Volume 05 Issue 01-2025
31
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
05
ISSUE
01
Pages:
31-36
OCLC
–
1368736135
A
BSTRACT
This article highlights methods for developing independent thinking skills in primary school students
through logical problems. It presents several logical problems along with their solutions.
K
EYWORDS
Mathematics, primary school, educator, independent thinking, word problems, critical thinking, simple
problems, complex problems.
I
NTRODUCTION
In the early years of our country's independence,
fundamental reforms in the field of public
education were initiated. Indeed, from then on,
“Nurturing spiritually advanced individuals,
elevating education and enlightenment, and
raising a new generation capable of realizing the
idea of national awakening will remain one of the
most important tasks of our state.”
In primary grades, where a child's consciousness
and thinking are just beginning to develop, the
teacher's expertise plays a crucial role. Their
ability to skillfully integrate modern technologies
into the educational process, explore new
methods and approaches in teaching, and
creatively
utilize
advanced
pedagogical
experiences is of utmost importance. Therefore,
Journal
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Research Article
DEVELOPING INDEPENDENT THINKING IN PRIMARY
SCHOOL STUDENTS THROUGH LOGICAL PROBLEMS
Submission Date:
October 28,
2024,
Accepted Date:
December 26, 2024,
Published Date:
January 23, 2025
Crossref doi:
https://doi.org/10.37547/ijasr-05-01-06
Mamasaidova Muhabbat Abdusalom qizi
Fergana State University, Lecturer, Doctor of Philosophy (PhD) in Pedagogical Sciences, Uzbekistan
Xakimova Oqilaxon Odiljon qizi
Fergana State University, 1st-year Master's Student, Uzbekistan
Volume 05 Issue 01-2025
32
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
05
ISSUE
01
Pages:
31-36
OCLC
–
1368736135
using modular teaching technology and preparing
to implement modern pedagogical technologies
in practice have become important requirements
for contemporary primary education. Modern
pedagogical
technologies,
firstly,
create
opportunities for students to easily and
enthusiastically acquire knowledge, skills, and
competencies. Secondly, they contribute to the
professional growth and spiritual development of
teachers.
As our esteemed President Sh. M. Mirziyoyev
emphasized: “Mathematics is the foundation of all
sciences. A child who excels in this subject grows
up intelligent and broad-minded, capable of
succeeding in any field.” Teaching students to
develop their thinking abilities leads to significant
transformations in society. This is because our
country has a great need for highly qualified
specialists who are confident, independent
thinkers, and proactive. The role of academic
subjects in shaping
students’ personal qualities is
invaluable. In this regard, mathematics education
bears significant responsibility. Textbooks are
primarily designed to develop students'
mathematical knowledge, imagination, reasoning,
logical, and independent thinking skills. They are
written with consideration of students’ abilities,
age, individual characteristics, and the need to
acquire 21st-century skills. The tasks are
structured in a spiraling manner, progressing
from simple to complex. As we know, in the field
of mathematics, using methods that foster
independent thinking and enhance creative
thinking is essential for providing students with
deep knowledge. This is a key task of primary
education. To accomplish this, new pedagogical
technologies have been introduced into the
educational process. These new technologies play
a vital role in the intellectual development and
maturation of primary school students. One of the
most widespread forms of pedagogical
technologies today is interactive methods.
The content of each subject at every stage of
education allows students not only to perceive
and memorize information but also to engage in
reflection by posing questions that require
analysis. Such activities play a decisive role in
shaping students' thinking abilities, including
recognizing questions, finding ways to clarify
them, performing necessary actions, and drawing
correct conclusions. This generalized ability to
think critically is at the core of the learning
process.
The ability to think logically is essential for
students. It is impossible to fully grasp material
without possessing even the most basic logical
thinking skills. Teaching and developing logical
thinking should be closely aligned with natural,
real-life situations. At the same time, pedagogical
tools must take into account the age-related
characteristics of a child's development (both
psychological and physical). While current school
curricula do include exercises for shaping logical
universal actions, given the need to foster
abstract thinking, it is logically appropriate to
develop an additional program aimed at
advancing logical thinking, which can be
incorporated into any lesson during the
educational process.
Volume 05 Issue 01-2025
33
International Journal of Advance Scientific Research
(ISSN
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2750-1396)
VOLUME
05
ISSUE
01
Pages:
31-36
OCLC
–
1368736135
Currently, there are various methods for shaping
logical universal learning actions. In order to
incorporate additional exercises to develop
logical thinking, each teacher must analyze and
consider the physical and psychological
characteristics of young students, taking into
account the individuality of each child. Such tasks
can be implemented not only during the
educational process but also in extracurricular
activities and virtually any lesson.
Solving mathematical problems is a crucial
component of teaching mathematics. It is
unimaginable to master mathematics without
solving problems. The practical application of the
theory of problem-solving in mathematics is an
essential method of instruction. Solving problems
plays a significant role in helping students grasp
theoretical material in primary grades and
enhances their thinking abilities. Problems are
structured based on a system of practical tasks.
This means that each new concept is solidified by
solving a problem that requires the application of
that concept, helping to explain its importance.
Simple problems are used to explore the content
of arithmetic operations, reveal the connections
between the operations and their components,
and familiarize students with relationships
between different quantities. Simple problems
serve as the foundation for developing the
knowledge, skills, and abilities necessary for
solving more complex problems.
In primary grades, the study of problems is
carried out by forming new concepts and
transitioning from solving simple problems to
solving more complex ones. This process involves
various simple problems related to addition,
subtraction, multiplication, and division
—
such as
finding the sum of identical addends, dividing
numbers into equal parts, multiplying and
dividing numbers, as well as problems related to
enlarging and reducing numbers. These problems
help students compare numbers and solve other
related problems. Additionally, methods and
games that aid in solving problems will be
explored.
One such game is "Think Up", which can be used
to stimulate students' creative and logical
thinking.
Didactic Task: Developing students' spatial
imagination.
Game Task: Enhancing students' logical thinking
abilities through solving circular problems.
Game Description:To play this game, a magnetic
board or a chalkboard, a picture of the planet, and
cards with written problems are prepared in
advance. The game is played as follows: A
magnetic plate is glued to the back of each card
with a problem written on it. The students
themselves must place the cards on the board in
the correct order as they progress.
For example,
Volume 05 Issue 01-2025
34
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
05
ISSUE
01
Pages:
31-36
OCLC
–
1368736135
the teacher could prepare a series of arithmetic
problems or logical tasks related to the theme of
the planet, and students will place the cards in the
correct sequence to form a solution path. This
exercise helps develop their logical thinking and
spatial reasoning.In this game, the teacher
explains to the students that as the airplane
slowly ascends from the ground, the answers to
the problems also progress in an increasing order.
The airplane ascends into the sky and gradually
descends to land. The teacher must monitor
whether the students solve the problems
correctly. If the students find the correct answers,
the airplane is flying correctly. To make the game
even more engaging, it can be referred to as the
"Circular Problems" game. This will not only help
students develop their logical thinking but also
make the learning process fun and interactive as
they visually follow the progression of the
airplane.
Game Description
: Students are introduced to
the rules of the game. Each student in the class is
given a numbered card with a number from 1 to
10 written on it. Then, they are given the
following task: the students who receive a card
must come to the front of the classroom and
arrange themselves in the correct order based on
their card numbers.The students need to find
their correct position in line according to the
number on their card. The student with the
number 1 stands first, the student with the
number 2 stands next to the student with the
number 1, and the student with the number 3
59+11
70+0
70-50
20+9
29+10
39+20
Volume 05 Issue 01-2025
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International Journal of Advance Scientific Research
(ISSN
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2750-1396)
VOLUME
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Pages:
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OCLC
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1368736135
stands next to the student with the number 2, and
so on. In the end, the students should be standing
in the following order:
Teacher’s Tasks for the Students:
1st Task: How many numbers smaller than 2?
Compare and answer by observing the numbers
on your classmates’ card
s.
2nd Task: How much greater is the number 5 than
the number 4? Compare and answer by observing
the cards in your classmate’s hands.
3rd Task: What is the number that comes directly
before the number 9 (its predecessor)? Students
should answer that it is 8. What is the number that
comes directly after the number 6 (its successor)?
Students should answer that it is 7.
4th Task: After which number and before which
number does the number 8 come? Students
should recognize that 8 comes after 7 and before
9.
In this game, students are taught to count both in
ascending and descending order by observing the
numbers on their cards. If any students
mistakenly take the wrong position in the line,
their error is explained, and they are guided to
stand in the correct position. For example, the
number 6 cannot be replaced by the number 7; it
is explained that the number 7 comes after the
number 6. Similarly, the number 10 does not
come before the number 9; it is explained that the
number 10 comes after the number 9. Through
this game, students internalize that each number
has a specific position. Solving problems is a
crucial component of mathematics education. It is
impossible to imagine learning mathematics
without solving problems. Problem-solving
enables the application of theoretical knowledge
to practice. To study the arithmetic of natural
numbers effectively, it is essential to use a system
of appropriate problems and practical tasks.
Understanding the meaning of arithmetic
operations, their relationships, and practical
applications helps students grasp the connections
between results and evaluate various quantities.
This fosters critical thinking and deeper
comprehension.
Thus, the process of shaping students' thinking is
crucially influenced by educational activities, and
the gradual complexity of these activities leads to
the development of logical abilities. However, to
activate and enhance children’s mental activity, it
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Volume 05 Issue 01-2025
36
International Journal of Advance Scientific Research
(ISSN
–
2750-1396)
VOLUME
05
ISSUE
01
Pages:
31-36
OCLC
–
1368736135
is advisable to introduce engaging and non-
standard tasks. Any activity aimed at solving
mental
challenges that aligns with the child’s
interest and actions contributes to the
development
of
thinking.
Therefore,
incorporating logical tasks, puzzles, exercises,
didactic games, and visual aids in lessons fosters
students’ ability to justify their opin
ions,
compare,
generalize,
clarify,
and
draw
conclusions based on proposed judgments.
Forming logical thinking in mathematics lessons
in primary school involves utilizing opportunities
to develop arithmetic operations by focusing on
the essence and content of each concept, linking
them to students' practical experiences, and
emphasizing visual aids. Teaching methods
should include comparison, conclusion drawing,
and concretization, along with analyzing
similarities across different operations to derive
general patterns. Exercises and problem-solving
tasks are fundamental to this process,
encouraging students to address errors and use
them as learning opportunities. In primary
mathematics lessons, teaching arithmetic
operations must consider the importance of
relationships
between
the
results
and
components of these operations. Mathematics
teachers should use recommended strategies that
enhance students’ reasoning skills, logical
justifications, and problem-solving abilities.
These strategies contribute significantly to
improving students’ overall mathematical
preparation, interests, and capabilities.
C
ONCLUSION
In conclusion, educational activities play a
decisive role in shaping students' thinking
processes. The gradual complexity of such
activities fosters the development of logical
abilities. However, to activate and enhance
children’s mental activity, it is effective to use
engaging, non-standard tasks. Activities that align
with a child’s interest and actions, aimed at
solving mental challenges, contribute to the
development of thinking. Logical tasks, puzzles,
exercises, didactic games, and visual aids in the
lesson help students develop the skills to justify
their opinions, compare, generalize, clarify, and
draw conclusions based on the judgments
presented to them.
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R.A.Mavlonova
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Vygotsky, L.S. Mind in Society: The
Development
of
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Psychological
Processes.
Cambridge,
MA:
Harvard
University Press.
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Polya, G. How to Solve It: A New Aspect of
Mathematical
Method.
Princeton,
NJ:
Princeton University Press.
4.
Skemp, R.R. The Psychology of Learning
Mathematics. Hillsdale, NJ: Lawrence Erlbaum
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