Egamberdiyeva Mohinur Fakhriddin kizi

Аннотация

INTRODUCTION Probability theory and combinatorics are two Traditional teaching methods, predominantly pivotal branches of mathematics that play a crucial characterized by lectures and textbook exercises, role in a wide array of disciplines, including may not effectively mitigate these challenges. Such statistics, computer science, physics, and approaches can lead to passive learning, where engineering. These fields provide the theoretical students are merely recipients of information foundation for understanding randomness, rather than active participants in the learning uncertainty, and the principles of counting and process. This can result in a lack of engagement and arrangement, which are essential in modeling and a failure to develop a deep understanding of the solving real-world problems. material. Despite their importance, the teaching of Recognizing these issues, this study seeks to probability theory and combinatorics presents explore alternative teaching methods that can significant challenges. The abstract nature of these enhance the learning experience in probability subjects can make them difficult for students to theory and combinatorics. The aim is to make grasp. Concepts such as probability distributions, learning more interactive, relevant, and engaging random variables, permutations, and combinations for students. Interactive learning involves students often require a level of abstract thinking that can be actively participating in the learning process, often daunting for learners. through discussions, problem-solving activities, https://www.theamericanjournals.com/index.php/tajas 13 THE USA JOURNALS THE AMERICAN JOURNAL OF APPLIED SCIENCES (ISSN – 2689-0992) VOLUME 06 ISSUE03 and collaborative projects. Relevance can be case studies that illustrated the application of achieved by connecting mathematical concepts to probability theory and combinatorics in various real-world applications, helping students see the fields such as science, engineering, and economics. practical value of what they are learning. Engaging This aimed to demonstrate the relevance of the teaching methods are those that capture students' subjects and motivate students to learn. interest and motivate them to learn, which can be Data Collection: facilitated by using a variety of teaching tools and techniques. To assess the impact of these teaching methods, data were collected on three key dimensions: