Research On The Change Of Content Setting Of Pythagorean Theorem In Chinese Mathematics Textbooks(1902-1949)

As Johannes Kepler said:“there are two great treasures of geometry: the first is Pythagorean theorem,and the second is golden section.”Pythagorean theorem,as the most basic theorem in plane geometry,is the first theorem connecting numbers and shapes in mathematics,which leads to the discovery of incommensurable metric,reveals the difference between irrational numbers and rational numbers,and causes the first mathematical crisis.Pythagorean theorem began to transform mathematics from the technology of calculation and measurement to the science of demonstration and reasoning.For thousands of years,people have given more than500 proofs of the Pythagorean theorem.It is the theorem with the most proving methods,which contains a lot of rich mathematical ideas and techniques.Since Xu Guangqi translated Euclid's ?Elements of Geometry?,China has not only gained a new understanding of the history of ancient Greek arithmetic,but also a deeper understanding of the value of the Pythagorean theorem in Chinese and Western cultures.Especially in the late Qing Dynasty and the Republic of China,the Pythagorean Theorem has become one of the core contents of middle school mathematics education.This research takes the Pythagorean theorem of Chinese middle school mathematics textbook from 1902 to 1949 as the research object,and takes literature research,historical research,analysis and comparative research as the main research methods According to the school system and curriculum standard,the course of development in was divided into the late Qing Dynasty(1902-1911),the early Republic of China(1912-1922),the Republic of China curriculum outline period(1923-1928),and the Republic of China curriculum standard period(1929-1949).It aims to comprehensively,systematically and deeply study the development characteristics of collusion in Chinese middle school mathematics textbooks,analyze the factors affecting its change,and strive to It provides reference and Enlightenmentfor the compilation of Pythagorean theorem in middle school mathematics textbooks.This study is divided into five parts,as follows:First,Pythagorean theorem in middle school geometry textbooks in the late Qing Dynasty(1902-1911).During this period,when the school system was initially revised,the middle school mathematics education in China mainly focused on learning Japanese mathematics education,and the compilation of geometry textbooks was mainly to translate and compile geometry textbooks of Japan and other countries.Therefore,first of all,it summarizes the proof methods of Pythagorean theorem content and the changing characteristics of theorem expression in geometry textbooks in the past ten years vertically;secondly,it selects the translated Japanese and American geometry textbooks for case analysis horizontally,and makes comparative analysis from the compilation concept,compilation form,content structure and other dimensions of textbooks,so as to understand this in detail from the micro level The changing characteristics and educational value of Pythagorean theorem in mathematics textbooks.Second,Pythagorean theorem in Geometry Textbook of middle school in the early Republic of China(1912-1922).During this period,Chinese traditional educational ideas,system models and knowledge systems began to undergo a difficult transformation under the impact of Western civilization,which also affected the development of geometry textbooks.In the early period of the Republic of China,education inherited the basis of the education reform in the late Qing Dynasty,and the development of middle school mathematics textbooks changed with each passing day.At this time,the self-made textbooks are gradually mature in this context.In this period,although the geometry textbooks compiled by our country usually refer to the textbooks of Europe and the United States and are properly selected,added and deleted,the organization and presentation of knowledge content have improved significantly.But the arrangement of Pythagorean theorem is not obvious.It has not completely got rid of the content and form of the previous textbooks,and there are still traces of geometry textbooks in the late Qing Dynasty.In this paper,the author selects the representative textbooks of this period,plane geometry of the Republictextbook,geometry of the Republic of China new textbook and the Chinese version of wendewuashi geometry,and makes a detailed comparative analysis of the arrangement of the content of Pythagorean theorem.Third,Pythagorean theorem in middle school mathematics textbooks during the period of the outline of curriculum of the Republic of China(1923-1928).After the promulgation of the "new school system" in 1922.Both the teaching methods and the compilation of textbooks have changed to some extent.Middle school textbooks integrate algebra,geometry,arithmetic and trigonometry into a hybrid teaching,breaking the original geometry textbooks completely.For the first time in China,the method of hybrid textbook writing can not only make students understand the connection between subjects,but also establish the unity of knowledge.It is also in the popularity of mixed teaching that the arrangement of Pythagorean theorem content is greatly affected,whether in the setting of chapters,the method of theorem proving,the setting of exercises after class are different from the past.Therefore,this paper selects the mathematics textbooks with important research value in this period,such as new type of mathematics textbook of Bligh's,primary mixed mathematics,new system mixed mathematics textbook and geometry of modern junior middle school textbook,and analyzes the arrangement and setting of Pythagorean theorem in detail.Fourth,Pythagorean theorem in middle school mathematics textbook during the period of curriculum standard of the Republic of China(1929-1949).In this stage,China has revised the mathematics curriculum standard three times,and the junior and senior high school curriculum standards issued in this period require learning plane geometry.The content of Pythagorean theorem appears in elementary and advanced textbooks respectively,but because of the different objectives of mastering the theorem,there are different chapters,resulting in different methods of proof.In addition,the course of experimental geometry was set up for the first time in 1932 to clarify the objectives and requirements of experimental geometry teaching.Both in understanding geometry and experimental geometry,the contents of the theorem were arranged.Although the degree of emphasis and teaching objectives are different,but from the perspective of algebra and geometry respectively,the importance ofPythagorean theorem and its important position in textbooks are reflected.Therefore,the contents of Pythagorean theorem in Fuxing middle school textbook and experimental geometry textbook are selected for detailed analysis.In this part,the author analyzes the changes of the content arrangement of Pythagorean theorem in middle school mathematics textbooks from 1912 to 1949.Fifth,In the above research,while presenting the historical and cultural background of each stage,the author's life and contribution to mathematics education are introduced appropriately.Sixth,Conclusion.First of all,this paper sums up the arrangement characteristics of Pythagorean theorem in Chinese middle school mathematics textbooks from macro and micro perspectives;secondly,it analyzes the factors that affect the arrangement changes of Pythagorean theorem in Chinese middle school mathematics textbooks from 1902 to 1949;thirdly,it sums up the characteristics of the arrangement changes of the proving methods of Pythagorean theorem in Chinese middle school mathematics textbooks from 1902 to 1949;finally,it summarizes the arrangement of Pythagorean theorem Changes provide inspiration and reference for the compilation of current mathematics textbooks.In summary,this study mainly studies the changes of the arrangement of Pythagorean theorem in Chinese middle school mathematics textbooks,taking1902-1949 as the time domain.This paper clarifies the arrangement of Pythagorean theorem in Chinese middle school mathematics textbooks from 1902 to 1949,and reveals the changing characteristics of Pythagorean theorem arrangement and the factors influencing the change.It shows that the characteristics of the content of Pythagorean theorem in middle schools in the late Qing Dynasty and the Republic of China can be used for reference in the construction of textbooks and the reform of teaching.