The Research On Symmetry Thought In Middle School Mathematics

Making a general observation of all times, the pursuing for the symmetry thought in mathematics has indicated the direction to the scientific research in certain degree. The symmetry thought does not have an important value in theory and practice, but also plays an important role in various trades and occupations, for example, architecture, arts, medicine, bioengineering, decoration, china and painting so on. Therefore, as far as I am concerned, the symmetry thought will benefit students all their lives no matter that they will take up scientific research or produce practice in the future. But the present Course Standard (the Nine Year Compulsory Mathematics Course Standard and Mathematics Course Standard (for senior middle school)) doesn't make a clear requirement on how much and what degree students should master it and how to master it. In view of the above questions, I think if only we, the teachers, study the teaching material carefully and guide students to observe carefully and summarize systematically, will the students master and use the symmetry thought well. This thesis uses the symmetry thought as a main clue and the mathematical teaching material as the object of study and it also uses the students'cognition rules with the correspondent knowledge of psychology and pedagogies to analysis the knowledge spots which have symmetry thought and explore its beautiful connotation. The thesis also studies the teaching methodology of these knowledge spots. While students are appreciating the beauty of the mathematics, they will subtly and gradually receives the influence of symmetrical thinking method. Therefore, students will actively use the symmetrical thinking method to solve the mathematical problems in middle school, which involve the knowledge of symmetrical thinking method, and they will learn the other subjects with the symmetrical thought. The students will incisively displays the foundation function of mathematics to the natural sciences. What's more, to us the teachers, we may use the symmetrical thought to design our teaching plans in our daily teaching and education. In the last chapter of this thesis, I provide detail examples, which have used the symmetrical thinking method, and they fully manifest the influence of symmetrical thinking method on the classroom instruction.The thesis has four chapters:The first chapter: Examples of Symmetrical Thinking Method in History. The examples are taken from the professors, such as Thales, Hermann Weyl, Zhang Dianzhou and Dai Qin. It discusses the embodying of the four scholars'symmetrical thought in the middle school mathematical teaching material, and analyses the influence of symmetrical thought in Zhou Yi upon the middle school mathematics.The second chapter: Symmetry in Middle School Geometry. It launches the elaboration from three aspects: flat surface artwork axial symmetry, centre symmetry and surface symmetry in space artwork.The third chapter: Symmetry in Middle School Algebra. It takes the origin of logarithm as an example to illustrate the importance of symmetry thought when choosing the base number of logarithm and it takes turns to discusses the symmetry thought in function and equation.The fourth chapter: the Influence of Symmetry Thought on the Mathematics of Middle School. It discusses the above topic from three aspects: First, the theoretical graph transformation has the symmetrical thought. Second, we can apply the symmetry thought to teaching and solving problems. The shadows of symmetry thought can be found in all subjects. Finally, it edifies the aesthetic education on the students in exerting a subtle influence on their thinking. I think the meanings of studying the symmetry thought in middle school mathematics is that it pushes the development of the mathematical forward, e.g., the consideration of inverse operation leads to the expansion of the number system. Moreover in the middle school mathematics, symmetrical thought contains rich esthetics thoughts and thinking methods. Exploring deeply the symmetry thought in teaching materials has important theoretical and practical meanings and especially has the value of esthetic education. Of course, the symmetrical thinking method in middle school mathematics covers broad aspects, which is waiting for our further studies.