METHODS OF DEVELOPING LOGICAL THINKING IN MATHEMATICS LESSONS IN PRIMARY GRADES

Аннотация

This article analyzes methods for developing logical thinking in mathematics lessons in primary grades. It emphasizes the importance of using innovative methods to cultivate students' logical reasoning skills, enhance their problem-solving abilities, and foster independent thinking. The use of logical problems, interactive games, and modern pedagogical technologies in mathematics lessons can significantly boost students’ interest andachievement. Keywords: primary education, mathematics, logical thinking, innovative methods, pedagogical technologies, interactivelearning. 1.INTRODUCTION Developing logical thinking is one of the key tasks of today's educational system. In particular, fostering analytical thinking skills during the teaching of mathematics in primary grades holds great significance. Through logical thinking, students are not only able to solve mathematical problems but also analyze everyday challenges and find effective solutions. To enhance logical thinking in mathematics education, teachers are required to use modern approaches and innovative methods. Today, the use of interactive technologies, game-based methods, problem-based learning, and information and communication tools can significantly increase students’ engagement and improve their thinking abilities. This article thoroughly examinestheeffectiveness of such methods and theirrole in theeducational process. 2.METHODSOF DEVELOPING LOGICAL THINKING 2.1SolvingLogical Problems and Challenges Logical problems help develop students' analytical thinking and problem-solving skills. Such tasks include puzzles, identifying mathematical patterns, and exercises that require logical reasoning. For example: Findingthelogical sequencein numbers: In thegiven task, students are asked tofind themissingnumberin a logical sequence. page1391 INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE ISSN:2692-5206,ImpactFactor:12,23 AmericanAcademicpublishers,volume05,issue04,2025 Journal: https://www.academicpublishers.org/journals/index.php/ijai Solution: In this sequence, numbers from 1 to 9 are arranged, but the number 6 is missing. Thus, themissingnumberis 6. Determiningrelationshipsbetween geometric shapes: Studentsare asked toidentify howmany triangles are present in agiven figure. Solution:There are atotal of12triangles in thefigure. Solvingverbal mathematical problems: Problem: Nodir has several friends. The sum of their ages is 48. After three years, the total willbe63.How many friends does Nodir have? Solution:(63 -48)÷ 3= 5.Thus, Nodirhas 5friends. Problem: Sardor is 7 years older than Nodir but 10 years younger than Umid. If Jasur is 4 years younger than Umid,find theage difference between Nodir and Jasur. Solution:Let Nodir's age beX. Sardor’s age =X+ 7. SinceSardoris 10years youngerthan Umid,Umid’sage = X+17. Jasur’s age =Umid’s age -4= X+13. Thus, theage difference between Nodir(X) and Jasur (X+ 13)is 13years. Such exercises encourage students to develop mathematical thinking and independent reasoning. Logical problems also help students understand relationships, identify cause-and- effect patterns, and find alternative solutionsin different situations. 2.2UsingGame Technologies Incorporating game elements into lessons increases students' engagement and makes learning enjoyable. Effective gamemethods include:  "Who’s the fastest?" – The student who solves a given problem correctly in the shortest timewins.  "Mathematical riddles"–Promotes logical thinking through problem-solving. page1392 INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE ISSN:2692-5206,ImpactFactor:12,23 AmericanAcademicpublishers,volume05,issue04,2025 Journal: https://www.academicpublishers.org/journals/index.php/ijai  "Number puzzles" – Focuses on identifying connections among numbers and arranging them correctly. Such games make lessons interactive and interesting, improving knowledge retention. Game technologies play an essential role in explaining difficult topics, creating a competitive environment, andenhancing students' interest inlearning. 2.3UsingModern Technologies Information and communication technologies play a crucial role in education. By using interactive learning platforms and mobile applications, students can independently solve logical problems. For example:  GeoGebra –Assistsin drawing and analyzing geometric figures.  Khan Academy – Provides opportunities to independently learn mathematical topics andsolvelogical problems. These technologies enable students to actively participate in lessons and encourage self- learning. Moreover, interactive tools help visualize complex concepts, making it easier to develop logical thinkingskills. 2.4Problem-Based LearningMethod Problem-based learning fosters students' ability to research and analyze independently. This methodinvolves the followingstages: 1. Aproblem is posed (e.g., amathematical challenge). 2. Studentsindependently oringroups analyze theproblem. 3. Discussionsand debates are conducted during thesolution pr