International Journal of Pedagogics
218
https://theusajournals.com/index.php/ijp
VOLUME
Vol.05 Issue04 2025
PAGE NO.
218-221
10.37547/ijp/Volume05Issue04-57
1
On the Question of Scientific-Historical and Inter-Subject
Relations of Physics and Mathematics in The Process of Their
Teaching
Nurillayev Bobomurot Nadzhmitdinovich
PhD, Associate Professor, Tashkent State Pedagogical University named after Nizami, Uzbekistan
Received:
28 February 2025;
Accepted:
25 March 2025;
Published:
28 April 2025
Abstract:
This article provides information on the importance of teaching physics in close connection with
mathematics in the preparation of future teachers in higher education institutions. Also mentioned is a brief
history of the relationship between physics and mathematics, the role of mathematics in teaching physics, an
important form of connection between physics and mathematics, and the importance of solving mathematical
problems of physical content.
Keywords:
Interdisciplinary communication, physical meaning, theory and experiment, mathematics, universality
of Newton's research, Schrödinger's equations, special theory of relativity, object, matrix, space, equations of
motion, history of physics.
Introduction:
At present, there is probably no need to
prove the importance of interdisciplinary connections
in the teaching process. They contribute to the better
formation of individual concepts within individual
subjects, groups and systems, the so-called
interdisciplinary concepts, that is, those whose full
understanding cannot be given to students in a lesson
of any one discipline (concepts of the structure of
matter, various processes, types of energy).
The modern stage of development of science is
characterized by the interpenetration of sciences into
each other, and especially the penetration of
mathematics and physics into other branches of
knowledge. The connection between academic
subjects is, first of all, a reflection of the objectively
existing connection between individual sciences and
the connection of sciences with technology, with the
practical activities of people.
The development of mathematics from ancient times
and physics to the present day has been the scientific
and methodological basis in the development of
natural and technical sciences (applied), in particular
physics and integrative connections with other sciences
(subjects).
Implementation of interdisciplinary connections helps
students to form a holistic understanding of the
phenomena of the surrounding reality and the
relationship between them. Therefore, they make
knowledge more practically significant and applicable
in the future profession, develop and increase interest
in the chosen profession. They help students to apply
the knowledge and skills that they have acquired while
studying some subjects, to use them when studying
other subjects, and give the opportunity to apply them
in specific situations [9].
Naturally, physical science includes: theoretical and
experimental parts. Physics is a fundamental science,
since it includes both theoretical and experimental
studies of material systems, and is the basis for other
natural sciences. Physics is an experimental science. An
experiment confirms or denies the conclusions of
physics, includes systematic observations, experiments
and measurements. The theoretical part provides for
generalizations,
classification
and
analysis
of
experimental data, the establishment of physical laws,
the advancement of scientific hypotheses and the
creation of scientific theories. Mathematics, too, as a
theoretical science, includes an applied aspect. In the
historical development of science, mathematics as the
basis of fundamental sciences forms abstract symbolic
and digital types, their relationships and a system of
rules for interaction between symbolic concepts, their
quantities in accordance with the internal logic of the
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International Journal of Pedagogics (ISSN: 2771-2281)
development of the subject of science. It is this
approach and connection in the perception and
mastering of the science of mathematics that is the
foundation of the evolutionary development of natural
sciences, in particular reflecting the internal logic of the
development of objects and phenomena according to
the laws of nature. Mathematics as a fundamental
science evolved, objectively, in certain stages during its
formation and development as part of the natural
philosophy of antiquity. The first, initial formation of
ancient mathematics was closely connected with the
measuring and computational issues of practice during
the formation of human civilization. Its further
development led to the abstraction and reflection of
objective reality in the forming and developing
consciousness of ancient man - mental representations
in the form of symbolic-sign models, systems and their
relationships with the original - an object or
phenomenon, in particular physical.
METHODOLOGY
In line with the above, it is clear that mathematics is a
product of abstract, mental activity of the human mind.
Therefore, the emergence of many areas of this science
is (a product) essentially abstract. The applied aspect of
their use is due to the search for solutions to various
types of equations - practical, mathematical problems.
Namely, such problems of mathematics in the study of
objects and phenomena of objective reality are one of
the applied aspects of its effective use in natural, in
particular physical science.
Rational use of intra- and interdisciplinary connections
and their relationships ensure the effectiveness of the
mathematical apparatus in research of natural
sciences, in particular physics. Another aspect of this
effectiveness is the scientific - logical reflection
(display) of qualitative and quantitative connections
with reality in the language of mathematics.
In the context of our study, some historical and
methodological aspects and stages of the development
of physics are analyzed.
In the XIX-XX centuries, after the recognition of
mechanics as a classical science, which is the main
foundation for the formation of physics and physical
theories.
It is necessary to note a certain historical and
meteorological orientation of the formation and
development of physical theories. In further
development, they received a generalized theoretical
and strict mathematical formulation. Thus, Kepler,
based on astronomical and mathematical data (Tycho
Brahe), rejected the theory of a circular planetary orbit.
Having excluded the centuries-old - Aristotelian
assertion that everything in nature is perfect, and a
circle is a perfect geometric figure and the planets
move in circles. Another mistake is the incorrect idea of
the supporters of the Aristotelian doctrine that
everything around (the Earth), i.e. reality is changeable,
and the Earth at rest is motionless.
To substantiate Kepler's conclusions, in the form of
physical laws, not only Newton's mechanics played a
major scientific role, but also his mathematical
contribution to the new direction of creating the theory
of differential and integral calculus. Newton and his
theory of gravitation, which proclaimed the universal
law of nature - the law of universal gravitation. The
influence of Newton's views on the development of
physics. Analytical geometry according to Newton and
the theory of motion of celestial bodies.
The universality of Newton's research is unique.
It should be emphasized that the history and
methodology of the development of science, in
particular physics, did not always require strict
mathematical justification when creating and
developing fundamental theories.
However, the disclosure of ideas and the content of
physical connections (various) objects and phenomena
was carried out by various logical and mathematical
methods, as well as signs, symbols and their
relationships in the interpretation of various solutions.
Thus, Maxwell used a system of partial differential
equations to generalize the results of numerous
experiments by Faraday and his predecessors.
It is appropriate to note that A. Einstein, when creating
the special theory of relativity based on the
generalization of Newtonian mechanics and various
approaches to the theory of relativity, did not use a
special, new mathematical apparatus. However, the
methodological approach to physical phenomena was
carried out on the basis of the relations between
energy, mass, speed (of light), space and time
formulated by Einstein. At the same time, many
physicists, especially experimenters, in an attempt to
reject Einstein's theory of relativity by experimental
tests, on the contrary, led to its correctness [1]. As a
result, the term "ether" turned out to be inadequate in
relation to space.
According to modern concepts, space is a physical
vacuum.
It should be noted that the harmonious structure of the
presentation of the special theory of relativity,
completed by Einstein-Minkowski, is based on
multidimensional geometry (topology) [2]. Thus, the
fundamental change in the approach to the
relationship between space and time according to
Euclid - Newton was the creation of the general theory
International Journal of Pedagogics
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International Journal of Pedagogics (ISSN: 2771-2281)
of relativity by Einstein, which finally changed the world
of Newtonian mechanics. Within the framework of the
general theory of relativity, which united the inertial
and non-inertial systems, the methodological
relationship is revealed based on the special theory of
relativity and the principle of equivalence, for this
Einstein chose Riemannian spaces, studied by
mathematicians long before the creation of the general
theory of relativity [2].
At the end of the 19th century, difficulties arose in
physically explaining the spectrum of thermal radiation
within the framework of classical physical theories
(Maxwell and others) [4]. This problem was solved by
Max Planck, in contradiction with Maxwell's theory -
classical electrodynamics, with thermal radiation,
energy is emitted not continuously (discretely), but in
separate portions - quanta. In this case, the energy of
each portion is directly proportional to the frequency
of the radiation and is determined by the formula [4].
The proportionality coefficient was called Planck's
constant, and it is equal to: h = 6.63 10-
34 J∙s. After
Planck's discovery, the most modern and profound
physical theory - quantum physics - began to develop.
Quantum physics is a section of theoretical physics that
studies quantum-mechanical and quantum-field
systems and the laws of their motion. The behavior of
all microparticles is subject to quantum laws. But the
quantum properties of matter were first discovered in
the study of the emission and absorption of light.
DISCUSSION
The attitude of scientists of that time to the proposal of
Max Planck was ambiguous. Such an attitude was
conditioned by the established ideas about the
continuity of natural processes and their main dynamic
parameters of the categories: energy, momentum and
angular momentum.
Another contradiction was the use of the
generalization of the quantum hypothesis to explain
the structure of levels. Niels Bohr's postulate that an
electron moving along a closed trajectory does not
radiate (energy) was in contradiction with Maxwell's
theory [4]. Since, the Bohr model of the atom explains
a large set of data on atomic spectra [3].
The Bohr model of the atom (the Bohr model, the Bohr-
Rutherford model) is a semi-classical model of the atom
proposed by Niels Bohr in 1913. He took as a basis the
planetary model of the atom put forward by Ernest
Rutherford. However, from the point of view of
classical electrodynamics, an electron in Rutherford's
model, moving around the nucleus, should emit energy
continuously and very quickly and, having lost it, fall
onto the nucleus. To overcome this problem, Bohr
introduced an assumption, the essence of which is that
electrons in an atom can move only along certain
(stationary) orbits, being on which they do not emit
energy, and radiation or absorption occurs only at the
moment of transition from one orbit to another.
Moreover, only those orbits are stationary, when
moving along which the angular momentum (angular
momentum) of the electron is equal to an integer
number of Planck's constants
As a result of this approach to the problem according
to Planck, it became possible to reconcile the
contradictions between Maxwell's theory and Bohr's
model.
It should be noted that M. Planck and N. Bohr did not
need to develop new methods of calculation in
mathematics for quantitative integration of radiation
spectra.
However, to implement quantum, a solid foundation
was needed, in line with the elimination of the above
contradiction. Such a foundation was the Schrödinger
equation. When deriving the famous equation,
Schrödinger relied on the mathematical theory of
magnetic operators. At the same time, it became
possible to introduce a general equation of motion,
which at h→0, in the limit, passed
into Newtonian
mechanics, where each value is specific and
understandable.
In the Schrödinger equation, there is little content
about the wave function. What is its physical meaning?
It should be noted that the physical meaning of the
function, initially, was not clear even to Schrödinger
himself [4]. Nevertheless, the wave formalism of
Schrödinger's theory was accepted, since it made it
possible to solve problems of quantum mechanics
using well-developed methods of mathematical physics
[5]. In 1926, the generally accepted idea of the physical
meaning of the wave function was accepted by the
hypothesis of the theoretical physicist Born, according
to which the square of the modulus of the wave
function determines the probability of detecting a
particle at a given point in space, i.e. the function
received a probable interpretation [4]. At the same
time, (1926) W. Heisenberg proposed a matrix form of
the equation of quantum mechanics. As Niels Bohr
notes [7], although Heisenberg was not familiar with
the basics of matrix calculus and he proposed rules for
operations with matrices.
CONCLUSION
The implementation of the idea of interdisciplinary
connections in pedagogy and teaching methods is
closely connected with the methodological views of
teachers on the problem of synthesis and analysis of
scientific knowledge as a specific expression of
differentiation of sciences. The theoretical and
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International Journal of Pedagogics (ISSN: 2771-2281)
practical solution to this problem changed in
accordance with the development of society, its social
orders of pedagogical science. The approval and
strengthening of the subject system of teaching in the
modern educational process is inextricably linked with
the development of the idea of interdisciplinary
connections [9].
From a brief analysis of the scientific, historical and
methodological foundations of the relationship
between physics and mathematics, the following
conclusions follow:
1. The scientific discovery of physical laws and patterns
is
based
on
the
corresponding
theoretical
mathematical apparatus of relationships, expressions
and theories in the form of a system of equations.
2. Physical theories, laws, various mathematical
methods and their relationships are interconnected
and interdependent.
3. New physical theories have been developed (are
being developed) by scientists (from different
countries), independently and objectively.
4. To focus the attention of teachers and students on
the key aspects of academic subjects that play an
important role in revealing the leading ideas of
sciences.
5. To form the cognitive interests of students by means
of a wide variety of academic subjects in their organic
unity;
6. To carry out creative cooperation between teachers
and students;
7. To study the most important ideological problems
and issues of our time by means of various subjects and
sciences in connection with life.
REFERENCES
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1968
Buravikhin V.A., Egorov V.A. Biography of the electron,
Moscow Publishing House "Znanie" 1885
Kudryavtsev P.S., Course in the history of physics.
Textbook. M.P., 1982, 448 p.
Nevanlinna R. Space, time and relativity. Moscow
Publishing House "Mir", 1966
Nikolaev P.N., History and methodology of physics,
Volumes 1 and 2, Moscow State University, 2014
Planck M. On Schrödinger's works on wave mechanics.
Moscow Publishing House "Nauka", 1975
Sitruchkov V.V., Yavorsky B.M. Issues of modern
physics. M. Education, 1973
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M.A.
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https://infourok.ru/mezhpredmetnie-svyazi-v-
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