Beauty Of Mathematics And High School Mathematics Teaching

According to the phenomenon that students in high schools are afraid of studying mathematics and the idea of embodying aesthetic value of mathematics in recent teaching reform of basic math course in our country, in this thesis, a subject named as " beauty of mathematics and mathematics teaching in high school " has been proposed after referring to overseas way of combining emotion development and beauty appreciation in mathematics study and analyzing the mini investigation on the relationship between the beauty of mathematics and the study interest of students.In this thesis, the theoretical and practical research on the beauty of mathematics and the relationship between the beauty of mathematics and mathematics teaching in high school has been carried out. The content of the thesis can be divided into two parts: 1.the basic content of the beauty of mathematics; 2.the basic problems of the beauty of mathematics and mathematics teaching in high school.The former two chapters constitute the first part of the thesis. In Chapter One proposes the concept and the definition of beauty and the beauty of mathematics, analyzing the essence and the connotation of them. Chapter Two focuses on the basic characteristics of the beauty of mathematics and its gradation which lays the theoretical foundation for the beauty of mathematics. The basic characteristics can be summarized as conciseness, symmetry, uniqueness and unity and the connotation, the manifestation and the ideology of each characteristic are analyzed in detail. In addition, the beauty of mathematics is divided into three levels in the sequence from exterior to interior and from junior to senior, i.e., external formal beauty, internal rational beauty and creative beauty.The latter three chapters constitute the second part of the thesis. In Chapter Three, the status and the functions of the beauty of mathematics in high school math teaching are described to offer the theoretical support for practice, among which the aesthetic function, the methodological function and the cultural function are emphasized. In Chapter Four, the process of cognition in high school math teaching from the recognition, the discovery, the appreciation to the creation or the application of the beauty of mathematics is put forward. Chapter Five shows the case study of the beauty of math in high school teaching. Conic section is taken as an example to unearth the beauty of mathematics in from the following three aspects: 1. the language beauty of conic section reveals the external formal beauty; 2. the methodological beauty and the logical beauty of conic section reflect the internal rational beauty; 3. the beauty of mathematics in conic section reveals the new value in internal knowledge structure of textbooks. Moreover, the application of the beauty of mathematics in high school math teaching is also discussed from the following four points of view: the pursuit of conciseness, the construction of symmetry, the utilization of unity and the discovery of uniqueness.The conclusions have been drawn in this thesis. 1. high school math teachers should pay much attention to the beauty of mathematics; 2. the ideological value of the beauty of mathematics should be embodied in high school math teaching. The thesis can be taken for theoretical reference to improve high school math teaching and the interest of math study of students by taking advantage of the beauty of mathematics.