A.A. Ermakova, I.V. Kuznetsova, Zh.L Zaitseva, F.A. Ikhsanova, A.S. Bezruchko,
M.M. Minshin, L.V. Juk, Brad Rankin, Fernando Reggianini, Hong Yuan, Christopher T.
Stripling, and Elizabeth Ackerman-Hicks.
The analysis of the research shows that in our country, in the Commonwealth of
Independent States and abroad, pedagogical research work on the application of
information technology tools and modern educational technologies in the teaching of
mathematics, “Mathematics”, “Algebra” research has been conducted to improve the
teaching methods of “Mathematics Teaching Methods” and “Mathematical Analysis”.
At the same time, although the research was carried out by scientists such as
D. Mahmudova, E.O. Sharipov, P.M. Aslanov, Y.N. Bibikov, I.S. Novikova, N.V. Sycheva,
L.P. Kuzmina on the methodology of teaching the department of differential equations in
our country and the Commonwealth of Independent States, examples and methods of
solving problems on it, in their research lectures and practical training in the teaching of
the department of differential equations, as well as in the organization of independent
learning, specialization in the organization of information technology and information
technology is not studied. Therefore, it is necessary to eliminate a number of problems in
the use of information and communication technologies and teaching technologies, in
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particular, the use of CASE-STUDY technology in the teaching of differential equations in
higher education institutions.
RESEARCH METHODOLOGY
Creating challenging situations for students in the teaching of mathematics,
especially in the department of "Differential Equations" on the basis of teaching
technologies in higher education institutions, it is important to express different opinions,
analyze, synthesize, compare and generalize the problem in different situations, as well as
to identify general, specific, typical cases, to draw conclusions. At the same time, it is
necessary to create a learning environment in which the teacher is able to ask specific
questions, ask questions about the situation, the solution of tasks. This can be done with
the use of modern information technology tools and teaching technologies [1]. Therefore,
as part of the study, we developed a model for increasing the effectiveness of teaching in
the section “Differential Equations” using modern information technology tools and
teaching technologies, including Case-Study technology (see Figure 1).
Today, due to the improvement of the computer and its practical programs, it is
necessary to use the tools of information technology to increase the effectiveness of
teaching subjects in the field of mathematics, in particular, lectures on the topic of
“Differential Equations”. One of such methods is the use of multimedia practical manuals
and mathematical practical packages in the course of computer science and information
technology in the teaching of “Differential Equations” [2]. Improving the mechanism of
using computer practical programs and mathematical practical packages in the teaching of
“Differential Equations” is explained by the development of students’ creative thinking and
the formation of competence [3]. Practical programs and mathematical practical packages
play an important role in solving examples and problems of differential equations and
analyzing their solutions, because the proof of theorems on differential equations is
visualized in the teaching of examples and problem solving [4]. Through such practical
manuals and mathematical practical packages, it is possible to effectively convey topics to
students in the section “Differential Equations” [5]. Therefore, it is recommended to use
the method of demonstration and practical training in the organization of lectures in the
section “Differential Equations”. It is recommended to use e-learning resources
(e-textbooks, e-learning materials), presentation programs and mathematical practical
packages when using the demonstration teaching method.
At the same time, it is recommended to use Case-Study technology in solving
examples and problems in practical classes in the section “Differential Equations”. It
teaches students to work independently and make independent decisions by creating
challenging situations. As a result, students develop the competence to solve examples and
problems on differential equations.
In addition to the organization of lectures and workshops on the section
“Differential Equations”, attention should be paid to independent learning. This is because
more hours are devoted to independent study than lectures and practical classes.
Therefore, it is necessary to improve the form of organization of independent learning in
the section “Differential Equations”. In improving the mechanism of independent learning
on differential equations, the use of information resource centers and science circles is
considered expedient. In information resource centers, it is advisable to use computer
diagnostic and computational software for self-assessment of students. That is, it is
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necessary to use computer diagnostic software tools (problem-solving software, non-
standard tests and crossword puzzles). In the circles, it is recommended to use the method
of oral teaching, i.e. explanation, blitz survey, Brain-Ring game technology. Students will
also be taught examples and problem-solving techniques to help them think creatively and
develop their competencies [6].
Objective: To increase the effectiveness of teaching “Differential
Equations” in higher education
—> Forms of training
Lecture > Practice > Independent
+ 3 + }
[ Forms of training | Information Circles
resource
у у + т J
Exhibition Practica || Colloquial Internet 1. Elective,
| у sources Mathematician
- Examples and у | Brain-Ring. Blitz
Teaching problem solving Shower, question,
aids with the help of flash light, Computer || 2. The Olympics.
т case-study Brain Ring diagnostic || 3. Examples and
technology and problem solving
1 : for creative
calculation hinki
1. E-learning resources. 2. Presentation пебиснов || 108
|| programs. 3. Mathematical practical 4. Tasks aimed at
developing
r ¥ ~| competence.
1. Practical programs that solve mathematical problems. 2.
Non-standard tests 3. Crosswords <
\ у
Outcome: The effectiveness of teaching “Differential Equations”
in higher education will increase
Blitz survey - game technology is aimed at teaching students to organize the
sequence of actions, to think logically and creatively, to choose the right information. This
technology is aimed at directing students to independent thinking in solving the problem.
Brain-Ring game technology is the development of students’ knowledge and
creative abilities, the ability to think independently and develop intellectual abilities. This
game technology creates the following opportunities: broadens students’ worldview in
mathematics; teaches students to prove, explain and defend their ideas; contributes to the
development of cognitive interest in the subject; develops the ability and skills to work in
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a team; forms a sense of collectivism and healthy competition; development of initiative
and activity; encourages perseverance to achieve goals.
It is advisable to conduct the brain-ring as a repetition and generalization lesson or
control lesson. In this case, it is taught in the classroom by a professor on a specific topic.
ANALYSIS AND RESULTS
Experimental work was carried out to determine the level of effectiveness of the
model of training efficiency (shown in Figure 1), developed in the framework of the study,
that is, the section “Differential Equations”. Experimental work was conducted among
students of pedagogical higher education institutions in the field of "Methods of teaching
mathematics." Using the Student-Fischer criterion, we conduct a mathematical-statistical
analysis of the level of efficiency of experimental work. Using this criterion, the formulas
4 4 у?
ХУ их, р, УХ
for the appropriate mean values, п scattering coefficients, itl
variance of the standard deviation, ‘” = VP, > and reliable deviationsé,, == of the
A D
n
= Lay . =,
estimates were used for the sample vn . According to the results of the
calculation, the average mastering rate of the experimental group was higher than that of
the control group, i.e increased by 8%.
CONCLUSIONS AND SUGGESTIONS
Applying the use of computer mathematical packages to increase the effectiveness
of teaching science subjects in the department “Differential Equations” will significantly
improve the quality of mathematical training of specialists. This is usually achieved by
significantly reducing the amount of time spent learning simple and homogeneous
examples and problem-solving techniques.
Based on the results of our research, we came to the conclusion that it is expedient
to use the Maple mathematical practical package in the numerical solution of examples and
problems on differential equations in the conduct of lectures. It is known that the solution
of differential equations is not always obvious, so it is important to develop methods for
solving approximate equations and to use the capabilities of mathematical packages in this
regard. In the approximate solution of the differential equation, that is, in finding a solution
that satisfies the initial or other condition, the question arises as to how to obtain clarity
before the student to obtain the graph of the solution sought.
It is possible to solve problems on differential equations using the Maple mathematical
practical package. The use of the Maple Mathematical Practical Package significantly reduces
the process of students solving high-order differential equations. Also, the Maple
Mathematical Practice Package allows you to solve a typical class of problems using motion-
appropriate procedures. Such procedures are reflected in the reference book of the Maple
mathematical practice package. The Maple Mathematical Practice Package is an effective tool
for graphically representing the results of differential equations. This is especially true when
solving practical problems in lectures or practical classes.
It can be concluded that when using the Maple Mathematical Practical Package,
there is no need to separate the approximate and analytical solutions of differential
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equations. The solution in the Maple Mathematical Practice Package, that is, the
visualization of the results of the calculations, is quite diverse, and students get rid of
redundant calculations and significantly reduce the time. As a result, differential equations
create an opportunity to analyze the properties of their solutions, to develop creative
activity and creative thinking.
REFERENCES
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mathematics teachers based on the use of information technologies// Dissertation for the
degree of candidate of pedagogical sciences. - Moscow, 2014. -231 р.
2. Danilkevich A.V., Methods of teaching multimedia technologies to future
specialists in the field of aesthetic and humanitarian management in the field of
professional education//Dissertation for the degree of candidate of pedagogical sciences.
- Volgograd, 2013. - 175 p.
3. Kapustina T.V., Theory and practice of creation and use in the pedagogical
university of new information technologies on the basis of the computer system
Mathematica (Faculty of Physics and Mathematics)//Dissertation for the study of the
degree of Candidate of Pedagogical Sciences. - M., 2001. - 254 p.
4. Nirenburg T.L., Methodical aspects of the application of the means of Derive in the
secondary school//Dissertation for the study of the degree of candidate of pedagogical
sciences. - SPb, 1997, - 168 p.
5. Ergashev J. B., Improving the content of professional training of future
mathematics teachers on the basis of an integrated approach // Author's abstract of
Doctor of Philosophy (PhD) in Pedagogy. - Tashkent, 2018. - 48 p.
6. Dyachenko S.A., Application of the integrated symbolic system of Mathematics in
the study of the course of advanced mathematics in higher education/ /Dissertation for the
study of the degree of candidate of pedagogical sciences. - Orel, 2000. - 164 p.
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