ESTHETIC EDUCATION IN MATHEMATICS LESSONS WITH THE USE OF SOFTWARE PRODUCTS
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The article deals with the possibilities of information-communication technologies (ICT) for the process of aesthetic education of future specialists teaching natural sciences, including mathematics. Electronic textbook "Mathematics" allows fully opens up all intellectual and creative opportunities for future experts, develops their imagination and broadens their horizons in the use of innovative computer technologies.
700-2247-1-SM.docx
УДК 37.06.322
ESTHETIC EDUCATION IN MATHEMATICS LESSONS WITH THE USE OF SOFTWARE PRODUCTS
A. Dautov1, K. Kozhabaev1, A. Aktaeva1, N. Gagarina1, V. Ludwig2, S.Zykrina1
1 Kokshetau State University after named Sh.Ualikhanov, Kokshetau, Kazakhstan
2 Kokshetau University after named A.Myrzakhmetov, Kokshetau, Kazakhstan
Abstract
The article deals with the possibilities of informationcommunication technologies (ICT) for the process of
aesthetic education of future specialists teaching natural sciences, including mathematics. Electronic textbook
"Mathematics" allows fully opens up all intellectual and creative opportunities for future experts, develops their imagination
and broadens their horizons in the use of innovative computer technologies.
Key words
Esthetic education; mathematical education; information and communication technologies; software product.
ЭСТЕТИЧЕСКОЕ ВОСПИТАНИЕ НА ЗАНЯТИЯХ МАТЕМАТИКИ С ИСПОЛЬЗОВАНИЕМ
ПРОГРАММНЫХ ПРОДУКТОВ
А. Даутов1, К. Кожабаев1, А. Актаева1, Н. Гагарина1, В. Людвиг2, С.Зыкрина1
1 Кокшеуский государственный университет им. Ш.Уалиханова, г.Кокшетау, Казахстан
2 Кокшеуский университет им. А.Мырзахметова, г.Кокшетау, Казахстан
Аннотация
В статье рассматриваются возможности информационнокоммуникационные технологии (ИКТ) в процессе
эстетического воспитания будущих специалистов на занятиях естественных наук и в том числе математики.
Электронный учебник «Математика» позволяет раскрыть в полной мере все интеллектуальные и творческие
возможности будущих специалистов, развивает их воображение, а также расширяет их кругозор в области
применении инновационных компьютерных технологий.
Ключевые слова
Эстетическое воспитание, математическое образование, информационнокоммуникационные технологии,
программные продукты.
Introduction
To form a harmoniously developed personality, the aesthetic education of future specialists must take an important
place. Because of its enormous potential, It is difficult to overestimate the role of mathematics in aesthetic education
Mathematics is very rich in beautiful formulas and proofs, and you can specify whole sections, for example: trigonometry,
the golden section, symmetry, algebra and number theory, and Boolean algebra, etc.
To efficiently disclose the esthetic potential of mathematics, one must assumes the full perception of mathematical
beauty, the development of esthetic senses and taste, an ideal of figurative thinking and logical culture, to orientate person
in his/her aspirations. According to like Zhokhova A.L., Vygotsky L. S., Dzhems V., Kozhabayeva K.G., Kornilov K.N.,
Peters E., Dalinger V. A. education by beauty and through beauty is, on the one hand, an important development tool of
motivation of the doctrine, and on the another a source for becoming an emotional person as one of the main components of
his/her esthetic culture [1 5]. It is a major problem to form an esthetic relation to mathematics as part of culture a when forming the outlook of a
person. [1:184]. He/she has to and can learn to perceive and feel the beauty of mathematical expressions and theoretical
designs, to estimate mathematical designs and works of mathematical culture from the esthetic positions inherent in the
subject when studying it [6]. Disclosing the beauty of mathematics will enable the preparation of future professionals, who
will use special methods to get creativity in the classroom, for life under modern conditions.
The development of the modern ICT does not eradicate the need for creativity, but on the contrary, demands higher
and higher levels of common cultural development, education, creativity and activity. Modern information technologies
open new didactic opportunities in realizing the goals of aesthetic education in mathematics classes [7:49]. These classes
should be used to add the teaching of aesthetic tastes and experiences to the beauty of mathematics, as well as to develop
multimedia tools through methods related to computer graphics and animation, etc.
The electronic textbook "Mathematics", developed by us, can positively influence the formation of aesthetic
qualities, increase interest in studying mathematics and informatics subjects, as well as increase the level of mathematical
knowledge with the use of the latest digital technologies and the level of development of the thinking activity of future
specialists.
This electronic textbook was designed for 3 credits, was created with the use of innovative information and
communication technologies, and is intended for experts. In the course of training, it is supposed to be used for laboratory
and practical work together with software products like Mathematica, Mathcad, Mathlab, Compass3D, and Maple and for
working in the online and offline modes.
The electronic textbook "Mathematician" developed by us has the following sections:
1. introduction;
2. symmetry;
3. numerical approximations;
4. algebraic calculations;
5. golden ratio;
6. processing image and analysis;
7. geometrical calculations;
8. an electronic library;
9. glossary;
10. test tasks;
11. typical solutions of problems. ;
The purpose and tasks of the electronic textbook are:
1. Identifying the relationship of mathematics with different areas of human activity and phenomena occurring in
nature.
2. Expanding the horizons in the application of mathematics.
3. Formation of common and mathematical culture of the person.
4. Esthetic development of the person.
5. Development of logical and figurative thinking in future experts.
6. Development of skills in working with information and communication technologies.
7. Development of skills in the development of modern electronic textbooks in the field of natural sciences.
According to us, it is the most appropriate to use the abovestated software products in the process of illustrative
and demonstrative work integration in the lessons of mathematics and computer science, as well as in the disciplines of the
natural sciences. The interdisciplinary approach is one of the priority areas in modern pedagogical science [8:96].
According to Russian scholars [7, 9, 10], "the mathematical apparatus and mathematical methods can be used in the study of
qualitatively different fragments of reality, …promote disclosure of their unity and thus indicate new ways of integrating
new knowledge ... "[11].
The interdisciplinary approach allows future specialists to understand the subject communication more fully, learn
to apply new innovative ICT capabilities, and to feel the aesthetic appeal of the sections of mathematics
The practical part of the electronic textbook is built in the course of performing laboratory, practical tasks in
software products
The practical part of the electronic textbook was built during the implementation of laboratory and practical tasks
in software like Mathematica, Mathcad, Mathlab, Compass3d, Maple, as well as in online and offline modes. .
Studying the fundamentals of the above tools of software products unite in themselves all innovative
communication technologies. They represent the opportunity to experiment and conduct experiments on modeling with
various solutions to problems, and to analyze and synthesize any kind of information. The computational and multifunctional system of the electronic textbook “Mathematics” is known as the most
powerful research and mathematical platform. Many examples show how it can be applied in various fields of the natural
sciences (see Fig. 1)
The software product Mathlab is a highlevel interpreted programming language, has a wide range of functions, an
integrated development environment, objectoriented capabilities and interfaces with programs written in other
programming languages (see Fig. 2). Programs written in Mathlab come in two types; functions and scripts. The main
feature of the Mathlab language is its wide possibilities for working with matrices, which the creators of the language
expressed in the slogan "Think vectorized".
The next package of application programs, Mathcad, allows you to create corporate and industryspecific means of
certified calculations in various branches of science and technology, including mathematics, providing a unified
methodology for natural aesthetic perception to illustrate the solution of various mathematics (see Figure 3) Maple is a powerful and versatile system that has become the standard of threedimensional design, thanks to the
simple mastery and wide possibilities of mathematical modeling of various objects (see Fig. 4).
Each practical, laboratoryexperimental task is accompanied by a lecture (using a presentation and a full text) on
the topic of the lesson. For example, when studying the topic "Vectors," "Matrixes," and "Tensors," students are asked to
get acquainted with the concept of a vector, a onedimensional vector, a multidimensional vector, matrices, and tensor.
They also get acquainted with the history of the origin and creation of vectors and matrices by their various forms, and with
the use of matrices and tensors in various fields of science. They are asked to compare, analyze and reveal their beauty in
nature and life. Vectors and matrices with their various kinds, the initial information about the complex plane and complex
numbers are involved in the classes on programming and the construction of algebraic computations.
It is then suggested that students do several practical exercises on the subject in various programs, to construct
various images of matrixes and vectors and also a tensor, and their compositions, to design an ndimensional image with
multimedia. While they perform these tasks they can use the possibilities of any program (graphics, animation, multimedia,
programming use of Script).
Let's show how Mathcad allows you to build and create matrix objects. As an example, let us consider the process
of solving a system of a linearalgebraic equation (SLAE) using the Gauss method. Consider the system of linear equations:
……………
¿
¿
¿
¿ We write the system in the matrix form: А * х = b,
¿
¿
¿
…………
A=¿
where
А – is the matrix of the coefficients;
b the right side of the constraints;
х is the vector of variables that you want to find.
Where Rang(A) = p. The process of solving SLAE on Mathcad is as follows (see Fig. 5).
Having received the image, it is possible to emphasize its beauty with various special effects of the program. To
transform it to even more interesting form see fig. 6
Conclusion
Proceeding from the above research of scientists, it can be concluded that aesthetic education occupies an
important place in the process of personality development.
If we use modern information and communication technologies, whose capabilities allow us to show the beauty of
mathematical objects, and the harmony of the shapes of geometric bodies, we can achieve even greater results in both
aesthetic education and in mathematical education.
One of the best tools for constructing and studying aesthetic objects of mathematics is packages with the use of
software products, such as: Mathematica, Mathcad, Mathlab, Compass3d, and Maple. They allow us to fully discover all
the intellectual and creative abilities of individuals, to develop their imagination, and to broaden the horizons of ICT. Thus, the use of the innovative technology of the above software products makes it possible to increase interest in
learning, to develop the information and technological culture and logical thinking of the future specialist to form an
optimal analysis of the task in its solution
Literary list:
1. Kozhabaev K.G. Educational and Developmental Training in Mathematics, and the Preparation for the Future
Teacher: Textbook / Kokshetau: Izd. KSU them. Sh. Ualikhanov, 2009. 273 p.
2. Zhokhov, A. L. How to help shape the world outlook of schoolchildren [Text] / AL Zhokhov. Samara: Ed.
Himself. GPU, 1995. 288 p.
3. Vygodsky LS Pedagogical psychology. Ed. V.V. Davydov. Moscow: Pedagogika, 1991. 480 p.
4. James B. Is there a Consciousness? // New Ideas in Philosophy. St. Petersburg, 1913. Issue 4.
5. Kornilov K.N. The Doctrine of Human Reactions. M., 1924.
6. Peters E. School Full of Life. M., 1912.
7. Dalinger V.A. CognitiveVisual Approach and its Features in Teaching Mathematics // Mathematics and
Informatics: Science and Education: Interuniversity Collection of Scientific Proceedings: Yearbook. Issue. 4. Omsk: Ed.
OmGPU, 2004. P. 4855.
8. Zhokhov AL Cognition of Mathematics and the Foundations of a Scientific World Outlook: Worldview on the
Direction of Mathematics [Text]: Proc. Help. Yaroslavl: Izdvo YAGPU, 2008. 183 p.
9. Smirnov E. I. Unified Mathematics in Problems as an Element of Integration of Mathematical Knowledge [Text]
/ EI Smirnov // Problems in Teaching Mathematics: theory, experience, innovations. AllRussia. Scientificpractical. Conf.,
cons. 115 Anniversary of Corporative Cor. APN USSR P. A. Larichev. Vologda: Russia, 2007. P. 6877.
10. Visual Modeling in Teaching Mathematics: Theory and Practice: Textbook / Ed. E.I. Smirnova. Yaroslavl: IPC
Indigo, 2007. 454 p.
11. Rozin V.M. Methodology: Formation and Modern State. Tutorial. Moscow: The Moscow Psychological and
Social Institute, 2005. 414p Fig. 6. Process of the solution of a task on Mathlab
Note on the authors:
Dautov Aibek, Ph.D student of mathematics, Kokshetau State University after named SH.Ualikhanov,
Kazakhstan, https://orcid.org/0000000277858799, [email protected]
Kozhabaev Kaiyrzhan, doctor of pedagogical sciences, Professor, Academician of the RAE, Kokshetau State
University after named SH.Ualikhanov, Kokshetau, Kazakhstan, [email protected]
Aktayeva Alkena, doctor Ph.D, associate professor, Kokshetau State University after named SH.Ualikhanov and
Almaty Technological University, Kazakhstan, [email protected]
Gagarina Nadezhda, candidate of technical sciences, Professor, A. Myrzakhmetov Kokshetau University, Almaty
Technological University, Kazakhstan, [email protected]
Ludwig Van Graan, MSc of IS technology, teacher at the department ISI, A.Myrzakhmetov Kokshetau
Гагарина Надежда, к.т.н., профессор, Кокшетауский университет им. А.Мырзахметова, Казахстан,
_08@
mail
. ru
gagarina
University, Kazakhstan, [email protected]
Zykrina Simbat, Ph.D student of mathematics, Kokshetau State University after named SH.Ualikhanov,
Kazakhstan, [email protected]
Об авторах:
Даутов Айбек,
Ш.Уалиханова, https
:// orcid
Ph.D – докторант математики,
. org
/0000000277858799, [email protected]
Кокшеуский государственный университет им.
Кожабаев Кайыржан, д.п.н., профессор, академик РАЕ, Кокшеуский государственный университет им.
_2008@
mail
Ш.Уалиханова, г. Кокшетау, Казахстан, labdid
. ru
Актаева Алкена, доктор Ph.D, профессор, государственный университет им. Ш.Уалиханова, Казахстан,
[email protected] Ван Граан Людвиг, магистр технологии ИС, преподаватель «ИСИ», Кокшетауский университет им.А.
Мырзахметова, Казахстан, [email protected]
Зыкрина Сымбат,
05 z @ mail
Ш.Уалиханова, sim
Ph.D – докторант математики,
Кокшеуский государственный университет им.
. ru
ESTHETIC EDUCATION IN MATHEMATICS LESSONS WITH THE USE OF SOFTWARE PRODUCTS
ESTHETIC EDUCATION IN MATHEMATICS LESSONS WITH THE USE OF SOFTWARE PRODUCTS
ESTHETIC EDUCATION IN MATHEMATICS LESSONS WITH THE USE OF SOFTWARE PRODUCTS
ESTHETIC EDUCATION IN MATHEMATICS LESSONS WITH THE USE OF SOFTWARE PRODUCTS
ESTHETIC EDUCATION IN MATHEMATICS LESSONS WITH THE USE OF SOFTWARE PRODUCTS
ESTHETIC EDUCATION IN MATHEMATICS LESSONS WITH THE USE OF SOFTWARE PRODUCTS
ESTHETIC EDUCATION IN MATHEMATICS LESSONS WITH THE USE OF SOFTWARE PRODUCTS
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