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THE ROLE OF PROBLEM-BASED TASKS IN DEVELOPING
MATHEMATICAL THINKING SKILLS OF LYCEUM STUDENTS
Nurmukhamedova Umida Bakhtiyar qizi
Teacher of Mathematics at ChDPU academic Lyceum
+998990446002
umidanurmukhamedova111@gmail.com
Abstract: One of the important tasks of Mathematics is the formation of
logical thinking, analysis, problem solving skills in students. Especially for students
studying at the Lyceum stage, these skills will be of great importance in scientific and
practical activities in the future. Mathematical thinking is the art of not only
memorizing formulas and rules, but also applying them in different situations,
analyzing new situations and finding solutions. In this regard, problem assignments
are an important tool in activating the thinking process of students, teaching them to
think independently.
Keywords: mathematics, independent thinking, problems, logical thinking,
formulas, rules, knowledge, practical training.
INTRODUCTION
Problem assignments allow students to analyze complex and ambiguous
situations. Through these assignments, the student learns to put their knowledge into
practice, independently acquires new knowledge and is taught to base their opinion.
Problem assignments are often multi-level, complex, and requiring different solution
paths that develop students ' analytical thinking, the ability to see logical connections.
At the same time, these assignments help to form qualities in students, such as
patience, perseverance and creativity. Another advantage of applying problem
assignments for high school students is that they develop students ' independent
learning skills. Students independently examine their knowledge when completing a
task, look for new information, analyze various sources and create their own
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solutions. This leads them to learn independently and actively, regardless of the
teacher's instructions alone. In this way, problem assignments increase students ' self-
control and self-assessment skills. The role of problematic tasks in the development
of Mathematical Thinking Skills is also their formation of a creative approach in
students. Problem assignments often require thinking outside of standard solution
paths. This allows students to experiment with new techniques, create their own
solutions, and express their opinion freely. As a result, students not only consolidate
their mathematical knowledge, but also develop creative thinking skills.
MATERIALS AND METHODS
In order to effectively incorporate problem assignments into the learning
process, teachers need to improve their methodologies. To do this, it is important to
choose and adapt assignments, taking into account the individual abilities, interests
and knowledge levels of students. Important factors are also the step-by-step complex
of assignments, giving students enough time and encouraging them. In this process,
the teacher must monitor the students ' thinking process, provide assistance when
necessary, and encourage them to think independently. While developing logical
thinking in students, problem assignments also serve to deepen their mathematical
knowledge. Through these assignments, students learn to put mathematical concepts
and rules into practice, strengthen their theoretical knowledge, prepare to acquire new
knowledge. At the same time, problem assignments form the skills of testing, error
detection and correction of their knowledge in students. Problem assignments also
develop students ' teamwork skills. Most often, these types of assignments are solved
in a group, which allows students to exchange ideas with each other, provide mutual
assistance and find a solution together. Teamwork increases communication skills in
students, training them to work responsibly and cooperatively. The role of problem
assignments in increasing interest in students is also great. Compared to simple and
standard assignments, problem assignments increase students ' interest in learning,
encouraging them to be active and creative. This in turn increases the effectiveness of
the learning process and improves the level of student mastery. [1]
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In order to achieve effectiveness in teaching problem assignments, it is
necessary to apply various pedagogical methods and approaches. Problem
assignments serve to develop students ' independent thinking, analysis, and creative
approach skills. Therefore, when teaching this type of assignment, it is important to
take into account the content of the methods, the interests of the students and the
features of the educational process. [2]
RESULTS AND DISCUSSIONS
The main idea of the problem teaching method is that students must
independently use their knowledge and skills to deal with problem situations in order
to acquire new knowledge. In this approach, the teacher not only provides theoretical
information, but also provides students with the opportunity to express their thoughts,
analyze the problem and test various solutions. This process forms independent
thinking and problem-solving skills in students, and also increases their creative
potential. In the method of project activity, students work together to carry out a
certain problematic task. In the process of completing the project, they go through
stages such as collecting data, analyzing it, finding solutions to the problem and
presenting the results. This method develops students ' teamwork skills, teaching them
to manage, communicate, and take responsibility.[3]
Project activities give students a real-life problem-solving experience that
increases their interest in reading. Discussion and discussion techniques are very
effective in teaching problem assignments. In these techniques, students freely
express their thoughts, listen to the opinion of others and compare different views.
This process increases students ' critical thinking and argumentation skills. Discussion
also teaches students to respect the opinions of others, to compromise, and to be
effective in communication. Through discussion, students have the opportunity to
consider problem situations from different perspectives, expanding their worldview
and range of knowledge. The Case-study, or case study method, is of practical
importance in teaching problem assignments. In this method, students are presented
with problematic situations derived from real life or scientific practice. Students
analyze these cases in an attempt to identify and find solutions to the problem. This
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approach allows students to practice theoretical knowledge and develops their
analytical thinking skills. The Case-study method encourages independent student
performance and prepares them for real-life challenges. Interactive methods are an
effective tool for attracting students ' attention and encouraging them to actively
participate in teaching problem assignments. With the help of Multimedia tools,
interactive presentations, online platforms and simulations, students learn problem
situations in a more interesting and understandable way. This method increases the
interaction of students, teaches them to apply new technologies and makes the
learning process more efficient. With interactive techniques, students have the
opportunity to test their knowledge in practice, which increases their motivation for
learning. The differential approach is based on taking into account the individual
characteristics of students when teaching problem assignments. Each student's level
of knowledge, ability, and learning style may vary. Therefore, the teacher should
formulate assignments in such a way that they correspond to the needs of each student.
This approach helps students to maximize their potential and increases their interest
in learning. Using a differential approach, students can learn at a convenient pace,
which increases the effectiveness of the reading process.[4]
CONCLUSION
In conclusion, problem assignments are an important tool in the development
of mathematical thinking skills of high school students. They form the skills of
independent thinking, analysis, creative approach and teamwork in students. Also,
problematic assignments serve to increase the interest of students and deepen their
knowledge. Therefore, it is important to pay special attention to problematic
assignments in the educational process, to effectively include them in the curriculum
and to improve the skills of teachers in this regard. This in turn contributes to the
further development of mathematical knowledge and thinking skills of Lyceum
students.
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