Formation of Mathematical Thinking Competence in Students as a

Scientific Pedagogical Issue

Kenjayeva Sanobar Ibragimovna

Jizzakh State Pedagogical University, Uzbekistan

Keywords: Student, Thinking, Mathematical Thinking, Ability, Competence, Scientific Pedagogical Problem, Pedagogy,

Education, School, Mathematics, Method, Method, Interactive Methodology, Analysis, Development.

Abstract: School education is a part of the continuous education system that requires special attention. The door to all

the opportunities necessary to achieve the effectiveness of quality education on a global scale is being opened

on a large scale. How to build a 21st century school system? such questions are also being considered at the

level of global education policy. Systematic work is being carried out in the environment of digitalization of

education, introduction of the most advanced methods of teaching on the basis of digital technologies related

to education and training, in accordance with the standards of world education. Today, global globalization

processes have an impact on the development of science, education, art, culture, sports, economy, business,

marketing, construction industry, production, and so on. it is known to everyone. In particular, the processes

of globalization have brought about important changes in the field of education. First of all, these are

characterized by transformation processes, that is, deep, new qualitative changes in the quality, efficiency,

structure, and functions of education. This article talks about the reasons why the development of

mathematical thinking competence is considered as a pedagogical problem and the methods of solving the

problem, as well as information about the opinions of scientists, types of thinking and existing problems in

school.

1 INTRODUCTION

It is clear from history that education is increasingly

becoming a global topic, that education can positively

change people's lives and ways of living, and that it is

a means of developing the country's development.

Moreover, today's era of globalization, the Internet,

the creation of artificial intelligence and digital We

are witnessing the development of technologies.

2 LITERATURE

To this day, the great mathematicians Al-Khorazmi,

Gauss, Pythagoras, etc., with the unique problems of

developing mathematical literacy and their solutions,

in the process of education and training, the use of

verbal forms of mathematical calculations in solving

life problems, and now E.M. Mardonov, A.H.

Avezov, S. Alikhanov, M.E. Jumayev, Sh.V.

Imomova, M.N. Ismoilova and others, as well as Alan

H. Schoenfeld, Richard Rusczyk, Joe Boaler, John

Mason, Leone Burton, Kaye Stacey, Randall

Maddox, Steven Strogatz In addition, Russian

scientists Ya.I. Perelman, M.A. Bantova, A.V.

Beloshistaya, G.N. Berman, S.I.Volkova, D.R.

Gonchar, T.E. Demidova, I.I. Martinov and others

also conducted research.

Ancient Greek mathematician Pythagoras

believed that numbers and geometry could be used to

understand the universe. Pythagoras and his followers

were interested in the spiritual development of man.

According to them, there is an inextricable

connection between mathematical ratios and music,

and music could be used to achieve mental balance.

As Pythagoras and his followers tried to unravel the

mysteries of the universe through thought, they were

inspired by such fields as number, proportion,

geometry, and music (Riedweg, C. 2005).

The great thinker scientist Al-Khwarazmi in his

work "Kitab al-muqaballa" explains the rules of

mathematics and algebra in general. It also shows

operations that use mathematical ideas. The main

purpose of this work is to teach the basic knowledge

of arithmetic and algebra, to understand their

important rules and to help learn arithmetic

operations. In addition, since the work shows

Ibragimovna, K.

Formation of Mathematical Thinking Competence in Students as a Scientiﬁc Pedagogical Issue.

DOI: 10.5220/0012664500003882

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 2nd Pamir Transboundary Conference for Sustainable Societies (PAMIR-2 2023), pages 60-64

ISBN: 978-989-758-723-8

methods, formulas and concepts, students are

expected to understand its basic environment and

methods of analysis, and it provides theoretical and

practical knowledge for students to perform analysis

through thinking, and to apply it in practice.

Alan H. Schoenfeld is a distinguished researcher

in mathematics education who has made significant

contributions to the field. In his book, Mathematical

Thinking and Problem Solving, Schoenfeld explores

various aspects of mathematical thinking and

provides insight into effective problem-solving

strategies. Schoenfeld emphasizes the importance of

developing mathematical thinking skills in students.

He believes that mathematical thinking goes beyond

simple calculation and includes a deep understanding

of mathematical concepts, the ability to apply these

concepts in a variety of contexts, and the ability to

reason and solve problems effectively. Schoenfeld

explores a variety of problem-solving techniques and

approaches to help students solve math problems. He

emphasizes the importance of persistence, flexibility

and creativity in problem solving (Alan H.

Schoenfeld. 2016).

Y. I. Perelman's approach to mathematical

thinking was characterized by deep intuition, rigorous

thinking, and great emphasis on understanding basic

concepts. He believed in the power of simplicity and

elegance in mathematical proofs, often sought

concise explanations and avoided unnecessary

complexity. He had a critical view of the

mathematical community and the culture around it. In

general, Perelman's views on mathematical thinking

emphasized the importance of deep understanding,

simplicity, and originality. He has demonstrated the

power of intuition and innovative approaches to

solving complex problems (Y.I. Perelman.2016).

According to M.E. Jumayev, mathematics allows

children to develop thinking, attention, memory,

creative imagination, observation. Also, mathematics

prepares the ground for students to improve their

logical thinking skills, to express their thoughts

clearly, correctly and comprehensibly. The task of the

teacher is to effectively use these opportunities in

teaching mathematics to children (M.E.Jumayev.

2018).

We cite several reasons why the competence of

mathematical thinking is considered as a scientific

pedagogical problem:

1. Complex expression of the theoretical

information given in the textbooks up to this day;

2. Pupils' inability to consciously master subjects

due to lack of cognitive activity;

3. The inability of graduates of general education

schools to correctly choose higher education

institutions in the field they are interested in;

4. Formation of students' habit of using theoretical

knowledge and formulas based on memorization;

5. Failure of the school teacher to guide students

according to their specific competencies;

6. Students' mathematical thinking competencies

are not developed;

7. Lack of systematic planning of practical

training for the development of mathematical

thinking competence.

3 RESULTS

We believe that scientific research on mathematical

thinking cannot meet the requirements of the 21st

century, when technology and technology are

developing, and people's lifestyles are being made

easier. Because, in the above-mentioned studies, it is

emphasized that students use a lot of theoretical and

complex scientific information by memorizing it.

This causes various inconveniences and difficulties

for students in completing problems and examples.

Because of this, students' interest in science gradually

fades. Such a situation is considered a pedagogical

problem. Today's student is quickly bored with such

complex theoretical knowledge, therefore, it is

necessary to develop concrete methods that develop

students' thinking and thinking competencies, that is,

to solve problems, it is necessary to carry out new

scientific and research work on this topic. For this

purpose, it is appropriate to teach students practical

skills and abilities that develop the ability to easily get

out of difficult life situations by giving up the

memorization option and thinking. During the article,

you can get acquainted with some methods of solving

problems through mathematical thinking.

First of all, let's pay attention to the meaning of

the word thought. Thinking is a mental process that

reflects the reality of the environment indirectly with

the help of speech, and is a mental activity aimed at

understanding social causal relationships,

discovering new things and predicting (G’oziyev E.

2002).

It is known from the basics of physiology that the

cerebral hemispheres are responsible for mental

activity. People with a dominant right hemisphere are

more emotional, which contrasts with imaginative,

abstract thinking. Such persons have a humanitarian

mind. If the left hemisphere dominates, the person has

more practical, analytical thinking and mathematical

Formation of Mathematical Thinking Competence in Students as a Scientiﬁc Pedagogical Issue

thinking. In general, there are 5 main categories of

human thinking:

- practical;

- artistic and figurative;

- humanitarian;

- mathematician (analytical);

- universal (synthetic) thinking.

As the title of the topic indicates, we believe that

mathematical thinking is the most common type of

thinking that needs to be developed for

schoolchildren. Mathematical (analytical) thinking is

very similar to practical thinking (Keith Devlin.

2012).

The development of mathematical thinking skills

is important for students' in-depth study of

mathematics. This allows students to develop

thinking skills in learning science, solving problems,

and solving important issues. Here are some ways to

develop mathematical thinking skills:

3.1 Encourage Thinking in the Process

of Solving Problems

In solving mathematical problems, students should

be made aware that they can face several problems

and solve them easily through their thinking skills. It

is also important to develop these skills. Students

should be encouraged to explore and tackle problems

in order to develop their problem-solving thinking

skills. It involves giving students input during

problem-solving, asking students for input at each

stage of problem-solving, and considering a wide

range of problems and taking their opinions and

comments into account, making joint decisions if

necessary. it is also possible to sufficiently stimulate

and develop students' thinking skills.

3.2 Reading out Math Problems

Reading math problems also develops students' deep-

thinking skills in solving all problems. In this way,

students will have the opportunity to think freely

among themselves, listen to each other, and get

acquainted with approaches that are suitable for their

own learning methods.

3.3 Finding Unusual Ways to Solve

Math Problems

Math questions and unusual ways to solve problems

also help students develop problem-solving thinking

skills. It also directs students to new approaches to

problem solving, creative thinking, self-expression,

and revealing leadership qualities.

4 ANALYSIS

Through mathematical analysis, students examine

mathematical problems and learn to think about ways

to solve them. By analyzing, students will be able to

understand and solve mathematical problems more

clearly, and they will be able to think about and accept

specific answers, and these skills will also develop.

4.1 Acquisition of Mathematical

Knowledge through Active

Observation

Considering the variety of existing problems in the

given problem, creative approach to these problems

will give rise to some thoughtful questions, of course,

the students should look at these questions as serious

problems, and also the questions that arise in the mind

of each student will be asked by other students. must

orally tell and read to the students. That is, students

understand mathematical knowledge through active

observation, paying attention to its smallest elements

in a more accurate, comprehensive and perfect way,

and also learn to evaluate how much they think and

how they think by comparing with their peers.

Through this method, the student learns to respect the

opinion of each peer as a person and to listen carefully

to them. With this convenient method, finding a

solution to the problem is also a little easier.

Observation is one of the main tasks for students in

learning and solving mathematical problems.

Students will also have the opportunity to express

themselves freely, find non-traditional ways to read

and solve mathematical questions and problems, and

reacquaint themselves with approaches that match the

methods they have learned.

4.2 Using Various Interactive Methods

That Develop Intellectual Abilities

in Each Session

This method helps students to think, to think, to

increase their interest in science, to analyze, to prove,

to conclude, to be active in class, to have healthy

competition, to compromise with each other and to

work as a team.

Regular use of these and other interactive methods

and mathematical thinking skills in solving problems

and issues leads to achieving high results in most

cases. Of course, students need such approaches in

the course of the lesson. Here, you can get a closer

look at one of the famous thinker Edward de Bono's

famous methods for developing different thinking

PAMIR-2 2023 - The Second Pamir Transboundary Conference for Sustainable Societies- | PAMIR

techniques and methods for creative thinking and

problem solving. Called the Six Thinking Hats, this

method focuses on solving problems using different

thinking hats. Each hat represents a different

approach to thinking. There are six different hats:

white hat (knowledge-based thinking), red hat

(emotional thinking), black hat (critical thinking),

yellow hat (positive thinking), green hat (creative

thinking), and blue hat (managerial thinking).

Such methods are a clear example of work on

improving the ability to think. The use of such

interesting interactive methods designed for each

problem-solving process can be a great reason to

dramatically increase the student's creative thinking,

critical thinking and problem-solving skills.

5 RESULTS AND DISCUSSION

It is known to everyone that the quality and content

of the lessons conducted in the school are of particular

importance in achieving the effectiveness of

education. Therefore, it is appropriate for us to pay

great attention to the organization of lessons at

school. It is precisely the development of students'

mathematical thinking competencies that is

considered as a pedagogical problem in the school.

Why here? the question is appropriate, of course. Not

only mathematics, if we consider all subjects,

schoolchildren cannot fully master subjects in class,

and this process continues until the students graduate

from school. At the same time, the student graduates

from school. The result is not long in coming. It

would be correct to say that the results of the entrance

exams for higher education, which are held every year

in the summer season in our country and continue in

a traditional manner, shed much light on the issue. It

is not difficult to understand what we want to say, just

thinking about it is enough. If we take a closer look at

the issue, the following questions and thoughts will

certainly arise:

- what percentage of school graduates correctly

choose a higher education institution that matches

their interests;

- is it possible to compare the knowledge of the

students from the general education school and the

knowledge from the private educational centers;

-why do parents think about which school to send

their children to, that is, it differs greatly from school

to school;

- are there specific methodical manuals on ways

to develop the thinking competencies of

schoolchildren.

In the era of rapidly developing information

technology, we are witnessing the continuous

development of innovations and changes in science,

education, technology, telecommunications and all

other fields. These processes also have an impact on

general education schools. That is, attracting the

attention of today's students to education is

considered as a problem. The reason is that the tools

that distract students' minds and imaginations, social

networks, internet games, the increasing desire to

earn money from childhood, lack of interest in

reading books, lack of self-confidence, some parents

the consequences of disrespecting mothers, teachers,

etc., easily keep them away from school, education,

and thinking. Because of this, we, as a community of

pedagogues, should be enthusiastic as a spreader of

knowledge, a teacher of spirituality and cultural

manners.

In the implementation of work aimed at students'

education at school, increasing their interest in

science, and developing their thinking skills, radical

changes and new textbooks were developed aimed at

teaching each subject from the initial stage of

education. Among other things, this article also serves

to solve the problems of developing students'

mathematical thinking competence.

It can be said that the subjects taught in general

education schools are very important for the student

to become a well-rounded person in all respects and

gain his place in society. In particular, if we look at

the example of mathematics, mathematical elements

are taught to children from the kindergarten age, this

knowledge is developed in general education school,

academic lyceum and later in higher education

institutions and serves them throughout their life. As

time goes by, the role of mathematics in life is

expanding, and its branches are also increasing.

Today, our way of life cannot be imagined without

mathematics. If we pay attention to the lesson loads

of general education schools, the largest hour of the

lesson is allocated to mathematics. The role of

mathematics in the development of students'

mathematical thinking is incomparable. More

specifically, developing mathematical thinking skills

today requires students to use multiple methods to

develop their thinking skills in solving mathematical

problems (

Kenjayeva S.I.).

6 CONCLUSION

The above-mentioned methods of developing

mathematical thinking skills teach students to think

broadly and speak freely when solving mathematical

Formation of Mathematical Thinking Competence in Students as a Scientiﬁc Pedagogical Issue

problems, and also encourage them to analyze

mathematical problems, think, and work with basic

mathematical interactive activities. and we can say

that it creates ample opportunities for deeper learning

of mathematics and brings students' mathematical

thinking skills to a high level. In particular, the use of

the last method mentioned above, i.e. "Using different

games, crosswords, puzzles and interactive methods

in each lesson" is one of the most common methods

in Finnish education, and it helps to develop students'

mathematical thinking competencies. aimed at

development. But this method is not widespread in

our country. Because teachers use such activity only

in open classes held twice a year. The method we

would like to propose is that each teacher, in each

lesson, should use a standard teaching method (taking

attendance, asking for homework, explaining a new

topic, reinforcing, evaluating and taking home) in

order to develop students' mathematical thinking.

assigning a task) should be abandoned and based on

a new approach, create lessons consisting of

interactive methods, puzzles, energizers and games.

During the explanation of the topic, it is necessary to

use real life examples, if necessary, with the help of

questions, it is necessary to ensure that the students

themselves participate in this process. For example, it

is very easy to explain numbers from 1 to 9 and 0 to

them based on real-life examples when introducing

elementary school students to numbers. If we look at

the example of the number 1, the creator of us is one,

the moon, the sun, mother, father and country are one,

and if we explain using certain examples from the

environment that surrounds us, such as one life to

live, then the number 1 means solitary in the minds of

the students. meaning will remain forever. In the

process of explaining the topic "Positive and negative

numbers", examples of positive and negative

characteristics of people in life, in the topic

"Derivation", explaining the first process of clothes

made of pure cotton, in the topic "Graph of a

quadratic function", electric wires, argimchak, in the

topic "EKUB and EKUK" using the general

characteristics of family members, parents and

children, in the topic "Circle and Circle" using

examples such as car wheels, ball, watermelon, to

show that each topic is related to life and why

students' thinking skills can be developed by

explaining the need.

Today, using the experience of Finnish

education, which shows the highest results in PISA

and PIRLS assessment programs worldwide, has

created a specific system in its education system and

is an example for other countries, more than 10,000

schools in our country. It can be the basis for creating

equality, healthy environment and alternative

education among students in educational schools. We

will cover the information about the use of interactive

methods in the next articles.

REFERENCES

Jumayev M.E.. Boshlang’ich sinflarda matematika o’qitish

metodikasi. – T.: Fan va texnologiya.- 2018. – 350 b.

Perelman Y.I.. Qiziqarli matematika. – T: Sharq. – 2016. –

Tarjimon: A.T. Xo‘jaxonov.

G’oziyev E. Umumiy psixologiya psixologiya

mutaxassisligi uchun. O’quv qo’llanma II kitob. – T.,

2002. – 93 b.

Alan H. Schoenfeld. (2016). Mathematical Thinking and

Problem Solving (Studies in Mathematical Thinking

and Learning Series) Mahwah, New Jersey, USA.

"Introduction to Mathematical Thinking" by Keith Devlin.

2012.

Riedweg, C. (2005). Pythagoras: His Life, Teaching, and

Influence. (W. H. Kluback & M. E. Pomeroy, Trans.).

Cornell University Press. (Original work published

2002)

De Bono, E. (1985). Six Thinking Hats. Little, Brown and

Company.

Kenjayeva S.I. umumta’lim maktabining ta’lim sifati

samaradorligini oshirishga kompetensiyaviy

yondashuv. - https://jdpu.uz/umumtalim-maktabining-

talim-sifati-samaradorligini-oshirishga-

kompetensiyaviy-yondashuv/.

PAMIR-2 2023 - The Second Pamir Transboundary Conference for Sustainable Societies- | PAMIR