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0QISQA XABARLAR
UDC 510.24
BASIC PRINCIPLES OF METHODS OF TEACHING MATHEMATICS
Sh.A. Kasimov
Tashkent State Transport University, Candidate of Physics and Mathematics, Docent
R.Kh. Kendjayev
Tashkent State Transport University, Candidate of Physics and Mathematics, Docent
R.A.Khikmatova
Tashkent State Transport University, Candidate of Physics and Mathematics, Docent, [email protected]
A.A.Eshkabilov Tashkent State Transport University, Docent
Abstract. In this article is considered the various approaches and techniques of teaching mathematics, which will help the teacher to plan instruction in the classroom in the most effective manner.
A few of the current trends in the methods and media used in mathematics instruction are mentioned here. These include the basic features of more recent ideas, which are the gift of educationists and psychologists. It is expected that teachers would try to fit them into their practical scheme of teaching.
Аннотация. В данной статье рассматривается различные подходы и методики преподавания математики, которые помогут учителю спланировать обучение в аудитории наиболее эффективным образом.
Здесь упоминаются некоторые из современных тенденций в методах и средствах массовой информации, используемых при обучении математике. К ним относятся основные черты более поздних идей, которые являются достоянием педагогов и психологов. Ожидается, что учителя постараются включить их в свою практическую схему преподавания.
Annotatsiya. Ushbu maqolada matematikani o'qitishning turli xil yondashuvlari va usullari ko'rib chiqiladi, bu esa o'qituvchiga o'qitishni eng samarali tarzda rejalashtirishga yordam beradi.
Bu maqolada matematikani o'qitishda qo'llaniladigan usullar va ommaviy axborot vositalarining bir nechta tendensiyalari keltirilgan. Bularga pedagoglar va psixologlarning manfaati bo'lgan so'nggi g'oyalarning asosiy xususiyatlari kiradi. Ularni o'qituvchilar o'qitishning amaliy sxemasiga moslashtirishga harakat qilishlari kutilmoqda.
Key words: major concern, growth rates, aptitude inventories, increasing efforts.
Ключевые слова: основная проблема, темпы роста, инвентаризация способностей, наращивание усилий.
Kalit so'zlar: asosiy muammo, o'sish sur'ati, qobiliyatlarni inventarizatsiya qilish, sa'y-harakatlarni kuchaytirish.
INTRODUCTION
The requirements of the law, the National Program for Personnel Training and the requirements of the teacher are being expanded. In the 21st century, pedagogue required extensive knowledge, thorough practical training, high pedagogical skills, competence and creativity. In preschool, personal qualities of a leader are important. The personality traits of a leader providing a humane factor in early childhood education: rigor, honesty, honesty, kindness and courtesy. These qualities should determine the importance of the educator to the learners.
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The personal qualities influence the skills of teaching and training. In the book "Critical analysis, strict discipline and personal responsibility must be the daily routine of every leader's work" by President Sh. Mirziyoev cited that "Independent thinking, dedicating modern science and professions, dedication to country, his people, continuing what we started The most mature and capable leader is the one whose mission is to bring the next generation to perfection". Indeed, in the development of socio-economic relations in the 21st century, it is becoming increasingly clear that human intelligence and spirituality are the main coordinating, developing factors and tools. That is why humanism has emerged as the basic principle of building a legal, democratic state and a free civil society based on a market economy [1].
The teaching and learning of mathematics have always been a major concern in education. Various commissions and committees have laid great emphasis on raising the quality of instruction in mathematics. The National Policy of Education (1986) lays down the importance of mathematics as a vehicle for developing creativity. Recent researches in the area of learning have led to a deeper understanding of "how pupils learn". As a result, a broad range of new approaches to the teaching of mathematics have been suggested to achieve optimal learning. The highly structured nature of mathematics, its language and methods of proof have also attracted the attention of psychologists and educationists. Consequently, the old methods of mathematics teaching which relied heavily upon rote learning and drill have been replaced by methods, which rely upon discovery and problem solving approaches.
Principles of Learners Development and Learning
Mathematics has always been the most important subject in the school curriculum. Traditional mathematics teaching has been found to be unsatisfactory. During recent years, the demand has grown to make mathematics teaching more imaginative, creative and interesting for pupils. Clearly, the demands made on the mathematics teacher are almost unlimited. The teacher must have a specialized understanding of the foundations of mathematical thinking and learning. The teacher should also possess skills to put together the whole structure of mathematics in the minds of students. He, like a master technician, should decide what kind of learning is worth what; realize and make use of motivation and individual differences in learning. She should be able to translate her training into practice. Finally, she should plan or design the instruction so that an individualized discovery-oriented (or problem-solving) learning is fostered.
How does one teach most effectively? Very simple: teach the child in the way he learns best. Therefore, it is necessary that the teacher understands how a child learns, and the factors which affect learning. Thus, the teacher has to understand the way in which growth and development affect learning. Some aspects of learning are now discussed.
1. A learner learns best, wheh he is clear about the purpose or goals to be achieved. It is better if he is guided by a self-selected goal. His purpose determines what he learns and the degree to which he learns.
2. Learner grow physically, mentally and socially at different times and with different growth rates. Various growth curves giving data about heights-weights, age, intelligence and interest or aptitude inventories which apply to learners of a given age group are available. However, deviations are observed many a time in a given group of learners.
The actual age at which each stage is attained varies considerably from learner to learner because of the differing cultural backgrounds and environment. There is no clear borderline between the end of one stage and the beginning of the next. However, what is important is that Piaget considers that the order in which the stages appear is fixed and this provides us with a framework against which we can examine the teaching strategy [2, 3].
Learning is a continuous development process. It is change in behaviour brought about by thinking while facing situations that call for making discoveries, recognizing patterns and
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formulating abstractions or generalizations in mathematics. A learner grows through experiences, which provide both security and adventure. A learner learns what he does himself. Inefficient rote learning does not cause permanent learning and results in frustration and dislike for the concept or subject. If an experience is motivating only then it stimulates the creative faculty of the learner, encourages exploration, and ensures the fullest development of the learner's mathematical potential. "Learning by doing" or the "discover approach" through carefully controlled situations or chosen problems has proved to be a sound teaching strategy and a highly motivating activity.
A closer examination of the vast literature on "mathematics learning" reveals mainly four levels or steps of learning.
1. Readiness ^ 2. Experi--> 3. Verbalization or ^ 4. Systematic
mentation symbolization generalization
The necessary conditions leading to the acquisition of new responses are (1) Real situations: first-hand experiences with concrete things, (2) intuition, exploration, discovery through investigation, (3) formulation: verbal or symbolic representation based on logical reasoning and (4) assimilation, classification, generalization or concept formation through thinking and reasoning.
New concepts are developed as an extension of previous learning. The process of learning as well as the product should be emphasized Generalizations in mathematics are formed inductively and applied deductively.
Trends in Organizing Content
Owing to the influence of professional mathematicians and due to the recommendations of national groups concerning updating the school mathematics curriculum, new considerations have come to be strongly emphasized during the past 25-30 years. These have a decisive impact on the planning of instructional strategies in mathematics.
1. Recent trends in selection of topics: The advancements and extensive use of technology has replaced manual computations almost completely. Thus, many traditional mathematical topics and skills (e.g., tedious simplifications with brackets and complicated calculations with very large numbers) have now become obsolete and are not emphasized any more. Arithmetic and algebra are now taught more meaningfully and in an integrated manner. The emphasis has shifted from deductive proofs in geometry to constructions and applications of geometrical properties. A clear distinction is made between the number system and the numeration system. The language of sets, relations and mappings is now used in verbal, symbolic and diagrammatic forms.
2. In planning instruction, mathematics does not appear as a static, readymade, prefabricated body of knowledge any longer. Rather, it is presented as an ever expanding, growing and lively subject. Pupils are being given more opportunity to experience typical processes of mathematical activity like looking for patterns, making quizzes, puzzles, analogies and proving arguments, etc.
3. The new textual material presents mathematics as a unified discipline of broad key concepts and fundamental structures. The emphasis is on developing conceptual, meaningful mathematics without minimizing the importance of proficiency in computational skills. It is now clarified to pupils "how" and "why" different operations take place before expecting them to master computational skills.
4. There are increasing efforts to show mathematics as a useful tool for studying other subjects. Better coordination between the teaching of mathematics and instruction in other subjects has been recommended [3, 4].
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It is a fault that the attitude of teachers and pupils towards the learning of mathematics is not clear. Some teachers lack confidence and feel insecure. They prefer to follow rigid and stereotyped curricula and methods, rely heavily on texts and use punishment as a mode of getting assignments done. This is because their own mathematics is often too fragmented to cope with the necessary understanding of extension of a topic and they find it difficult to relate one topic to another. The crisis of attitude among children is very well reflected in their performance, failure and dislike for the subject. It is felt that problem-solving in mathematics presents to both the teacher and the pupils an opportunity to redeem this very sad situation. Problem-solving is an individual or a small group activity, most efficient when done cooperatively with free opportunity for discussion. As a consequence, it permits the incorporation of a wide range of levels and styles of thinking and development. Problem-solving reflects the process of mathematics. It increases a learner's ability to think mathematically. The method of problemsolving is a method of thinking, of analyzing, and of learning how to find the answer to a question or problem using known ideas. Learning through problem-solving is a progression from known ideas to unknown ideas, from old ideas to new ideas and from the simple to the complex. Problem-solving essentially results in an increased ability to think and generate ideas of mathematics. Problem-solving does not mean doing the block of exercises at the end of each chapter or unit.
The process of problem-solving involves
a) Sensing, accepting and definig a problem which is intriguing or meaningful to learners of the relevant age. The problem need not always be real. The only important factor is acceptance of the problem by learners as their own.
b) Considering the relationships which exist among the elements of the situation. Identifying data and information, making knowns and unknowns explicit, presenting data, etc., are a few skills required at this stage.
c) Pursuing the plan of action to a tentative answer. This includes techniques such as trial and error, defining terms and relationships using empirical arguments and control of variables.
d) Testing the result.
e) Accepting the result and acting on it.
The problems have many sources. They may be found in the environment or may be related to some area of living, they may be real (project type) or mental (puzzle or quiz) type.
Problem-solving situations may be used by the teacher for three purposes: (a) for helping learners develop mathematical ideas, (b) for the application of known mathematical ideas in new situations, (c) for the analysis of the method of problem-solving [4, 5].
The basic techniques, which help, are the same for all the three categories. These are drawing a diagram, restating the problem in one's own words, dramatizing the situation or preparing a model, replacing the numbers (quantitative aspects) by variables and rearranging data, estimating an answer, arguing backwards logically, i.e. from "to prove" to "what is given" and discover the relationships between the known and the unknown.
Example. Ask the learners to draw a number of triangles. Ask them to measure the angles of each triangle and find their sum.
Conclusion: The sum of three angles of a triangle is 180o (approximately).
You can also ask learners to cut the three corners of the triangles and put them at a point so that they form a straight line.
The studies of Jean Piaget make it clear to us that a learner's mental growth is a continuous process from birth and that his thought processes are by no means those of an adult. The stages of cognitive development, which Piaget claims, are important for the teaching of mathematics.
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Conclusion
This article discusses the principles of learners development and learning as the understanding of these principles helps us in planning lessons effectively. Recent trends in organizing content and importance of problem-solving approach have also been elaborated.
Methods of teaching mathematics are very important as these help the teacher to transact the contents of Mathematics effectively to the learners. The usage of these methods enables the teacher to make mathematics teaching more imaginative, creative and interesting for learners. To give a comprehensive view and understanding of methods to be used for teaching of mathematics, the various methods of teaching mathematics have been discussed in this article.
REFERENCES
1. Mirziyoev Sh.M. Critical analysis, strict discipline and personal responsibility should be the daily rule of every leader's activity. -T.: Uzbekistan, 2017.
2. Lahdenpera, J.; Postare, L.; Ramo, J. Supporting quality of learning in university mathematics: A comparison of two instructional designs. 2019.
3. Harackiewicz, J.M., & Priniski, S.J. (2018). Improving student outcomes in higher education: The science of targeted intervention. Annual Review of Psychology, 69. 2018.
4. Lassani, A.; Yunus, A.S.M.; Abu Bakar, K.B.T. Comparison of New Mathematics Teaching Methods with Traditional Method. People Int. J. Soc. Sci. 2017.
5. Pintrich, P.R. A motivational science perspective on the role of student motivation in learning and teaching contexts. Journal of Educational Psychology, 4. 2003.
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