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INTERACTIVE METHODS IN TEACHING MATHEMATICS: CASE STUDY METHOD Rashidov A.Sh.
Rashidov Anvarjon Sharipovich - PhD Student, DEPARTMENT OF MATHEMATICS, FACULTY OF PHYSICS AND MATHEMATICS, BUKHARA STATE UNIVERSITY, BUKHARA, REPUBLIC OF UZBEKISTAN
Abstract: new pedagogical technologies are the product of goal-oriented forms, methods and tools of education, in particular, mathematics education. Observations show that in most cases, the teacher works alone during the lesson, and students remain observers. In this work, one of the teaching methods to connect the teaching of mathematics with life, to develop students' thinking skills, to increase the effectiveness of teaching is to talk about the "Case-study" method, examples of which are given and related to mathematics. Examples are given on the compilation of cases from the topic "Detecting of indefiniteness, L'Hopital's rule" on the subject of "Mathematical Analysis".
Keywords: new pedagogical technology, case-study method, types of cases, State Educational Standards (SES) and model curriculum, working curriculum, e-learning resources.
Large-scale reforms are being held in the development of Mathematics and science in the country today, and government decisions are being adapted to improve the content of Mathematics education with life, to increase the effectiveness of teaching, to bring up a harmoniously developed generation for a fast-growing society. At the same time, the introduction and application of new pedagogical technologies in the process of teaching Mathematics is directly related to the requirements of the time.
New pedagogical technology is a product of goal-oriented forms, methods and tools of education, in particular, Mathematics education. Observations show that in most cases, the teacher works alone during the lesson, and students remain observers. This kind of education does not increase the intellectual thinking of students, does not increase their activity, and does not extinguish their creative activity in the educational process. In addition, lessons based on advanced pedagogical technology [1-9] help students to integrate their knowledge. develops students' thinking, teaches independent, creative thinking. After all, the upbringing of a harmoniously developed generation is an important sign of the cultural and educational development of society, the spiritual maturity of the nation. In this work, we will try to explain the essence of the method "Case-study" on the example of the subject of Mathematical analysis.
"Case-stage" - derived from the English word ("case" - a real situation, event, "study" -to study, analyze) to carry out teaching based on the study, analysis of specific situations is a focused method.
The essence of the Case stage method is that participants are invited to think about a real-life situation, which describes not only the practical problem, but also the learning material that needs to be mastered in the process of solving the problem. The analysis of the situation in this way also has a strong influence on the student's pre-experience of future professional activity, which is the basis for the emergence of interest and motivation to study.
Let's take a look at the mathematical types of case studies in the case study method, which is gaining popularity today. They are divided into:
1) Practical cases;
2) Educational cases;
3) Scientific research cases.
Types of cases Formation of mathematical cases
The meaning of the case Brief definition of Case Assignments
Practical Life situations that apply mathematical knowledge The full content and model of the case model are formed. In this case, you can add alternatives to find the optimal option
Educational (didactic) Conditions of the educational process in the field of mathematics The content of the case study is described. In this case, there are problems within the problem. Case studies are used to solve such problems in a department of Mathematics.
Scientific research The process of creating and researching, interpreting, and applying mathematical models Case assignments are based on incomplete information. Mathematical models are constructed using mathematical symbols and concepts for a number of situations, which can be used to solve problems in many areas of mathematics using the case-study method.
Theme: Detecting of indefiniteness. L'Hopital's rule.
The main purpose of case: Theoretical and practical issues of teaching the subject "Mathematical Analysis", the theme "Detecting of indefiniteness. L'Hopital's rule" is an example of how to develop an e-learning module and develop conclusions and recommendations for improving teaching.
Learning process Outcomes:
• To develop students' knowledge of the L'Hopital rule in detecting indefiniteness.
• To develop students' ability to use L'Hopital rule to detect indefiniteness.
• Organize training sessions using information and communication technologies.
To successfully complete this case, students must first have the following knowledge and skills:
Student should know: The concept of functions. the limit of the function, the product of the functions.
Student should fulfill: study the topic independently; identifies the nature of the problem; promotes ideas; learns to make independent decisions by critically reviewing data; have their own point of view and draw logical conclusions; works independently with educational information; compares, analyzes and summarizes data;
Student should acquire: communication skills; presentation skills; collaborative skills; problem-solving skills.
Case object - undergraduate 1st year students.
Sources of information:
♦ 5130100 - SES and Model Curriculum for Undergraduate Mathematics;
♦ Mathematical Analysis Science Module;
♦ Special literature, e-learning resources, working curricula and others.
CASE QUESTIONS
0
1. Give a definition to the — indefeniteness.
0
2. Express the first rule of L'Hopital.
<x>
3. Give a definition to the — indefeniteness.
4. Express the second rule of L'Hopital.
CASE TASKS
* 1. Case task: lim(x — 2arctgx) ln x x—w
2. Case task: wi \ . xx ln(1 — x) + tg — lim 2 x—w ctgnx
3. Case task: 1 lim(1 + sin2 x)g 2 x—0
Case task:
4. lim(cos 2x)x 2 x—0
Table 3. Version II of Case tasks
1. Case task: f 1 > lim ax — 1 x x—w V J
■ K 2. Case task: cos x • ln( x — a)
-- lim K ' x —a ln(ex — ea)
3. Case task: lim(1 — x)ln x x—
4. Case task: lim f x — U 1 S—Vi v ctgx 2cos x J
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