EIJP ISSN: 2751-000X
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MODELING PROBLEMS OF LOGICAL THINKING IN PRIMARY CLASS MATHEMATICS
LESSONS
Rakhimova Nargiza Mekhriddinovna
Teacher of the Primary Education Department of the Bukhara State Pedagogical Institute, Uzbekistan
ORCID
: https://orcid.org/0009-0004-6700-0686
Temirqulova Maftuna Telmon qizi
3rd course of student, Uzbekistan
AB O U T ART I CL E
Key words:
Model, modeling, cognitive,
problem solving, Modeling logical thinking.
Received:
02.11.2024
Accepted
: 07.11.2024
Published
: 12.11.2024
Abstract:
Models are created for various purposes
(analysis of the studied processes, verification or
demonstration of a new idea, method, system; to
study and change reality, as a means of
forecasting) and in a clear and concise form the
studied system, process, characteristics of the
idea; allows you to get important things about the
connections and relations of the object. V.V.
According to Davydov, the model will contain an
image of the studied object. According to the
nature of the description of the modeled system,
there are modeling of the structure (structural
models) and modeling of the operation of the
processes occurring in it (flow or process models).
To solve the second problem, mathematical
modeling is the most effective. Modeling involves
the use of abstraction and idealization. Reflecting
the essential features of the original, the model
acts as a kind of implementation of abstraction.
The effectiveness of modeling as an achievement
of consistency between model and reality is
complicated by uncertainty, an important feature
of models in the humanities. E. N. Gusinsky,
studying the characteristics of social and
humanitarian systems, emphasizes that they
always have conscious and unconscious motives,
are determined not only by past experience, but
also are influenced by many factors of the current
environment and the external environment. A.N.
VOLUME04 ISSUE11
DOI:
https://doi.org/10.55640/eijp-04-11-26
Pages:140-144
EUROPEAN INTERNATIONAL JOURNAL OF PEDAGOGICS
ISSN: 2751-000X
VOLUME04 ISSUE11
141
Dakhin emphasizes the complexity of modeling
humanitarian systems, because they do not have
clear components that make up the system - each
of the components can "over time" become a
pedagogical bifurcation point and dominate the
design of goals and teaching technology.
This article talks about the modeling of logical
issues, the need for its application, the diversity of
educational content, and the increase in
requirements for the quality of education.
INTRODUCTION
On July 9, 2019, President Shavkat Mirziyoyev announced "State support for the
further development of mathematics education and sciences, as well as measures to fundamentally
improve the activities of the V.I. Romanovsky Institute of Mathematics of the Academy of Sciences of
the Republic of Uzbekistan signed the decision. Forming the knowledge and skills of schoolchildren,
educating them in the spirit of loyalty to national and universal values, increasing the prestige of the
teaching profession and the quality of pedagogues, improving textbooks and educational methodical
complexes based on the requirements of the times, bringing school educational institutions to
international standards. in order to establish responsive modern models, as well as in accordance with
the state program for the implementation of the Development Strategy of New Uzbekistan for 2022-
2026 in the "Year of Honoring Human Values and Active Neighborhoods":
In 2022 - 2026, in accordance with the National Program for the Development of School Education
(hereinafter referred to as the "Development Program"), the National Curriculum developed on the basis
of international best practices for school education as the main directions of the development program
full implementation and implementation of modern textbooks created by local and foreign authors,
increasing the prestige of the teaching profession in society, creating favorable social conditions for
pedagogues and adequately encouraging their work, the role of teachers in providing education and
training to young people A number of efforts are being made to increase their responsibility and demand
for continuous professional development.
METHODS
Problem solving and mathematical modeling. Problem solving and mathematical modeling involve two
main methods: solving mathematical problems and solving real-world problems using mathematical
methods. Both processes require mathematical analysis, logical thinking, and modeling skills. Let's take
a closer look at them:
Problem solving. Problem solving is the process of solving a specific problem using specific mathematical
methods. This includes the following steps:
1. Understanding the problem: It is necessary to understand the problem and define its main goals. For
example, understanding how an equation or expression works.
2. Creating mathematical models: Trying to understand the problem through mathematical modeling.
For example, creating equations or graphs for a problem.
1. Choosing a solution: Choosing the right method or algorithm to solve a problem. It can be algebraic
methods, geometry, statistical analysis, etc.
2. Implementation of the solution: Applying the chosen method or algorithm and calculating the result.
3. Check the result: Check the correctness of the solution and, if necessary, revise the calculations.
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Mathematical modeling. Mathematical modeling is the process of analyzing and solving real-world
problems using mathematical methods. This includes the following steps:
1. Problem definition: Identifying a real-world problem or process and creating a mathematical
representation of it.
2. Creating a mathematical model: Transforming the problem into a mathematical model. Equations,
functions or statistical models can be created for this.
3. Analyzing the model: Analyzing the creative mathematical model and checking its accuracy. For
example, comparing model results with real data.
4. Model Tuning: Further fitting and tuning of the model with real data. This usually requires changing
the parameters of the model.
5. Using the model: Applying the created model to solving a real problem and evaluating the results.
Mathematical modeling is used in various fields, such as economics, engineering, biology, social sciences,
etc. It helps you better understand real-world processes and helps you make decisions.
Singapore's mathematical literacy is highly regarded globally and is one of the successful parts of the
country's education system. Singaporean mathematics education is mainly known for the following
aspects:
1. Educational programs. Singapore's mathematics curriculum is robust and structured.
The curriculum includes in-depth study of mathematical concepts and strengthening them through
practical exercises.
Program:
• Reinforcement of secondary mathematics: Students are focused on a deeper understanding
of
mathematics from the elementary grades.
• Problem Solving Strategies: Emphasis is placed on generating and analyzing problems, logical thinking,
and creative approaches.
2.
Teaching methods. Singapore uses the "Mathematics 3D" methodology in mathematics
education:
• Model
-Diagram (Model-Method): Helps students understand mathematical problems through visual
models. For example, "bar charts" are used to represent issues graphically.
• Problem Solving: Students are taught different techniques to help
them solve different types of
problems.
• Effective Teaching: Teachers use effective strategies and innovative methods to motivate students to
better understand mathematics.
3. A well-studied system of education. Singapore's mathematics education system includes the following
elements:
• Teacher training: Teachers receive advanced training and are familiar with the latest methods in
mathematics education.
• Guides and resour
ces: There are well-developed guides, textbooks and online resources for
mathematics education in Singapore.
4. International assessment. Singaporean students consistently perform well in international
assessments, particularly PISA (Programme for International Student Assessment) and TIMSS (Trends in
International Mathematics and Science Study). These results confirm the high quality of mathematics
education in Singapore.
5. Innovation and research. Singaporean mathematics education is constantly being innovated and
researched. New methods are tested to improve curricula and teaching methods.
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6. Individualization of education. In Singapore, it is important to support students based on their
individual needs. It helps in developing students' mathematical skills and makes it possible to maximize
the potential of each student.
Individual approach: There are learning methods and support tailored to the individual needs of students.
This will help to maximize the potential of each student. For example, Singapore math programs:
• "My Pals Are Here!": A series of tutorials aimed at teaching students mathematical concepts in a fun
and interactive way.
• "Singapore Math": A guide and resources developed for the application and teaching of Singapore
Math programs internationally.
In PISA studies, real-life problem situations presented in a context are given, not the usual mathematical
problems in our textbooks. We remind you that in a typical standard math problem from our textbooks,
there are given quantities (knowns) and an unknown quantity to be found. It is required to find the
unknown using the given information. In this case, the givens are enough to find the unknown, and they
are neither too few nor too many. PISA tasks are not a mathematical problem, it consists of the stage
that comes before the mathematical problem - the description of the problem situation (context). It is
necessary to study the problem situation described in the context of the task by reasoning and express
it in mathematical language, that is, to bring it to a mathematical problem. Only after that, the problem
will be solved with the help of mathematics.
Mathematical literacy means solving problems using mathematics on the one hand, and mathematical
reasoning on the other. Mathematical reasoning is strongly emphasized in PISA research as an important
central aspect of the problem-solving cycle. Mathematical literacy includes students' activities such as
"expressing the problem in a given life situation in mathematical language (mathematical modeling)",
"applying mathematics", "interpreting and evaluating the found mathematical solution in relation to the
given problem" based on mathematical reasoning. . Below, for the sake of brevity, we refer to these
activities as "reasoning", "expressing", "applying" and "interpreting and evaluating".
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