EDUCATIONAL REFORM, MATHEMATICAL CONCEPT, METHODOLOGY FOR DESCRIBING MATHEMATICAL CONCEPTS

Аннотация

Mathematics education is one of the main factors for the development of science and technology in any society. The thorough mastery of mathematical concepts by students depends on the methods and methodologies in the education system. Therefore, the reform of education and the development of a methodology for effectively describing mathematical concepts are one of the urgent issues of today. This article discusses the methodology for describing mathematical concepts and theimportance ofchanges being introduced intotheeducation system. Keywords: Mathematical literacy, Abstraction, Interactive methods, GeoGebra, Desmos, Gamification, Virtual and augmented reality, Online platforms, Portfolios, Coursera, Khan Academy, Brilliant Introduction. Today, information technologies and modern pedagogical approaches require fundamental changes in the educational process. The main reasons for educational reform are:Adaptation to the digital learning environment - Since students are accustomed to learning through the use of modern technologies, it is necessary to use interactive tools in describing mathematical concepts. Obsolescence of existing methodologies - Traditional approaches sometimes prevent students from fully understanding mathematical concepts. Development of creative and logical thinking - Mathematical concepts should serve not only as rules and formulas, but also as a means of solving problems, forming logical thinking and innovative approaches. Increasing mathematical literacy – Through educational reform, it is possible to develop the ability to apply mathematical concepts not only within the framework of science, but also in everyday life. Mathematics is a fundamental science, and its concepts are based on precise definitions. Mathematical concepts have thefollowing characteristics: http://www.internationaljournal.co.in/index.php/jasass 97 Volume15Issue03, March2025 Impact factor: 2019: 4.679 2020: 5.015 2021: 5.436, 2022: 5.242, 2023: 6.995, 2024 7.75 Certainty and consistency – Mathematical concepts, unlike other sciences, have precise definitionsand laws. Abstraction –Someconcepts are abstract innature and are difficult to describe visually. Consistency –Each new concept is formed based onprevious knowledge. Methodological approaches of teachers play an important role in explaining mathematical concepts. Various methodologies can be used to effectively explain mathematical concepts. The most importantmethods are listed below: Providingaclear definitionand examples When explaining mathematical concepts, first of all, it is necessary to provide a clear and simple definition.For example: Aparallelogram is aquadrilateral whose oppositesides are parallel. Later, thisconcept can becompared with examples and contrasting concepts to further clarify it. Usinggraphics and visuals Using diagrams, graphs, and images is very useful for explaining mathematical concepts to students.For example: Whenit comes to thecoordinate system, it iseffective toexplainbydrawing clear graphs. Step-by-step explanation Since mathematical concepts are complex, they should be explained step by step. For example, when studying thetopicofequations, it isnecessary to first introduce algebraicexpressions. Givingreal-life examples Relatingmathematical concepts to real life helps tounderstand them better. For example: The concept of interest is more understandable to students if it is explained through examples of bankloans, discounts, and thetax system. Usinginteractive methods Thefollowing interactive methods are effectiveinexplainingmathematical concepts: Pairwork –Students canreinforce theirknowledge byexplainingto each other. Discussion – Students improve their logical thinking skills by explaining a certain concept in http://www.internationaljournal.co.in/index.php/jasass 98 Volume15Issue03, March2025 Impact factor: 2019: 4.679 2020: 5.015 2021: 5.436, 2022: 5.242, 2023: 6.995, 2024 7.75 different ways. Problem solving – Mathematical concepts are more effective when taught through practical problems. Useofdigital technologies and programs Various mathematical programs and applications can be used in the modern education system. Forexample: GeoGebra – An interactive program for explaining geometry and algebraic concepts. Desmos – A convenient tool for drawing and analyzing functions and graphs. Requirements for the description of mathematical concepts in education reform The clear description and explanation ofmathematical concepts should bereformed in thefollowing areas: Introduction of modern pedagogical approaches – Teachers should use practical and interactive methods,not just theoretical information. Individualized approach – Since each student has a unique learning style, customized methods shouldbe developed. Integrating mathematics and other subjects – Mathematical concepts can be made more understandable by linking them to computer science, physics, and economics. Improving the assessment system – Students’ understanding of m