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TECHNOLOGY OF TEACHING THE TOPIC OF PROJECTIONS DEFINED BY
NUMERALS
Bozorova Sevara Ravshan kizi
Bachelor's student of the "Fine Arts and Engineering Graphics"
Direction
Annotation:
This article explores modern pedagogical technologies for effectively teaching the
topic of projections defined by numerals in engineering graphics and descriptive geometry. The
study emphasizes interactive methods, digital visualization tools, and step-by-step instructional
strategies to enhance students’ spatial imagination and mathematical thinking. The integration of
numerically defined projections into the curriculum not only strengthens technical drawing skills
but also improves learners’ ability to interpret complex spatial relationships. The paper also
analyzes challenges faced by students and proposes solutions for better comprehension and
engagement.
Keywords:
projections, numerals, teaching technology, engineering graphics, descriptive
geometry, spatial thinking, technical drawing, interactive learning
The concept of projection is one of the main sections of engineering graphics and drawing
geometry, which studies the principles of constructing images of objects projected onto a plane.
The concept of projections defined by numbers is based on the method of expressing and
determining projection images through numerical coordinates. This approach is widely used in
the fields of drawing geometry, engineering graphics and 3D modeling. Projections defined by
numbers are images of geometric objects projected onto a plane, which are clearly defined
through numerical coordinates. In this approach, each point or drawing element (lines, planes,
points) is expressed using precise mathematical formulas and numbers. Numerical projections
have the following basic principles: each geometric object is defined by coordinates, dimensions
and shapes are expressed with precise mathematical accuracy, and allow for automated image
creation in graphics and computer systems. This projection method is especially widely used in
engineering graphics, computer graphics, and drafting geometry.
Numerical projections are fundamentally different from traditional projection methods. In this
case, the laws of geometry are given using numerical coordinates and mathematical expressions.
In the fields of engineering and architecture, such projections have the following important
values: accuracy and precise measurements - allow for automatic calculation and verification of
drawings using computer programs; automation - geometric objects can be numerically defined
and automatically drawn in CAD (Computer-Aided Design) programs; 3D modeling - serves as
an important basis for creating three-dimensional models. Numerical projections are widely used
in the following areas: engineering graphics - for accurate projection of industrial details and
structures, architecture - for developing projections of buildings and structures, geodesy and
cartography - for determining the exact coordinates of the earth's surface, computer graphics and
animation - for creating three-dimensional models.
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Numerical projection methods have the following basic principles: a correct coordinate system -
points, planes and bodies are defined using coordinates; projection relations - each geometric
shape is described based on certain projection rules; mathematical formulas - changes in bodies
in projections are carried out through precise mathematical calculations. Understanding
numerical projections requires knowledge of the coordinate system, vector algebra and analytical
geometry.
The use of modern educational technologies in teaching this topic is effective. The following
methodological approaches are considered the most effective: the use of computer programs -
conducting practical exercises using AutoCAD, SolidWorks and other engineering programs,
practical examples and tasks - explaining each projection method with real-life examples,
interactive learning - explaining the essence of projections to students through 3D modeling and
visual technologies. Through these methods, students can clearly understand and apply
numerically defined projections in practice.
Numerical projections are an important part of modern engineering and drawing geometry. This
projection method provides greater accuracy, automation and easy modification compared to
traditional projection methods. In order to effectively teach this topic, it is necessary to pay
attention to the use of computer technology and practical exercises in the educational process.
Numerical projections are one of the important sections of geometry and are widely used in
drawing geometry, engineering graphics and technical design. This method is used to determine
the spatial location of objects and construct their projections. Three main parameters are used to
define numerically defined projections based on the Cartesian coordinate system: ∆x (length
change), ∆y (width change), and ∆z (height change). Using these parameters, it is possible to
accurately describe the dimensions of objects in space and their projections.
The word technology entered science in 1872. It comes from the Greek "techos" - craft, skill
and "logos" - doctrine or science. In short, it means "science of skill". Today, some people
think that pedagogical technology is only related to information technology and the use of
TSO, computers, distance learning, or various techniques that must be used in the teaching
process. This is not true. The main basis of pedagogical technology is the technologies
selected by the teacher-trainer and students-students to jointly achieve a guaranteed result
from the given goal. The expression "pedagogical technology" was first introduced in 1970
by the Japanese scientist T. Sakamote. According to the scientist, pedagogical technology
(teaching technology) is a field of knowledge related to a system of guidelines that ensure
the acceptability of teaching. Professor N.F. Talizina believes that pedagogical technology
consists in identifying rational methods for achieving a given educational goal. Professor N.
Saidahmedov says that pedagogical technology is a project of a certain pedagogical system
that can be implemented in practice. According to Professor M. Ochilov, pedagogical
technology is a set of methods and techniques used in the learning process, taking into
account the interaction of human potential and technical means, in order to facilitate the
forms of education, guarantee their results and objectively evaluate them. This concept is
defined by UNESCO as follows: pedagogical technology is a systematic (designed) method
(method) for identifying, creating, and applying all processes of teaching and learning,
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taking into account technical means, human potential and their interaction, in order to
optimize the forms of education. Pedagogical technology is a set of methods and tools used
in the learning process to achieve the intended goal of education. Pedagogical technology
has existed for a long time, both old and new. However, as society develops, it increasingly
sets new social demands on education, and the educational process is enriched and updated
with modern advanced methods and techniques.
There are many areas of pedagogical technology. The current traditional education is the
classroom system, which was formed in the 17th century on the basis of the didactic
principles of Ya.A. Comenius and is currently the most widely used in schools around the
world. Modern pedagogical technologies were created mainly to improve this system in
various directions and are currently developing in various directions. They are pedagogical
technologies based on improving the pedagogical process, directing it to the student;
pedagogical technologies aimed at activating and intensifying student activity; pedagogical
technologies based on didactic improvement and redevelopment of educational material;
pedagogical technologies based on effective management and organization of the
educational process; pedagogical technologies adapted to nature; developmental educational
technologies, etc. [9].
The realization of the goal and the achievement of a guaranteed result in education depend
on the collaborative activities of both the teacher and the student, as well as the goals they
set, the chosen content, method, form, and means, that is, technology.
The choice of technology for the teacher and the student to achieve the goal is up to them,
because the main goal of both parties is to achieve a specific result, in which the teacher
selects the technology to be used depending on the level of knowledge of the students, the
nature of the group, and the circumstances, for example, to achieve the result it is necessary
to work with a computer, perhaps a film, handouts, drawings and posters, various literature,
information technology will be needed, these depend on the teacher and the student.
At the same time, it is necessary to design the teaching process in advance, in this process
the teacher must take into account the specifics of the subject, the place and conditions, the
subject, and most importantly, the student's capabilities and needs, and the ability to
organize collaborative activities, only then can the desired guaranteed result be achieved. In
short, the student must be brought to the center of education.
In order for the teacher to see each lesson as a whole and visualize it, it is necessary to
design the process of the upcoming lesson. In this case, it is of great importance for the
teacher to draw up a technological map of the upcoming lesson, because the technological
map of the lesson is drawn up for each topic, each lesson based on the nature of the subject,
science being taught, the capabilities and needs of students. The technological map of the
lesson can be compared to the scenario of all technological processes from the arrival of
porcelain raw materials in the form of clay at the factory to the finished bowl.
It is not easy to draw up a technological map, because for this the teacher needs to be aware
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of pedagogical, psychological, special methodologies and information technologies, as well
as know a lot of methods and techniques. The colorfulness and interest of each lesson
depends on the planned technological map of the lesson, carefully thought out in advance.
The form in which the technological map of the lesson is drawn up depends on the teacher's
experience, goals and discretion. No matter how the technological map is drawn up, it
should reflect the lesson process as a whole and fully reflect the clearly defined goal, task
and guaranteed result, the technology of organizing the lesson process. The structure of the
technological map frees the teacher from writing an extended lesson outline, since all
aspects of the lesson process will be reflected in such a map.
The construction of the technological map, based on the capabilities and needs of the
student, brings him to the center of education as a person. This makes it possible to increase
the effectiveness of teaching.
Treating students as individuals in the teaching process, using various pedagogical
technologies and modern methods, encourages them to think independently, freely, research,
approach each issue creatively, feel responsible, conduct scientific research, analyze, use
scientific literature effectively, and most importantly, increase their interest in reading,
science, pedagogy, and their chosen profession.
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